Malgorzata E Arlet
email: maarlet@yahoo.com

Lynne A Isbell

Ants Kaasik

Freerk Molleman

Rebecca L Chancellor

Colin A Chapman

Raivo Mänd

James R Carey

Małgorzata E Arlet

M E Arlet

Determinants of reproductive performance among female Gray-cheeked mangabeys (Lophocebus albigena) in Kibale National Park, Uganda

Keywords: primates, Old World monkeys, birth rate, reproductive maturation, female reproductive success

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

Introduction

Differential reproductive success is a crucial component of natural selection and thus it is important to determine the social and ecological factors that influence lifetime reproductive success. For females, one of the key influences is differential access to food. Because female reproductive success is thought to be limited most by access to food [START_REF] Trivers | Parental investment and sexual selection[END_REF], in group-living species competition over food may favor the expression of female dominance hierarchies [START_REF] Wrangham | An ecological model of female-bonded primate groups[END_REF][START_REF] Van Schaik | The ecology of social relationships amongst female primates[END_REF][START_REF] Isbell | Ecological models of female social relationships in primates: similarities, disparities, and some directions for future clarity[END_REF]. In such species, higher-ranking females often have better access to food than lower-ranking females [START_REF] Clutton-Brock | Maternal dominance, breeding success and birth sex ratios in red deer[END_REF][START_REF] Harcourt | Dominance and fertility among female primates[END_REF], and this is then expected to result in reproductive skew. Indeed, differences in reproductive parameters among females of disparate ranks have been reported in several primate species. For example, higher-ranking females give birth at earlier ages than lowerranking females among yellow baboons (Papio cynocephalus) [START_REF] Altmann | Determinants of reproductive success in savannah baboons Papio cynocephalus[END_REF], mandrills (Mandrillus sphinx) [START_REF] Setchell | Reproductive parameters and maternal investment in mandrills (Mandrillus sphinx)[END_REF] and chimpanzees (Pan troglodytes) [START_REF] Pusey | The influence of dominance rank on the reproductive success of female chimpanzees[END_REF]). Higher-ranking females also have shorter interbirth intervals among olive baboons (P. anubis) [START_REF] Barton | Feeding competition among female olive baboons, Papio anubis[END_REF], long-tailed macaques (Macaca fascicularis) [START_REF] Van Noordwijk | Competition among female long-tailed macaques, Macaca fascicularis[END_REF], Japanese macaques (M. fuscata) [START_REF] Sugiyama | Population dynamics of Japanese monkeys with special reference to the effect of artificial feeding[END_REF], and chimpanzees [START_REF] Pusey | The influence of dominance rank on the reproductive success of female chimpanzees[END_REF]. Finally, higherranking females have higher infant survival among long-tailed macaques (van Noordwijk and van Schaik 1999) and chimpanzees [START_REF] Pusey | The influence of dominance rank on the reproductive success of female chimpanzees[END_REF].

Reproductive success is also affected by lifespan, and lifespan may be shortened by predation. Predation may also interact with social rank differences in affecting reproductive success. For example, predation may exacerbate rank differences in reproductive success because lower-ranking females may be at greater risk of predation when they are excluded from central and safe feeding places (e.g., long-tailed macaques at Ketambe, Sumatra and chacma baboons (P. ursinus) in the Mkuzi Game Reserve, South Africa; [START_REF] Van Noordwijk | Competition among female long-tailed macaques, Macaca fascicularis[END_REF][START_REF] Robinson | Do female chacma baboons compete for a safe spatial position in a southern woodland habitat?[END_REF].

Females that survive long enough to have multiple offspring gain experience with infant care that improves infant survival and thus reproductive success. For females that survive to older ages, it may be possible to observe changes in their reproductive strategies as they age. For instance, female reproductive strategies may change according to future reproductive and survival prospects (the terminal investment hypothesis: [START_REF] Th | Reproductive effort and terminal investment in iteroparous animals[END_REF]. Many studies of mammals have shown, for example, that older females have heavier infants and higher offspring survival (e.g., red deer, Cervus elaphus: Clutton-Brock 1984; Nile lechwe, Kobus megaceros: [START_REF] Bercovitch | Age-specific changes in reproductive effort and terminal investment in female Nile lechwe[END_REF]; red squirrels, Sciurus vulgaris: [START_REF] Descamps | Age-specific variation in survival, reproductive success and offspring quality in red squirrels: evidence of senescence[END_REF]; Hanuman langurs, Semnopithecus entellus: [START_REF] Dolhinow | Rank and reproduction among female langur monkeys: aging and improvement[END_REF][START_REF] Borries | Dominance, age, and reproductive success in free-ranging female hanuman langurs (Presbytis entellus)[END_REF]; rhesus macaques M. mulatta: [START_REF] Silk | Gestation length in rhesus macaques (Macaca mulatta)[END_REF]; Barbary macaques M. sylvanus: [START_REF] Paul | Reproductive senescence and terminal investment in female Barbary macaques (Macaca sylvanus) at Salem[END_REF]). However, it is often unclear to what extent greater survival of infants of older mothers is a function of experience or physiology.

At advanced reproductive ages females may decline in their reproductive output (particularly in terms of birth rate) as a result of age-associated physiological deterioration (the senescence hypothesis: [START_REF] Weladji | Age-related reproductive effort in reindeer (Rangifer tarandus): evidence of senescence[END_REF]. A reduction in fecundity as females age has been observed, for example, in olive baboons [START_REF] Strum | Variation in fecundity with age and environment in olive baboons (Papio anubis)[END_REF], Japanese macaques [START_REF] Koyama | Population dynamics of Japanese monkeys in Arashiyama[END_REF]; but see [START_REF] Fedigan | Lifetime reproductive success in female Japanese macaques[END_REF]), rhesus macaques [START_REF] Drickamer | A ten-year summary of reproductive data for free-ranging Macaca mulatta[END_REF][START_REF] Hoffman | Terminal investment and senescence in rhesus macaques (Macaca mulatta) in Cayo Santiago[END_REF], and Hanuman langurs [START_REF] Dolhinow | Rank and reproduction among female langur monkeys: aging and improvement[END_REF].

Reproductive output may also decline over time as a result of determinate reproduction. Females are born with a set number of oocytes, and as females cycle, the pool of available oocytes diminishes and females may enter a post-reproductive phase near the end of their life, i.e., menopause [START_REF] Waser | Post-reproductive survival and behavior in a free-ranging female mangabey[END_REF][START_REF] Bell | The cost of reproduction[END_REF][START_REF] Atsalis | Reproductive aging in captive and wild common chimpanzees: factors influencing the rate of follicular depletion[END_REF][START_REF] Perheentupa | Aging of the human ovary and testis[END_REF][START_REF] Pavelka | Costs and benefits of old age reproduction in the Arashiyama West female Japanese macaques[END_REF].

The number of oocytes present at birth may depend on the nutrition of the mother before the daughter's birth, whereas the depletion rate of oocytes may depend on the rate of cycling and the frequency of pregnancies. The pregnancy rate may depend on nutrition and thus social rank, which may again be a function of the mother's rank, if female rank is "inherited". Therefore, it is difficult to predict the effect of rank on reproductive aging, but it is likely to play a role.

Female reproductive success may also be influenced by males. Males may have a positive effect on birth rates (per female) via infanticide [START_REF] Borries | Infanticide in seasonally breeding multimale groups of Hanuman langurs (Presbytis entellus) in Ramnagar (South Nepal)[END_REF][START_REF] Fedigan | Impact of male takeovers on infant deaths, births and conceptions in Cebus capucinus at Santa Rosa, Costa Rica[END_REF][START_REF] Fruteau | Infanticide risk and infant defence in multi-male freeranging sooty mangabeys, Cercocebus atys[END_REF] or by accidental deaths of infants during aggressive interactions among males [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF]), both of which may reduce interbirth intervals while nonetheless reducing reproductive success. A positive effect on birth rate may be more likely when immigrant males join the groups because the risk of infanticide increases and there may be heightened aggression at those times. Immigrant males may also improve conception rates as a result of outbreeding. Indeed, female gray-cheeked mangabeys (Lophocebus albigena) preferentially mate with novel males [START_REF] Arlet | Indications for female mate choice in greycheeked mangabeys Lophocebus albigena johnstoni in Kibale National Park, Uganda[END_REF][START_REF] Arlet | Mating tactics in male grey-cheeked mangabeys (Lophocebus albigena)[END_REF]. In addition, greater numbers of resident males in groups may improve birth rates or reproductive success indirectly by providing stronger protection or defense of larger or better quality home ranges used by females [START_REF] Robinson | Do female chacma baboons compete for a safe spatial position in a southern woodland habitat?[END_REF]).

In addition to social factors, female reproductive performance may be affected by fluctuations in environmental factors such as food abundance [START_REF] Altmann | Life history of yellow baboons: physical development, reproductive parameters and infant mortality[END_REF][START_REF] Dunbar | Demographic and life history variables of a population of gelada baboons (Theropithecus gelada)[END_REF][START_REF] Strum | Variation in fecundity with age and environment in olive baboons (Papio anubis)[END_REF]. In some African ecosystems, rainfall serves as a reliable proxy for plant productivity [START_REF] Mcnaughton | Ecology of a grazing ecosystem: the Serengeti[END_REF], and in many primate species, births tend to be seasonal [START_REF] Butynski | Guenon birth seasons and correlates with rainfall and food[END_REF]. Even aseasonally breeding primates, however, may be affected by variation in rainfall and thus food abundance. Among yellow baboons in Amboseli National Park, Kenya, for instance, shorter interbirth intervals are correlated with higher amounts of rain [START_REF] Altmann | Life history of yellow baboons: physical development, reproductive parameters and infant mortality[END_REF].

Although the factors that affect female reproductive performance have been comparatively well studied in terrestrial baboons and macaques, investigations of reproductive performance in arboreal, forest-dwelling papionin primates are rare. To our knowledge, the only such species in which female reproductive performance has been investigated are long-tailed macaques (van Noordwijk and van Schaik 1999) and Assamese macaques (M. assamensis; [START_REF] Fürtbauer | Reproductive and life history parameters of wild female Macaca assamensis[END_REF].

Gray-cheeked mangabeys are arboreal, forest-dwelling, African monkeys that are closely related to baboons [START_REF] Harris | Nuclear gene trees and the phylogenetic relationships of the mangabeys (Primates: Papionini)[END_REF][START_REF] Burrell | Mitochondrial evidence for the hybrid origin of the kipunji, Rungwecebus kipunji (Primates: Papionini)[END_REF]. Like baboons, they live in multi-male, multi-female groups, but group sizes are typically smaller than those of baboons [START_REF] Waser | Feeding, ranging and group size in the mangabey, Cercocebus albigena[END_REF][START_REF] Henzi | Evolutionary ecology, sexual conflict, and behavioral differentiation among baboon populations[END_REF]. Also like baboons, females usually remain in their natal groups throughout life and have stable, linear dominance hierarchies (Chancellor and Isbell 2009a, b), whereas males disperse from their natal groups and compete with other males for rank as they attempt to join other groups around sexual maturity [START_REF] Olupot | Correlates of intergroup transfer in male grey-cheeked mangabeys[END_REF]. Mangabeys are predominantly frugivorous [START_REF] Waser | Feeding, ranging and group size in the mangabey, Cercocebus albigena[END_REF]Chancellor and Isbell 2009a), and appear to be aseasonal breeders [START_REF] Wallis | Sexual behaviour and reproduction of Cercocebus albigena johnstoni in Kibale Forest, western Uganda[END_REF][START_REF] Olupot | Lophocebus albigena Grey-cheeked mangabey[END_REF].

This study explores to what extent sociality, ecology, and phylogeny contribute to the reproductive performance of female gray-cheeked mangabeys, information that is useful for assessing the generality of baboon and macaque derived patterns to other papionin genera. Based on theoretical expectations and empirical findings of other papionins, we predict the following: 1) high-ranking female gray-cheeked mangabeys will have higher reproductive output than lower-ranking females via earlier maturation (as measured by estrous cycle initiation), younger ages at first birth, and higher birth rates; 2) fertility will decrease with age independent of rank; 3) greater numbers of immigrant and resident adult males will lead to increased birth rates, and; 4) greater rainfall and higher abundance of Ficus spp. fruits will be positively correlated with conception and therefore the number of births 6 months later.

Methods

Study area and subjects

We conducted the study in Kibale National Park, Uganda (0°13' -0°41'N and 30°19' -30°32'E), near the Makerere University Biological Field Station. Kibale (795 km 2 ) is a moist, evergreen, medium altitude forest with a mosaic of swamp, grassland, thicket, and mature and colonizing forest [START_REF] Chapman | Tropical tree community shifts: Implications for wildlife conservation[END_REF]. The gray-cheeked mangabey population in Kibale has been studied intermittently since the 1970s. Despite a typically bimodal pattern of yearly precipitation, with more rain falling in March-April and September-November [START_REF] Struhsaker | The red colobus monkey[END_REF]Isbell 2012;Valtonen et al. 2013), there appears to be no detectable birth seasonality in this population [START_REF] Wallis | Sexual behaviour and reproduction of Cercocebus albigena johnstoni in Kibale Forest, western Uganda[END_REF][START_REF] Olupot | Lophocebus albigena Grey-cheeked mangabey[END_REF]. We report data from four habituated groups (BT1, CC, MK and LC1) studied from 2004-2012, which ranged in size from 10 to 23 individuals (Table 1). -12(14.3) 15-22 (16.9) 16-23 (19.6) 10-17 (12.9) Adult females 4-7 (5.9) 4-7 (5.4) 6-8 (7.0) 3-5 (4.5) Adult males 2-7 (3.6) 1-4 (2.4) 3-8 (5.1) 1-4 (1.9) Subadult (both sexes) 0-3 (1.3) 0-2 (0.9) 0-2 (1.4) 0-2 (1.4) Juveniles (both sexes) 0-4 (2.5) 0-4 (2.6) 0-7 (2.3) 0-4 (2.0)

Between August 2004 and July 2006, each group was observed for an average of three days per month (Chancellor and Isbell 2009a). Between August 2006 and December 2012, each group was followed for up to six consecutive days on a five-week rotation schedule [START_REF] Arlet | Reproductive tactics influence cortisol levels in individual male gray-cheeked mangabeys (Lophocebus albigena)[END_REF]).

We began identifying females in January 2004. Females were initially identified as individuals using natural markings such as relative body size, nipple color and size, and tail characteristics (scars, shape, and thickness of hair). The number of adult females ranged from 21 (2007-2008) to 26 (2009, 2011-2012), with a mean of 22.6 females per year. Two adult females immigrated into our groups, one transferred to a non-study group, and nine disappeared. Analyses are drawn from a total of 38 adult females over the nine-year period.

When a new infant was first seen in a group, we counted it as a birth. Since we did not follow the groups continuously, pregnancy losses, stillbirths, or very early mortality could have occurred without our knowledge. We defined infants as animals less than 18 months old [START_REF] Waser | Intergroup interaction in a forest monkey: the mangabey Cercocebus albigena[END_REF]. During this study, 76 infants were born in the four study groups, including 12 infants to primiparous mothers. Infants were considered to have died when they were no longer seen, since infants are unlikely to survive by themselves.

Age and rank of adult females

We knew approximate birth dates (within 6 weeks) for all 12 adult females who matured and gave birth for the first time during this study. Females were classified as mature when they exhibited a sexual swelling for the first time. These were all 6-8 years old by the end of the study. We could also estimate birth months for two females who were still dependent on their mothers when our study began. We categorized the ages of the other older 24 females into four-year intervals (based on [START_REF] Strum | Variation in fecundity with age and environment in olive baboons (Papio anubis)[END_REF] female: young multiparous (8-12 yrs), middle-aged multiparous (12-16 yrs), old multiparous (16-20 yrs) and very old multiparous (over 20 yrs). We estimated age classes based on relative size, skin condition of perineal sexual swelling, nipple length, and general marks of aging, such as wrinkled skin on the face and the neck, saggy skin around the face, and thinning hair.

We calculated female ranks as in [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF]. Briefly, we used focal and ad libitum sampling to record agonistic interactions. We recorded 136-318 dyadic agonistic interactions per group, including nonphysical threats (e.g., facial displays), approachavoids (i.e., moving away from another who is approaching), supplants (i.e., taking the place of another), physical contact (e.g., biting, tail-pulling, and pushing), and chases (i.e., aggressively pursuing another) (see also Chancellor and Isbell 2009a, b). We constructed dominance matrices for each group, with rank order determined by minimizing the number of reversals against the hierarchy (i.e., interactions below the diagonal).

Table 2. Individual female gray-cheeked mangabeys according to group and rank, along with their putative or known ages (at first year of study) and maternal relationships (mother given in parentheses). All groups had dominance hierarchies that rarely changed, the exceptions occurring when females rose in the dominance hierarchy as a consequence of deaths of highranking mothers or their daughters (see also Chancellor and Isbell 2009a, b). Between 2004 and 2012, 6 females changed from low-to high-ranking or vice versa, and they were classified in each year separately.

Identification of estrous cycles based on sexual swellings

Female gray-cheeked mangabeys exhibit sexual swellings that cover a relatively small area ventral to the base of the tail [START_REF] Rowell | Reproductive cycles of the mangabey Cercocebus albigena[END_REF][START_REF] Chalmers | Behaviour and female reproductive cycles in a captive group of mangabeys[END_REF][START_REF] Danjou | Contribution a l Etude du Comportement Sexuel de Cercocebus albigena[END_REF][START_REF] Wallis | Sexual behaviour and reproduction of Cercocebus albigena johnstoni in Kibale Forest, western Uganda[END_REF]). The swelling increases in size and color gradually, deepening to pink at maximum swelling. As estrus passes, the swelling deflates and turns dark purple (Deputte, 1991;[START_REF] Wallis | Sexual behaviour and reproduction of Cercocebus albigena johnstoni in Kibale Forest, western Uganda[END_REF]. Sexual swellings last on average 17-38 days in three phases: quiescence to peak swelling lasting 4-14 days, peak swelling lasting 2-4 days, and deflation lasting 7-14 days [START_REF] Danjou | Contribution a l Etude du Comportement Sexuel de Cercocebus albigena[END_REF]Deputte, 1991;[START_REF] Rowell | Reproductive cycles of the mangabey Cercocebus albigena[END_REF][START_REF] Wallis | Sexual behaviour and reproduction of Cercocebus albigena johnstoni in Kibale Forest, western Uganda[END_REF].

During observations, we noted the condition of each female as either having no sexual swelling (not cycling) or having a visible sexual swelling, with different degrees of swelling also noted, i.e., inflating, peak, or deflating (cycling). Twelve females began cycling during the study. In captivity, mangabey estrous cycles average 31.2 days, with a range of 29 to 38 days (Deputte 1991). With our observation schedule, we were able to note the reproductive state of each female every 28-35 days. Since we did not follow each individual every day, we could not obtain precise information about variation in the length of estrous cycles and dealt with this issue statistically (see "data analysis" section below).

Presence of immigrant males

After August 2006, we noted the presence of immigrant males with the focal group.

Immigrant males were adult males who joined any of the groups during the year. All immigrants except one entered the groups as low-ranking males. However, one of the immigrants rose from low-ranking to high-ranking rapidly after the dominant male left the group. Once the males were in a group for 6 months, we considered them resident males because by this time their glucocorticoid profiles became indistinguishable from those of resident males [START_REF] Arlet | Reproductive tactics influence cortisol levels in individual male gray-cheeked mangabeys (Lophocebus albigena)[END_REF], suggesting that they had become integrated into their groups. As males become integrated, they engage in fewer aggressive interactions within groups and infant mortality decreases [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF]. Immigrant males were present with the groups for 27% of our observation time.

Rainfall and phenological data Data on rainfall were collected daily at the research station and served as a general indication of food abundance. As the majority of the gray-cheeked mangabey diet consists of fruit [START_REF] Waser | Feeding, ranging and group size in the mangabey, Cercocebus albigena[END_REF][START_REF] Olupot | Long-term variation in mangabey (Cercocebus albigena johnstonii Lydekker) feeding in Kibale National Park, Uganda[END_REF]Chancellor and Isbell 2009a) and the most highly preferred fruits are figs (Ficus spp.) [START_REF] Waser | Intergroup interaction in a forest monkey: the mangabey Cercocebus albigena[END_REF][START_REF] Janmaat | Evidence for spatial memory of fruiting states of rain forest fruit in wild ranging mangabeys[END_REF][START_REF] Janmaat | Exploring new areas: how important is long-term spatial memory for mangabey (Lophocebus albigena johnstonii) foraging efficiency?[END_REF], we also focused on the abundance of ripe and unripe figs (both of which are eaten by gray-cheeked mangabeys) as recorded between 2003-2012. We monitored 300 Ficus spp. trees of 33 fig species along phenology transects [START_REF] Chapman | A long-term evaluation of fruiting phenology: importance of climate change[END_REF]. Each month the crowns of these species were visually examined and the presence of unripe and ripe fruits was noted on a scale from 0-4 with 0 being absent and 4 being maximally abundant.

Statistical analyses

We performed all analyses using the statistical software R (R Development Core

Team 2011). We used generalized linear mixed models (GLMM), using the lme4 package [START_REF] Bates | lme4: Linear mixed-effects models using S4 classes[END_REF] to test 1) the effects of adult female rank and age as predictor variables on the timing and frequency of estrous cycles, and 2) adult female rank and age, total number of males present, rainfall, and abundance of ripe and unripe Ficus spp. fruits (around the time of conception) on birth rates.

Given that latencies between observation days per female were irregular, to estimate the number of estrous cycles we implemented a Poisson rate regression model with group as a random effect and the logarithm of observation time as an offset. Using the logarithm of the observation time as model offset is a device for correcting the differences in the observation period for Poisson rate models [START_REF] Faraway | Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models[END_REF]. We used 31.2 days as the length of an average cycle in our analyses, and we counted the occurrence of maximum sexual swellings directly ('peaks') or indirectly (by 'inflating' or 'deflating' stages). This gave us the number of estrous cycles without pinpointing the dates of each peak phase, as well as the number of days for which we had enough observations to detect full cycles. We also counted the number of infants that a female had during our observation period and excluded 175 days for gestation and a minimum of 300 days for lactation periods (if the infant survived; Deputte 1991).

We analyzed the effects of dominance rank on estrous cycles in three ways by fitting three separate GLMMs. As in [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF], we labeled those 1-2 females per group who won 54-92% of the encounters in their group during a given year "high-ranking" and all other females "low-ranking" because they lost those encounters. First, we first compared high-vs. low-ranking females. As there are multiple ways to quantify relative dominance ranks, to test for consistency with this dichotomous rank categorization, we assigned ranks to females on an inverse scale where the highest ranking individual is 1, the second 0.5, the 3rd 0.33, etc., and we also checked an even distribution where the highest rank is 1, the lowest is 0, and all other individuals are placed at regular intervals between them [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF].

For the GLMM involving the effects of female rank and age, total number of immigrant and resident males present, rainfall, and abundance of ripe and unripe Ficus spp. fruits on birth rates we implemented a logistic regression with individual female and the time period as random factors to account for possible correlation for observations for the same female and for the same 6-month time period, respectively. Correlation of successive 6-month time periods (for a particular female) was taken into account using a predictor in the model that described the proportion of time that a female was unavailable to give birth in a period (due to giving birth during one of the earlier periods). Births were aggregated into 6-month periods (i.e., for each female for a particular period, 1 indicated that the female gave birth, and 0 that she did not). This aggregation was necessary as sometimes the exact birth date was not known and several of the predictors were not measured frequently enough to produce a reliable estimate for a shorter time interval, the exceptions being rainfall data which were recorded daily and Ficus spp. data which were recorded each month. All predictors were offset by 6 months to coincide with conceptions associated with observed births (mean gestation length: 175 days, Deputte 1991). Weighted means were calculated for predictors where appropriate. There were no significant differences among groups in this analysis, the SD of the random effect of group being zero. We used AIC to select the best model for predicting birth rates. T-tests were used to compare difference between high-and low-ranking females in reproductive parameters. A Kruskal-Wallis test was used to test the effect of the survival of previous infants in their first year on interbirth interval.

Results

Population patterns of reproductive performance

We confirmed that gray-cheeked mangabeys are aseasonal breeders as births occurred in every month of the year (Figure 1). On average, females gave birth to their first infants after 11.5 cycles. The overall birth rate was 0.36 births per female per year (i.e., approximately 1 birth every 3 years), but there was considerable variability as 25% of the population had a birth rate estimate lower than 0.22 and another 25% had higher than 0.44. Females losing their infants within the infant's first year of life resumed cycling and had shorter interbirth intervals than females whose infants survived (mean: 16.7 and 30.3 months, respectively; Kruskal-Wallis rank sum test, χ 2 = 20.08, df = 1, p < 0.001).

Figure 1. Distribution of births per month in gray-cheeked mangabeys from 2004-2012 in

Kibale National Park, Uganda.

Female dominance rank and age relative to timing of and frequency of estrous cycles

High-ranking females matured earlier than low-ranking females. Among those that matured during the study, high-ranking females had their first estrous cycle two months earlier, on average, than low-ranking females (HR range = 5.0 -5.25 yrs, mean ± SD = 5.1 ± 0.1, N = 4; LR range = 5.1 -6.2 yrs, mean ± SD = 5.4 ± 0.4, N = 9; exact birth dates were not known for two females; t-test, t = -1.94, df = 10.11, p = 0.041, 1-tailed).

Reproductive maturation relative to mother's rank did not change substantially when we modeled rank using the alternatives of inverse and even rank distributions.

Among these maturing females, high-ranking individuals had a mean of 13 estrous cycles before the birth of their first infant (N = 5, SD = 2.4), while low-ranking females had a mean of 10 estrous cycles before their first birth (N = 7, SD = 3.3; t-test, t = 1.76, df = 9, p = 0.112, 1-tailed). Nonetheless, high-ranking females gave birth to their first infants significantly earlier (a year earlier on average) than low-ranking females (6.8 yr, N = 5 high-ranking females vs. 7.8 yr, N = 7 low-ranking females; t-test, t = 3.21, df = 10, p = 0.009). From these data, and taking into account the gestation period of 175 days, we estimated the length of estrous cycles. For high-ranking females, average estrous cycle length was 31.2 days, and for low-ranking females, 33.6 days.

Cycle frequency decreased with age. At mean relative rank, older females had fewer estrous cycles (z = -8.08, p < 0.001, Table 3). We observed cessation of reproductive activity in two old females (> 20 yrs). Female KB (low-ranking, BT1 group) gave birth at the beginning of 2009 and afterward did not resume cycling. In 2004, when Chancellor started following LC1 group, female NB (high-ranking) was not cycling. NB kept her position as alpha female until she disappeared at the end of 2007, and throughout this time she did not cycle.

Interactions between rank and age on estrous cycles 12.5 yr, females of higher relative rank had more estrous cycles (z = -4.40, p < 0.001; Table 3, Figure 2). At mean relative rank, older females had fewer estrous cycles; z = -8.08, p<0.001; Table 3, Figure 2). However, there was an interaction between rank and age, whereby the number of estrous cycles did not decrease as rapidly for high-ranking females (z = -1.96, p = 0.049; Table 3, Figure 2).

Variables predicting birth rates

The model with the best fit included age, rank, the interaction between age and rank, presence of immigrant and resident males, and abundance of fig fruits, but not rainfall.

We found that as adult females in the population aged, their birth rates declined significantly (z = -2.93, p = 0.003, Table 4; Figure 2). High-ranking females had on average higher birth rates than low-ranking females during the younger ages, but by the average age of 12.5 years this difference no longer existed (Figure 2).

[Insert Table 4 here]

The numbers of immigrant and resident adult males in the group at the time of conception were both positively associated with birth rate (z = 2.88, p = 0.004 and z = 2.31, p = 0.021, respectively; Table 4).

Ficus spp. fruit availability during conception was significantly positively correlated with frequency of births (z = 2.51, p = 0.012; Table 4). However, there appears to be no relationship between rainfall and conceptions as rainfall fell out of the final model.

Discussion

Our results showed that rank, age, greater numbers of immigrant males, and greater numbers of resident adult males are all important influences on female reproductive performance in gray-cheeked mangabeys. We also found an association between Ficus spp. fruit abundance around the time of conception and thus the temporal distribution of births. Gray-cheeked mangabeys' maturation and reproductive aging appear to be similar to baboons, mandrills and macaques, and other papionins that are typically more terrestrial, suggesting that broad habitat preferences exert little influence on females' reproductive performance.

Female gray-cheeked mangabeys live in female-resident groups with linear dominance hierarchies (Chancellor and Isbell 2009a, b). Regardless of their ranks, all females are able to breed, albeit with different success. Although the reproductive skew of high-and low-ranking female gray-cheeked mangabeys is not as great as in some mammalian species where low-ranking females do not reproduce at all [START_REF] Creel | The African wild dog: behavior, ecology and conservation[END_REF], being a low-ranking female does appear to be disadvantageous in gray-cheeked mangabey societies, at least in early adulthood.

High-ranking female gray-cheeked mangabeys begin developing sexual swellings indicating the start of sexual cycling at younger ages and they begin reproducing a year earlier than low-ranking females. They also have more cycles before they conceive. This latter finding might suggest that initial cycles are anovulatory. Earlier age at first reproduction is correlated with high rank, as has been observed in other primates, e.g., rhesus macaques and mandrills [START_REF] Bercovitch | Life history costs and consequences of rapid reproductive maturation in female rhesus macaques[END_REF][START_REF] Setchell | Reproductive parameters and maternal investment in mandrills (Mandrillus sphinx)[END_REF]. Highranking females appear to have shorter and more frequent cycles than low-ranking females, and this continues throughout their lives. Reproductive aging also appears to be slower for high-ranking females than for low-ranking females as suggested by a slower decline in estrous cycle frequency over time. The rank effect is most obvious for younger females. After age 12.5, high-and low-ranking females converge in having similar birth rates. A slowing of birth rates and cycle frequency with age has also been documented in olive baboons [START_REF] Strum | Variation in fecundity with age and environment in olive baboons (Papio anubis)[END_REF], rhesus macaques [START_REF] Gagliardi | Age as a determinant of reproductive success among captive female rhesus macaques (Macaca mulatta)[END_REF][START_REF] Hoffman | Terminal investment and senescence in rhesus macaques (Macaca mulatta) in Cayo Santiago[END_REF], mountain gorillas (Gorilla beringei, [START_REF] Robbins | Age-related patterns of reproductive success among female mountain gorillas[END_REF], and Barbary macaques [START_REF] Paul | Reproductive senescence and terminal investment in female Barbary macaques (Macaca sylvanus) at Salem[END_REF].

Our study also reveals a decline in reproductive rate at advanced ages, especially in cycling rate, but also in birth rate, and in some cases, reproductive cessation (postreproductive lifespan/menopause). Reproductive cessation in our study species was previously reported by [START_REF] Waser | Post-reproductive survival and behavior in a free-ranging female mangabey[END_REF]. Reproductive aging of females is a conspicuous phenomenon in humans, but is not ubiquitous among other animals [START_REF] Jones | Diversity of ageing across the tree of life[END_REF][START_REF] Roach | Population biology of aging[END_REF]. In primates, age effects on reproductive rate tend to be small, and reproductive cessation is absent or confined to the oldest [START_REF] Johnson | Ageing, infecundity and reproductive senescence in freeranging female rhesus monkeys[END_REF][START_REF] Wasser | Ageing and social rank effects on the reproductive system of free-ranging yellow baboons (Papio cynocephalus) at Mikumi National Park, Tanzania[END_REF][START_REF] Pavelka | Reproductive termination in female Japanese monkeys: A comparative life history perspective[END_REF][START_REF] Robbins | Age-related patterns of reproductive success among female mountain gorillas[END_REF]Johnson and found in captive gray-cheeked mangabeys (Deputte 1991) as well as in several other primate species, including Sanje mangabeys (Cercocebus sanjei) [START_REF] Fernandez | Reproductive characteristics of wild Sanje mangabeys (Cercocebus sanjei)[END_REF] and captive golden-bellied mangabeys (C. agilis) [START_REF] Walker | Reproductive parameters and life-history variables in captive golden-bellied mangabeys (Cercocebus agilis chrysogaster)[END_REF]), Hanuman langurs [START_REF] Borries | Infanticide in hanuman langurs: social organisation, male migration, and weaning age[END_REF], chacma baboons [START_REF] Cheney | Factors affecting reproduction and mortality among baboons in the Okavango Delta, Botswana[END_REF], and blue monkeys (Cercopithecus mitis) [START_REF] Cords | Life history of Cercopithecus mitis stuhlmanni in the Kakamega Forest, Kenya[END_REF][START_REF] Cords | Infanticide in Cercopithecus mitis stuhlmanni in the Kakamega Forest, Kenya: variation in the occurrence of an adaptive behavior[END_REF]. This suggests that infanticide could be an effective reproductive strategy for the male graycheeked mangabeys of Kibale and may in part explain aggression toward infants by immigrant males [START_REF] Arlet | Mating tactics in male grey-cheeked mangabeys (Lophocebus albigena)[END_REF]). However, there is no direct evidence of infanticide in this species despite many years of observation. In a previous study, we showed that immigrant male presence in groups was associated with an increase in infant mortality but not through confirmed infanticide: 86% of the infants that died after falling from trees during fights between adult males fell when immigrant males were present in the group, and 46% of the infants that disappeared healthy did so while immigrant males were clearly present (compared to 23% when immigrant males were clearly absent) [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF].

The positive association between immigrant males and birth rate found in this study may exist because the greater infant mortality associated with immigrant males shortens interbirth intervals. It is also possible that the positive association between immigrant males and birth rate exists because females preferentially mate with novel males [START_REF] Arlet | Indications for female mate choice in greycheeked mangabeys Lophocebus albigena johnstoni in Kibale National Park, Uganda[END_REF]). Similarly, we found that birth rates were positively associated with greater numbers of resident adult males. It has been suggested that having more adult males within the group helps females maintain or even increase their food supply when males are involved in intergroup competition [START_REF] Robinson | Do female chacma baboons compete for a safe spatial position in a southern woodland habitat?[END_REF]. There is some support for this in gray-cheeked mangabeys. Male gray-cheeked mangabeys have a characteristic loud call, the whoop-gobble that function in part to mediate intergroup spacing because groups move away from the direction of whoop-gobbles from other groups [START_REF] Waser | Experimental playbacks show vocal mediation of intergroup avoidance in a forest monkey[END_REF][START_REF] Olupot | Lophocebus albigena Grey-cheeked mangabey[END_REF]. High-ranking males give the most whoop-gobbles but this is dependent on the number of males in groups; high-ranking males in groups with more males give more whoop-gobbles than high-ranking males in groups with fewer males [START_REF] Arlet | Mating tactics in male grey-cheeked mangabeys (Lophocebus albigena)[END_REF]. Moreover, males are aggressive toward other groups more often than are females and they are more likely to be aggressive toward other groups during periods of low food abundance and with patchily distributed foods [START_REF] Brown | Food and range defence in primates[END_REF]. Thus, having more males in gray-cheeked mangabey groups may be advantageous to females because more males may be more effective in protecting food resources for females. Since food is crucial to female reproductive success and greater access to foods can increase birth rates, the relationship between resident males and higher birth rates may be causal if indeed males protect the food supply for females in their groups.

The link between female reproductive success and nutrition is apparent in the close association between birth rate and monthly abundance of figs at conception, an important food resource for mangabeys in Kibale. Figs are also important in the timing of female chimpanzee reproduction at the same site [START_REF] Sherry | Reproductive seasonality in chimpanzees and humans: ultimate and proximate factors[END_REF]. Indeed, food appears to be an important limiting factor for female reproductive success in this mangabey population, as may also be the case for many other primate species [START_REF] Dittus | The evolution of behaviours regulating density and age-specific sex ratios in a primate population[END_REF][START_REF] Isbell | Contest and scramble competition: patterns of female aggression and ranging behavior among primates[END_REF][START_REF] Thompson | Diet and reproductive function in wild female chimpanzees (Pan troglodytes schweinfurthii) at Kibale National Park, Uganda[END_REF][START_REF] Mccabe | Reproductive seasonality in wild Sanje mangabey (Cercocebus sanjei), Tanzania: relationship between the capital breeding strategy and infant survival[END_REF]. Our data confirm that gray-cheeked mangabeys respond to food availability in an opportunistic fashion, with females being more likely to conceive when figs are abundant. Such a capital breeding strategy might be expected for a frugivore in Kibale since fruiting phenology generally does not follow a clear seasonal pattern [START_REF] Chapman | Fruit and flower phenology at two sites in Kibale National Park, Uganda[END_REF][START_REF] Chapman | A long-term evaluation of fruiting phenology: importance of climate change[END_REF].

In conclusion, our study provides evidence for fitness benefits of high dominance rank independent of age in female gray-cheeked mangabeys, reproductive aging in the wild, and slower reproductive aging in higher-ranking females compared to lowerranking females. These findings are qualitatively similar to other papionins and it appears that broad substrate and habitat differences, i.e., arboreal life in a forest vs. terrestrial life in more open habitats, are less important than phylogeny in determining reproductive performance. We also provide evidence suggesting a benefit to female reproductive output in having multiple males in their groups. Finally, we confirm that reproduction in this population of gray-cheeked mangabeys is aseasonal, perhaps a reflection of unpredictable fig fruiting patterns in Kibale.

Table 3 .a

 3 Parameter estimates for the quasi-Poisson model of female cycle frequency of gray-cheeked mangabeys in Kibale National Park for the years 2004-2012. Logarithm of the number of days observed was used as an offset. The rank of the individual minus the average rank of all females. b The age of the individual minus the average age of all females.

Figure 2 .

 2 Figure 2. Changes in cycle frequency and birth rate with age in high-vs. low-ranking female gray-cheeked mangabeys in Kibale National Park, Uganda for the years 2004-2012 (model result, see text). Gestation and lactation periods have been omitted and thus a year might correspond to a longer period in time. This figure is based on local polynomial regression fitting. Due to the small sample size of the data, the actual proportions are variable and as such are not useful for plotting. This figure is presented for illustrative purposes as the actual effects are analyzed using statistical models. HR = high-ranking females; LR = low-ranking females.

Figure 1 .

 1 Figure 1. Distribution of births per month in gray-cheeked mangabeys from 2004-2012 in Kibale National Park, Uganda.

Figure 2 .

 2 Figure 2. Changes in cycle frequency and birth rate with age in high-vs. low-ranking female gray-cheeked mangabeys in Kibale National Park, Uganda for the years 2004-2012 (model result, see text). Gestation and lactation periods have been omitted and thus a year might correspond to a longer period in time. This figure is based on local polynomial regression fitting. Due to the small sample size of the data, the actual proportions are variable and as such are not useful for plotting. This figure is presented for illustrative purposes as the actual effects are analyzed using statistical models. HR = high-ranking females; LR = low-ranking females.

Table 1 .

 1 Ranges and means (in brackets) of group compositions in gray-cheeked mangabey population in Kibale National Park, Uganda between 2003 and 2012.

		BT1	CC	LC1	MK
	Group size	10

Acknowledgments

We thank the Uganda Wildlife Authority, Uganda National Council for Science and Technology, and personnel at the Makerere University Biological Field Station in Kanyawara for permission to work in Kibale National Park. We thank all the field assistants that worked with us during these years: Kaseregenyu Richard, Katusabe Swaibu, Irumba Peter, Sabiti Richard, Akora Charles, Koojo John for their invaluable assistance in the field. Thanks also to Linda-Liisa Veromann for help in entering behavioral data. This research was supported by funds from the Leakey Foundation and the Department of Anthropology, University of California at Davis to RLC, NIH/NIA grants PO1 A6022500 and PO1 A608761 to JRC, "Mobilitas" postdoctoral grant MJD56 to MEA, and NSERC grants to CAC. The Estonian Ministry of Education and Science and the European Regional Development Fund supported RM and FM (targeted financing projects numbers 0180004s09 and 0180122s08, ESF 9215,7406, 7699, 7522, 8413 and GD6019; Center of Excellence FIBIR). This study complies with the current laws of Uganda. Finally, we appreciate the comments and suggestions by the editor and two anonymous reviewers to improve the manuscript.

Kapsalis 2008; [START_REF] Videan | Reproductive aging in female chimpanzees (Pan troglodytes)[END_REF][START_REF] Herndon | Menopause occurs late in life in the captive chimpanzee (Pan troglodytes)[END_REF][START_REF] Tian | Reproductive parameters of female Macaca mulatta tcheliensis in the temperate forest of Mount Taihangshan, Jiyuan, China[END_REF]. Any reduced frequencies of cycling and birthing may be confounded by longer lactation periods, partly because older female gray-cheeked mangabeys have higher infant survival, and females tend not to conceive during this period [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF]. However, we excluded these periods from our analyses of cycle and birth rates. As reproductive aging is often interpreted as follicular depletion [START_REF] Atsalis | Reproductive aging in captive and wild common chimpanzees: factors influencing the rate of follicular depletion[END_REF][START_REF] Hawkes | Do women stop early? Similarities in fertility decline in humans and chimpanzees[END_REF], higher-ranking females may start with more oocytes, or deplete follicles at a slower rate.

Higher-ranking females may endow their daughters with higher reproductive potential, thus preparing them for inheriting their high rank, which we show to be associated with long reproductive life. This may in turn explain why higher-ranking females tend to have relatively more female offspring [START_REF] Arlet | Maternal investment and infant survival in gray-cheeked mangabeys (Lophocebus albigena)[END_REF]: daughters are able to reliably benefit from their mother's high rank. Slower follicular depletion may potentially be explained by higher-ranking females spending a larger proportion of their life pregnant, even though follicular depletion will be faster at other times given their higher cycling rate.

Estrous cycle lengths in our population are within the range of those found in a captive population of gray-cheeked mangabeys. Deputte (1991) pointed out two patterns in the captive population: a short 29.9-day cycle and a long 37.7-day cycle. The average cycle length of high-ranking females in our study is longer than the 'short cycle' of captive females (31.2 days) whereas the cycle length of low-ranking females is shorter than the 'long cycle' of captive females (33.6 days). Unfortunately, no information is available about the dominance ranks of the nine studied females from Deputte's study.

Birth rates can increase as a result of lower infant survival or greater access to food, both of which can shorten interbirth intervals. In gray-cheeked mangabeys, the death of an infant shortens the interbirth interval by approximately one year. Shortened interbirth intervals after the deaths of infants, through infanticide or other causes, have also been

Ethical standards

The study complies with the current laws of Uganda.


K Aoudia

N Brinis

L Chaal

B Saidani

L Benyahia

C Chassenieux

C Deslouis
email: claude.deslouis@upmc.fr

Electrochemical Characterization of Viscoelastic Solutions of Supramolecular Polymers in phosphonium-based ionic liquids

Keywords: Bis-urea, toluene, ionic liquid, EIS, rate constant, rheology

We have combined electrochemical, rheological and light scattering measurements to investigate the viscoelastic character of solutions of (2,4-bis (2-ethylhexylureido) toluene) (EHUT) in toluene in the presence of two ionic liquids: (trihexyl (tetradecyl) phosphonium hexafluorophosphate "Cyphos 110") and (tris(pentafluoroethyl) trifluorophosphate "aph4-cph12") used to substantially increase the solution conductivity required for the electrochemical study.

The heterogeneous rate constant k 0 of the Fc/Fc + redox couple, the diffusivity (DFc), and the equivalent capacitance values of the double layer were measured in the presence and in the absence of EHUT. For Cyphos 110, the viscosity of solutions increases in the presence of EHUT, but the diffusion current exhibited no fluctuations. By opposition, for aph4-cph12, strong fluctuations of the diffusion current allowed to assign a viscoelastic character to the solutions when EHUT is added.

Rheological and light scattering measurements revealed that the two ionic liquids act as chain stoppers for EHUT supramolecular chains. However, aph4-cph12 maintains the viscoelastic character of the EHUT solution whereas Cyphos 110 destroys the supramolecular structure.

Introduction

Supramolecular polymers are aggregates of small molecules which self-associate in solvent through non-covalent bonds. It was recently emphasized that they can be used in a variety of applications [START_REF] Bosman | Supramolecular polymers at work[END_REF][START_REF] Sabadini | Bis-Urea-Based Supramolecular Polymer: The First Drag Reducer for Hydrocarbon Solvents[END_REF] and that for a given chemical structure of their monomer, their self assembled structures depend strongly on various parameters such as temperature, solvent and concentration [START_REF] Lortie | Structural and Rheological Study of a Bis-urea Based Reversible Polymer in an Apolar Solvent[END_REF]. In particular, it has been mentioned that such self assembled structures may feature a viscoelastic character at low concentration in apolar organic solvent [START_REF] Colombani | Selective synthesis of non-symmetrical bis-ureas and their self-assemblyw[END_REF][START_REF] Van Der Gucht | Multiple Shear-Banding Transitions in a Supramolecular Polymer Solution[END_REF][START_REF] Bellot | Thermodynamic Description of Bis-urea Self-Assembly: Competition between Two Supramolecular Polymers[END_REF]. Like wormlike micelles do in aqueous media [START_REF] Cates | statics and dynamics of worm-like surfactant micelles[END_REF][START_REF] Yang | Viscoelastic wormlike micelles and their applications[END_REF], Bis-urea based low molar mass compound namely EHUT (2, 4-bis (2-ethylhexylureido) toluene) has been reported to self-assemble in nonpolar solvents into two distinct supramolecular structures, i.e. either a long hydrogenbonded filament, or thicker and more rigid tubes depending on the experimental parameters (Temperature and concentration) [START_REF] Bellot | Thermodynamic Description of Bis-urea Self-Assembly: Competition between Two Supramolecular Polymers[END_REF]. Moreover, hydrodynamic drag reduction (DR) in a Couette cell was observed for EHUT in octane and in toluene, allowing thereby highlighting this system as the first self-assembled drag reducer for hydrocarbon solvents [START_REF] Sabadini | Bis-Urea-Based Supramolecular Polymer: The First Drag Reducer for Hydrocarbon Solvents[END_REF]. As well as surfactants, which may achieve high drag reduction amounts in water [START_REF] Myska | Differences in the flow behaviors of polymers and surfactant dragreducing additives[END_REF][START_REF] Hu | Rheological and rheo-optical characterization of shear-induced structure formation in a nonionic drag-reducing surfactant solution[END_REF], one can expect that supramolecular polymers are liable to repair themselves after mechanical degradation due to the reversible character of their self-association process. This is a decisive advantage over linear polymers which are irreversibly broken after their drag reducing action.

The occurrence of drag reduction in both polymer and surfactant solutions has often been associated to viscoelastic properties such as the existence of a first normal stresses difference.

These drag reducing solutions in turbulent flow display correlatively anomalous effects in laminar flows (e.g. Weissenberg effect, anomalous pressure drop/flow rate behavior, entrance flows) as shown for polymer solutions [START_REF] Bilgen | On the orifice flow of dilute polymer solutions[END_REF][START_REF] Ouibrahim | Rheology of polymer solutions in laminar capillary tube flows[END_REF][START_REF] Fruman | Dilute polymer flows at high strain rates: A correlation of data[END_REF][START_REF] Halliwell | Investigation into the anomalous behavior of Pitot tubes in dilute polymer solutions[END_REF] and their drag reducing ability can therefore be studied in well-defined laminar flows.

It has been reported that by using electrochemical methods in polymer or surfactant aqueous solutions, the mass transfer measured towards a rotating disk electrode in laminar flow exhibits a first order transition [START_REF] Deslouis | Microscopic aspects of surfactants action on flow induced corrosion[END_REF][START_REF] Boutoudj | Mass transfer in a laminar elongational flow of a drag reducing surfactant[END_REF] for a critical value of the angular velocity of the disk This transition is marked by a significant drop of the mass transfer rate which turns unsteady and is characterized by an hysteresis cycle. This behavior was caused by the elongational strain existing at the outer limit of the hydrodynamic boundary layer and was considered as a signature of the viscoelastic character of the fluid [START_REF] Boutoudj | Mass transfer in a laminar elongational flow of a drag reducing surfactant[END_REF][START_REF] Chaal | Mass transfer rate and conductivity instabilities in surfactant solutions submitted to a laminar elongational flow[END_REF][START_REF] Chaal | Wall shear stress mapping in the rotating cage geometry and evaluation of drag reduction efficiency using an electrochemical method[END_REF]. The transition was also accompanied by flow birefringence in the hydrodynamic boundary layer attesting the presence of elongated objects (stretched polymer chains [START_REF] Deslouis | Electrochemical and optical studies of a stable to unstable transition in a polymer solution flowing close to a rotating disk[END_REF] or disantangled threadlike micelles).

The main motivation for the present work was to carry out an electrochemical mass transport study with a rotating disk electrode in laminar flow for a supramolecular polymer in toluene to see if it displays the same features as those depicted previously for polymers and surfactants in aqueous solution. A particular interest of proving then the viscoelastic properties as a major indication of the drag reducing ability of such solutions is to limit direct tests in turbulent flows which imply large volumes and high flow velocities.

However, due to the weak or non polar character of such a solvent, electrochemical measurements are difficult to carry out due to low conductivity.

To overcome this difficulty and referring to a previous work [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF], we have used ionic liquids for increasing the solution conductivity. Indeed, room temperature ionic liquids have recently gained increasing interest for electrochemical applications [START_REF] Zhang | Practical Considerations Associated with Voltammetric Studies in Room Temperature Ionic Liquids[END_REF][START_REF] Galinski | Ionic liquids as electrolytes[END_REF], due to their unique chemical and physical properties, including negligible vapor pressure, high chemical and thermal stability, and also a large electrochemical potential window [START_REF] Hapiot | Electrochemical reactivity in room-temperature ionic liquids[END_REF][START_REF] Hadi Ghatee | Temperature dependence of viscosity and relation with the surface tension of ionic liquids[END_REF][START_REF] Stoppa | How ideal are binary mixtures of room-temperature ionic liquids?[END_REF]. Room temperature ionic liquids when their cations and anions are properly chosen should then afford a good conductivity and can be used as supporting electrolytes in organic solvents [START_REF] Allen | A mechanistic study of the electro-oxidation of bromide in acetonitrile and the room temperature ionic liquid, 1-butyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide at platinum electrodes[END_REF].

It has been shown that room temperature ionic liquids based on two bulky ions: a phosphonium cation and a fluorophosphate anion allowed an electrochemical kinetic study with a rotating disk electrode when dissolved in toluene taking ferrocene/ferrocenium (Fc/Fc + ) as redox couple [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF][START_REF] Duffy | Macroelectrode voltammetry in toluene using a phosphonium phosphate ionic liquid as the supporting electrolyte[END_REF][START_REF] Comminges | Determination of Viscosity, Ionic Conductivity, and Diffusion Coefficients in Some Binary Systems: Ionic Liquids + Molecular Solvents[END_REF]. Obviously such a study is quite impossible with solid ionic salts as supporting electrolytes.

In this work, we investigated the influence of a bis urea compound (EHUT) on mass transport of ferrocene in toluene to a rotating disk electrode in the presence of two ionic liquids based on a common cation, namely trihexyl(tetradecyl)phosphonium and two different anions: hexafluorophosphate (further named "Cyphos 110") and tris(pentafluoroethyl) trifluorophosphate (further named "aph4-cph12"). In parallel, the effect of the concentration of ionic liquids on the rheological and structural properties of the solutions was measured. It will be shown that the effect of the anion of the ionic liquids can be deleterious to the supramolecular structure since they act as so-called chain stoppers.

Both voltammetric response for the ferrocene oxidation and Electrochemical Impedance Spectroscopy (EIS) were analyzed. Therefore, a second objective of the work was to determine the heterogeneous rate constant k 0 of the ferrocene/ferrocenium (Fc/Fc + ) redox couple and the diffusivity (D Fc ) in a toluene/ Cyphos 110 and in toluene/ Cyphos 110 /EHUT so as to complete the relevant values already obtained for those quantities in the presence of aph4-cph12 [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF].

2 Experimental section 2.1 Materials: EHUT (2, 4-bis (2-ethylhexylureido) toluene) was synthesized by reacting racemic 2-ethylhexylamine with 2,4-toluene diisocyanate. Details of the synthesis and purification of EHUT have been reported else-where [START_REF] Lortie | Structural and Rheological Study of a Bis-urea Based Reversible Polymer in an Apolar Solvent[END_REF][START_REF] Boileau | Soluble supramolecular polymers based on urea compounds[END_REF].

Bifunctional monomer EHUT

Toluene (>99%) was purchased from VWR and was used as a solvent for the sample preparation without further purification. Ferrocene (Fc) was obtained from Sigma Aldrich (98% purity) and used at 1mM. Cyphos 110 and cph4-cph12 were purchased from Strem Chemicals and Merck respectively. Due to the low conductivity of the solutions, the electrochemical measurements were impossible at concentrations below 0.075M in Cyphos 110 and could be extended down to 0.03M in cph4-aph12.

Cyphos 110 & aph4-cph12

Samples were prepared by dissolving EHUT in toluene at 10 g/L with 1mM of ferrocene by stirring over night at 50 °C. The same procedure also held for EHUT/Cyphos 110 and EHUT/aph4-cph12 mixtures in order to reach stationary state. Figure 1 shows the aspect of EHUT/Cyphos 110 mixtures for two different temperatures. Above 35 °C the solutions were homogenous and transparent; below 35°C they displayed phase separation and turned turbid and heterogeneous. All experiments were therefore carried out at 35 °C.

< Figure 1 > 2.2 Methods: 2.2.1 Rheology. Measurements were performed with a stress-controlled rheometer, ARG2 from TA Instruments equipped with a cone-plate geometry (angle = 1°, diameter = 60mm) or plate-plate (diameter = 40mm) depending on the viscosity of the sample. The temperature was controlled with a Peltier system. The samples were protected by a solvent trap to prevent evaporation.

Steady-state shear stress was measured as function of the applied shear rate ranging from 10 -2 to 10 3 s -1 .

Light Scattering.

Light scattering measurements were done using an ALV-CGS3 system operating with a vertically polarized laser (wavelength λ = 632nm) at various scattering angles θ between 70 and 150°, corresponding to scattering vectors q=4πn/λsin(θ/2) ranging from 0,017 to 0,029 1/nm with n the refractive index of the solvent. The duration of the experiments was set to 6 minutes per angle in order achieving a good signal-to-noise ratio for correlation functions.

The solvent was filtered through 0.2µm Teflon filter before preparing solutions. The intensity autocorrelation functions g 2 (t) obtained from dynamic light scattering were analyzed in terms of a continuous distribution of relaxation times (eq. 1):

∫ ∞ - = 0 1 ) / exp( ) ( ) ( τ τ τ d t A t g (Eq.1)
Here g 1 (t) is the normalized electric field autocorrelation function and is related to g 2 (t) via the so-called Siegert relation. The REPES routine was used to obtain the distribution of relaxation time A(τ) [START_REF] Jakes | Regularized Positive Exponential Sum (REPES) Program -A Way of Inverting Laplace Transform Data Obtained by Dynamic Light Scattering[END_REF].

The hydrodynamic correlation length, ξ, was calculated by using the Stokes-Einstein relation (eq. 2):

      = 2 1 6 q kT τ πη ξ (Eq. 2)
where k is the Boltzman's constant, T the temperature and η the viscosity of the solvent.

Electrochemistry.

Electrochemical measurements have been performed in toluene/Cyphos 110 and toluene/aph4-cph12 solutions by use of the oxidation current of ferrocene (Fc) to ferrocenium (Fc + ) according to the following scheme:

+ - + Fc Fc e
This system was chosen because the electrochemical kinetics of Fc/Fc + has been investigated in several polar organic liquids for which it serves as a reference redox system in the presence of ionic liquid as supporting electrolyte [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF][START_REF] Boxall | Apparent Anomaly during Rotating Disk Voltammetry in Ionic Liquids[END_REF].

In order to overcome the low conductivity of the solutions, a special electrode arrangement has been used in this work and was described elsewhere [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF] ; it consisted of three electrodes among which two platinum wires (0.5 mm) embedded in a Bakelite resin shaped as a rotating rod. One electrode was positioned at the rotation axis and served as working electrode and the other one was in its close vicinity serving as pseudo reference electrode. The special electrode arrangement required the use of a rotating contactor (supplier TACUSSEL, EAD Pt/Pt model) with two independent solid contacts. The rotating disk electrode rotation speed (Ω) has been varied between 0 and 1200 rpm. The system was completed with a platinum grid of large area serving as counter electrode. The solution volume was about 20 mL and the temperature was set at (35 ± 0.2) °C.

Prior to the measurements, the working electrode surface was polished with fine emery paper (grade 2400), carefully rinsed with distilled water and dried.

Electrochemical experiments combined current-potential (I-V) curves and Electrochemical Impedance Spectroscopy diagrams. I-V curves were carried out under potentiokinetic conditions at a scan rate of 20 mVs -1 or in quasi steady-state conditions with potential steps of 50 mV, the measurements being taken after current stabilization. Impedance measurements have been performed between 100 kHz and 100 mHz with 10 points per frequency decade and a signal amplitude of 100 mV rms which allowed fulfilling linearity conditions due to the high electrolyte resistance value. Measurements were carried out using an AUTOLAB interface.

Impedance data have been analyzed using a home-made software (SIMAD) allowing fitting both frequency-dependent analytical expressions or equivalent electrical circuits composed of discrete elements as resistances, capacitances, inductances or diffusion impedance. mM respectively. Selecting several Fc concentrations allowed a better approach of the kinetical parameters of Fc oxidation and enabled to complete the kinetical analysis already carried out in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF] with aph4-cph12, the other ionic liquid. In Figure 2d, I-V curves in the presence of 10 g/L of added EHUT are reported.

Results and discussion

< Figure 2 >

One can observe that a quasi horizontal plateau current is defined over several hundreds of mV for the lower two Fc concentrations (0.2 and 0.5 mM). It corresponds to diffusionconvection controlled conditions, the current increasing with the disk rotation speed.

The I-V curves for the 1 mM Fc concentration display otherwise a slope immediately after the onset of a plateau current (Figure 2c).

This slope can be presumably ascribed to parasitic faradaïc currents due for instance to residual water within the ionic liquid or to the ionic liquid itself. Water purposely added to the toluene/ionic liquid mixture till 100 ppm in the absence of Fc does not substantially increase the current (not shown). The slope appears to be steeper in the presence of EHUT (Figure 2d):

This compound is not electroactive in the explored potential domain but brings another source of parasitic current, which explains the steeper slopes when it is added. However, an attempt to correct the I-V curves from the parasitic currents is questionable because the potentials reference is different between the measurements with Fc (and therefore determined by the Fc/Fc + potential) and without it.

The onset of the diffusion plateau with potential substantially increases with the rotation speed (about +1V/ Fc/Fc + at 0 rpm and shifted to about + 3V/ Fc/Fc + at 1000 rpm) for the 1 mM Fc concentration which is a consequence of the large value of the ohmic drop resistance (see further with the Electrochemical Impedance Spectroscopy measurements). As a consequence, the existence of this large ohmic drop resistance forbids performing additional measurements with higher Fc concentrations since they would result in a significant shift of the overpotential necessary for reaching the diffusion plateau, then exceeding the limits of the potential range of the potentiostat. However, in our previous paper, it has been possible to run such an analysis even with 10 mM Fc concentration since the use of an higher amount of ionic liquid allowed to reduce the resistance value. Therefore k 0 values measured in this work have been compared to the previous ones [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF]. In the present study, since we mainly focused on the analysis of the mass transport data for understanding the viscoelastic properties of the solution, the choice of concentrations of 1 mM and below for Fc and 0.25 mm for the disk radius (r) were the best compromise.

The values of the plateau current, I P , measured in Figure 2 have been plotted as a function of the square root of the angular disk velocity Ω 1/2 in Figure 3. The resulting linear variation I P = α + βΩ 1/2 fully agrees, for the three Fc concentrations, for the part βΩ 1/2 with the Levich equation [START_REF] Levich | Physicochemical Hydrodynamics[END_REF]:

ν Ω - ∞ = 2 / 3 1 / 6 1 / 2 L I 0.62nc FD A.
Where n is the number of exchanged electrons (equals to 1 here), c ∞ is the redox concentration (in mol cm -3 ), F is the Faraday number (96485 C), ν is the kinematic viscosity (in cm 2 s -1 ), D is the diffusion coefficient (in cm 2 s -1 ) and A is the electrode area (in cm 2 ).

The positive intercept, α, of the curves extrapolated to Ω = 0 is indicative of the presence of a parasitic current which does not depend on convection.

< Figure 3 >

The I p currents determined for Fc oxidation at 1 mM concentration in Cyphos 110 (0.075 and 0.085M) or in Cyphos 110/EHUT mixtures display also a linear dependence on Ω 1/2 (not shown). α and β values have been reported in table 1 as well as both dynamic (η) and kinematic (ν) viscosities for the different mixtures. Table 1 also reports the Fc diffusion coefficient (D) and the Schmidt number Sc = ν/D values. The mixtures without EHUT show higher diffusivities ranging from 3 to 5 10 -5 cm 2 s -1 , slightly depending on the Cyphos110 concentration, whereas in the presence of EHUT, diffusivity decreases, because of an increase in viscosity, according to the Stokes-Einstein relation. In ref [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF], Fc diffusivity was measured around 1.43 10 -5 cm 2 s -1 at 22 °C.

To ensure that mass transport was convection-diffusion controlled even at the lower rotation speed, we have evaluated the Peclet number (Pe). The latter is a dimensionless parameter which characterizes the ratio of convective to diffusion transport. Pe = Re.Sc where Re is the Reynolds number (Re = Ωr 2 /ν). Then Pe = Ωr 2 /D. When Pe >> 1, the transport is dominated by forced convection. For Ω ∼ 10 rad s -1 , D ∼ 3 10 -5 cm 2 s -1 and r = 0.025 cm, Pe ∼ 200 which excludes the influence of natural convection even at this low rotation speed.

It is noteworthy that the fluctuations of the current as well as the drop of its mean value above a critical angular velocity that are both observed in the case of wormlike micelles in aqueous medium [START_REF] Boutoudj | Mass transfer in a laminar elongational flow of a drag reducing surfactant[END_REF][START_REF] Chaal | Mass transfer rate and conductivity instabilities in surfactant solutions submitted to a laminar elongational flow[END_REF] as a signature of a viscoelastic character of the fluid, do not exist in the present conditions (0.075 to 0.1mol.L -1 Cyphos 110 at 35°C). I-V curves at Cyphos 110 concentrations below 0.075 mol L -1 could not be exploited because the diffusion plateaus were shifted to higher overpotentials and could not be observed.

(ii) aph4-cph12.

I-V curves have been plotted in the same conditions as above in terms of Fc concentration and temperature, with and without EHUT and for three ionic liquid concentrations: 0.03, 0.04 and 0.05 mol L -1 . Diffusion plateaus were present even for the lowest ionic liquid concentration investigated.

Levich behavior (I L ∝ Ω 1/2 ) was confirmed for the three concentrations. α, β, D and Sc values in the absence of EHUT have been reported in table 1. The lower ionic liquid concentrations explain the low values computed for the Schmidt number.

In the presence of EHUT, the Levich behavior was still observed but only at the lower rotation speed. Quite remarkably, for a critical rotation speed, the current slightly decreased, deviating from the Levich line, and intense fluctuations of the current arose and persisted till the higher rotation speed of 2000 rpm (see Figure 4 in which the grey domains depict the extent of the current fluctuations).

< Figure 4 >

When decreasing the rotation speed, the same current values as those found when it was increased were measured. Furthermore, the fluctuations ceased at the same critical rotation speed i.e. around 300 rpm for 0.03 mol L -1 and 500 rpm for 0.04 mol L -1 . Lastly, at 0.05 mol L -1 there is no more transition and the Levich regime is valid till 2000 rpm.

Therefore, apart from the hysteresis which was not observed here, the supramolecular polymer solution exhibits the same features with a rotating disk electrode -i.e. current drop and strong fluctuations of the diffusion current-as polymer and surfactant solutions do. In all cases, this could be related to the elongated nature of the objects in the presence of flow with an elongational component. For the rotating disk electrode, the maximum value of the elongational strain is of the order of Ω at the outer limit of the hydrodynamic boundary layer [START_REF] Deslouis | Microscopic aspects of surfactants action on flow induced corrosion[END_REF].

For polymer chains, this behavior has been associated to the coil ↔ stretch transition predicted by De Gennes [START_REF] De Gennes | [END_REF] and the critical rotation speed was related to a Deborah number De of the order of 1 (De being the ratio of a characteristic time of the polymer chain-precisely the Zimm relaxation time-and a characteristic time of the flow, here Ω -1 ). Therefore, the higher the molecular weight (and thus, the longer the chain), the lower the critical rotation speed.

< Figure 5 >

Similarly, such a first order transition with the onset of mass transfer fluctuations was observed for drag reducing cationic surfactant solutions [START_REF] Deslouis | Microscopic aspects of surfactants action on flow induced corrosion[END_REF][START_REF] Boutoudj | Mass transfer in a laminar elongational flow of a drag reducing surfactant[END_REF][START_REF] Chaal | Mass transfer rate and conductivity instabilities in surfactant solutions submitted to a laminar elongational flow[END_REF]. Obviously the relaxation time deduced from the condition De ∼ 1 cannot be meant to represent a Zimm relaxation time for surfactant solutions. It has been independently established that the drag reduction efficiency of these solutions increases when the counter ion to surfactant concentrations ratio, ζ, increases. These solutions present a shear thinning behavior with a characteristic time (defined from rheological measurements by the intersection of the low shear rate pseudo Newtonian plateau and the high shear rate power law regime) which increases with ζ [START_REF] Rose | Drag reduction and rheological properties of cationic viscoelastic surfactant formulations[END_REF].

Structural changes were also observed with the increase of ζ, in particular an elongation of the worm like micelles (as evidenced from tapping mode AFM in air on a surface having weak surface interaction with the lying micelles [START_REF] Chaal | Characterisation of counterion and surface influence on micelle formation using tapping mode atomic force microscopy in air[END_REF]) or a transition between sparse individual micelles at low ζ and entangled ones at higher ζ values their number and length being increased [START_REF] Wu Ge | Effects of chemical structures of para-halobenzoates on micelle nanostructure, drag reduction and rheological behaviors of dilute CTAC solutions[END_REF]. The characteristic time deduced from the electrochemical data could result from the geometric average of two times, a time corresponding to the scission of the micelles and a time corresponding to their reptation [START_REF] Cates | statics and dynamics of worm-like surfactant micelles[END_REF]. Some of these analogies exist for the supramolecular polymer solutions [START_REF] Ducouret | Rheological characterisation of bis-urea based viscoelastic solutions in an apolar solvent[END_REF] and will be addressed with the rheological and light scattering data further reported.

Concurrently, the viscoelasticity of the EHUT solutions can be qualitatively assessed by observing the effect of the rotation of a rod in a 0.03 mol L -1 concentrated solution (Figure 5): one can see that the fluid rises up instead of forming a vortex around it, evidencing a Weissenberg effect, characteristic of the normal stresses difference.

Electrochemical Impedance Spectroscopy data (i) Cyphos 110

The same nine different mixtures as those used for the steady-state measurements, the characteristics of which are reported in table 1, have been investigated by electrochemical impedance spectroscopy measurements and the diagrams were recorded at the half wave potential. All impedance diagrams (as for example that displayed in Figure 6a for Cyphos 110 (0.1 M)/toluene/1mM ferrocene mixture) contain a large semicircle capacitive loop in the high frequency range and a diffusion convective loop in the low frequency range. The high frequency loop does not correspond, as usual, to the parallel association of the charge transfer resistance and the double layer capacitance as explained later. In fact, the loop corresponding to charge transfer at medium frequency is hardly detectable here as it was in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF] for the aph4-cph12 because of the lower Re value in this latter case. Here, it is located at the transition between the high frequency loop and the diffusion loop and could be evaluated only by the fitting procedure.

In addition, in the very low frequency range, the diagrams obtained for the Fc concentration of 1 mM display an inductive loop irrespective of the Cyphos concentration (e.g. see Figures 6a-b). Conversely, this loop does not exist at lower Fc concentrations (e.g. Figure 6c).

The existence of this very low frequency inductive loop could result from the precipitation at the electrode surface of ferrocenium whose solubility appeared to be quite low (around 0.5 mM) as measured in aph4-cph12 [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF].

These features were accounted for by using two electrical equivalent circuits including a charge transfer resistance R t for the electron exchange in ferrocene oxidation, and a diffusion impedance Z d for the diffusion-convective transport of ferrocene from the bulk solution to the electrode surface. The diameter of the large high frequency capacitive loop corresponds to the electrolyte resistance due to the ionic liquid, on which a geometric capacitance was set in parallel due to the possible combined effects of the volume capacitance of the solution and/or artefacts resulting from the close vicinity of the wiring for the reference and working electrodes and a parasitic capacitance due to the potentiostat. This large high frequency loop is generally not visible in aqueous solutions because R e values are usually much lower. This interpretation was supported by the presence of the same loop in the absence of redox species (results not shown). The inductive behavior was taken into account in the relevant electrical equivalent circuit (Figure 7b) by adding in parallel to Z d an adsorption resistance R ad in series with an inductance L. Q, a constant phase element and n the associated exponent, replacing the usual double layer capacitance, is put in parallel to R t and defines a constant phase element impedance as:

( )

1 CPE n Z Q jω = (1)
The resulting electrical equivalent circuits are shown in Figure 7a-b It must be noted that Z d is not included in the "Faradaïc" branch with R t as usually done in the Randles circuit because the presence of the constant phase element on parallel to Z d results in irrealistically large Sc values. In fact the large R d values combined with the equivalent double layer capacitance C eq (see further) provide characteristic frequencies in the range of the characteristic convective diffusion frequencies.

< Figure 6 > < Figure 7 >
The simulated diagrams using the electrical equivalent circuits of figure 7 have been fitted to the experimental diagrams to deduce the different parameters values. In general, if the overall quality of the fitting procedure is satisfactory with a quality factor χ around 1 by assigning a random relative error of 1% on the modulus in the whole frequency range, one must be aware that at low frequency, the scattering in the data entails a poorer determination of the "faradaïc" parameters (i.e., R t , Z d , R ad , L) due to the large R e value. The quality of the fit is in the same range for the mixtures with or without EHUT which involves that the level of fluctuations of the limiting diffusion current is similar, and this excludes the onset of large random fluctuations as those observed with surfactants displaying viscoelasticity in aqueous solutions [START_REF] Boutoudj | Mass transfer in a laminar elongational flow of a drag reducing surfactant[END_REF].

The Schmidt number values are rather scattered but are evenly distributed around the value originating from steady-state measurement. Taking an average of the steady-state and impedance measurements provides a value of D ∼ 4 10 -5 cm 2 s -1 .

Regarding other parameters such as R t , R e , Q, n, they can be used to derive two quantities: the heterogeneous rate constant k 0 of the Fc/Fc + reaction and the equivalent double layer capacitance C eq . According to the work of Brug et al. [START_REF] Brug | the analysis of electrode impedances complicated by the presence of a constant phase element[END_REF]:

1 1 1 1 / n n / n eq e t C Q (R R ) - - - = + (2)
and k 0 value can be determined as defined in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF]:

( ) ( )

0 1/ 2 1/ 2 0 2 2 0 = t ox red RT k n F AR C C (3)
Interfacial concentrations can be expressed as functions of the bulk concentrations in simple cases. For example, when only one species is present in solution, then, as in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF], the measurement at the half wave potential (here for the oxidation step) yields the condition k 0 values given in table 2, except for one value corresponding to Cyphos(0.1 M)/Fc(0.2 mM), are quite well gathered around 2 10 -3 cm s -1 , close to the value which was found in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF] for aph4-cph12. So, it can be assumed following the conclusions of Fontaine et al. [39] for Fc oxidation in Ethyl methyl midazolium/TFSI that the electron transfer dynamics should be strongly influenced by the counter ion motion being highly slowed down.

C eq values conversely are somehow larger (centered around 10 µF cm -2 ) and it could be thought that in that potential range, the specie most likely to be adsorbed, and playing the role of the compact layer, would be hexafluorophosphate anion which is much smaller than aph4-cph12 investigated in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF].

(ii) aph4-cph12 Some electrochemical impedance spectroscopy measurements have been performed for the three lowest aph4-cph12 concentrations (0.03 mol L -1 to 0.05 mol L -1 ). The low conductivity of the solutions renders the fitting procedure more delicate and the characterization of the medium frequency and very low frequency parameters is therefore poorly accurate. The values have also been reported in table 2 for the 0.03 mol L -1 concentration in the absence of EHUT. Sc value is in the same range as that originating from steady-state data and k 0 is of the same order of that given in [START_REF] Brinis | Heterogeneous electron transfer and diffusivities of ferrocene/ferrocenium couple in toluene/phosphonium-based ionic liquid solutions[END_REF] for higher ionic liquid concentrations. In addition, in agreement with steady state measurements, low frequency data appears strongly scattered when fluctuations are present, which obviously affects Z d . Without Cyphos 110, EHUT solution exhibits a high zero shear viscosity, about 10 5 times that of toluene, due to the self assembly of EHUT molecules into supramolecular structures through hydrogen bonding [START_REF] Colombani | Selective synthesis of non-symmetrical bis-ureas and their self-assemblyw[END_REF].

viscosity measurements

With increasing the amount of Cyphos 110, the zero shear viscosity sharply decreases. In addition, the relaxation time taken as the reciprocal of the crossing value between the pseudo Newtonian plateau for low shear rate values and the power law domain, sharply decreases to very low values and can no more be measured in the covered shear rate range for the highest concentrations. These results reflect the so called chain stopper effect of Cyphos 110 on EHUT association [37, 40, and 41].

For achieving a proper comparison between these flow measurements and the RDE geometry, in the latter case, the shear rate By opposition, viscosity measurements with the aph4-cph12 (see Figure 9) show conversely that for the concentration range investigated, the characteristic relaxation times can be measured. The critical shear rate increases when increasing the aph4-cph12 concentration.

Therefore the characteristic relaxation time decreases accordingly. The values of 8 and 25 s -1 for respectively 0.03 and 0.04 mol L -1 are in rough agreement with 30 and 50 s -1 corresponding to the critical velocities given by the electrochemical steady-state data despite the fact that the flow geometries are pretty different.

From the rheological data it was deduced that in the presence of EHUT a characteristic time was measurable only for the aph4-cph12 and decreased when increasing the concentration of ionic liquid; this feature was in qualitative agreement with the characteristic time deduced from the critical velocity marking the onset of strong fluctuations and departure from the Levich law. The light scattering data indicated that, while in the absence of ionic liquid the EHUT supramolecular polymer formed an entangled network, this structure was broken when the concentration of Cyphos 110 is higher than 0.01mol L -1 , whereas it persisted till 0.04 mol L -1 for aph4-cph12. The latter one is thus a less efficient chain stopper than the former. It could be also inferred that the length of the individual chains measured in the investigated concentration range was too short to give rise to any viscoelastic effects. All data correspond to toluene/ Cyphos 110(0.1 M L -1 ) mixtures.

Captions of the Figures

[Fc] = () 1 mM; () 0.5 mM; () 0.2 mM.

3. 1 . Electrochemical measurements 3 . 1 . 1

 1311 Steady-state data in toluene/ionic liquid with and without EHUT (i) Cyphos 110.Measurements were first performed in toluene/Cyphos110 solutions containing only Fc at concentrations of 1 mM, 0.5 mM or 0.2 mM at T= 35°C. 10 g/l EHUT were further added to the 1 mM solution. Figures2(a, b, c)) show a typical aspect of I-V curves for different rotation speeds obtained with Cyphos 110 (0.1 M) and Fc concentrations of . 0.2, 0.5, and 1

  the two species are at equal concentrations, and the measurement is done at the half wave of the oxidation step, then:

Figure 8

 8 Figure 8 represents the viscosity of EHUT solution at 10 g/L in toluene with various amounts

  the periphery of the disk electrode from the component parallel to the disk plane of the velocity vector, V P , The shear rate domain covered ( electrochemical experiments ranged from about15 to 150 s -1 for Ω varying between 100 and 1000 rpm. Therefore, at the shear rate applied by the electrode (between min • γ and max • γ ) the regime is Newtonian beyond 0.03 M of Cyphos 110. Above this concentration the solutions of EHUT are still viscous which explains the lower current limit actually observed in the presence of bis-urea.

Figure 1 :

 1 Figure 1: pictures of mixtures in toluene of EHUT/Cyphos 110 (10g.L -1 /0.075M), a) T < 35°C, b) T ≥ 35°C.

Figure 2 :

 2 Figure 2: Current potential curves of Fc oxidation in toluene/ [Cyphos 110] 0.1M solution for different RDE rotation speeds between 100 rpm and 1200rpm. (a) [Fc] = 0.2 mM; (b) [Fc] = 0.5 mM. The plots have been recorded in quasi steady-state. (c) [Fc] = 1 mM; (d) [Fc] = 1 mM with 10g/l EHUT added to the solution. Plots for (c) and (d) conditions have been recorded at 20 mV s -1 ; T=35°C.

Figure 3 :

 3 Figure 3: Limiting diffusion current vs.  1/2 from data in current potential curves of Figure 2, T=35°C.

Figure 4 :

 4 Figure 4: Limiting diffusion current vs.  1/2 ; T=35°C. All data correspond to toluene/(ach4-cph12(0.03 or 0.04 M L -1 )/1mMFc mixtures. (a) 0.03 M L -1 ach4-cph12; (b) 0.04 M L -1 ach4-cph12. Blank solution or with added 10 g.L -1 EHUT.

Figure 5 :

 5 Figure 5: Photo of a 0.03 M L -1 aph4cph12 + 10 g/l EHUT solution ( = 1000 rpm) showing Weissenberg effect.

Figure 6 :

 6 Figure 6: Impedance diagrams in Nyquist coordinates (real part/-Imaginary part) recorded at the half wave of the ferrocene oxidation. Solution: toluene, Cyphos 110; (a) Cyphos 110(0.1 M) [Fc] = 1mM,  = 300 rpm; (b) Cyphos 110(0.075 M) [Fc] = 1mM,  = 100 rpm; (c) Cyphos 110(0.1 M) [Fc] = 0.2 mM,  = 300 rpm; T = 35°C.

Figure 7 :

 7 Figure 7: Electrical equivalent circuits used for analyzing the EIS data with or without EHUT: (a) circuit for [Fc] = 1 mM; (b) circuit for [Fc] = 0.2 and 0.5 mM.

Figure 8 :

 8 Figure 8: Influence of Cyphos 110 addition on the viscosity of EHUT solution (10 g L -1 ) in toluene at 35.0 °C.

Figure 9 :

 9 Figure 9: Influence of ach4-cph12 addition on the viscosity of EHUT solution (10 g L -1 ) in toluene at 35.0 °C.

Figure 10 :

 10 Figure 10: The dynamic correlation length of EHUT (10g/l) in toluene (+1mM fc) at 35.0 °C as a function of the concentration of the ionic liquid. ( ) Cyphos 110; ( ) ach4-cph12.

Table 1 :

 1 Parameters values deduced from the data of figures 3 and 4 and calculated from the Levich equation.

	Ionic liquid	Concentration mol L -1	×10 4 η η η η	×10 2 ν ν ν ν	µΑ α α α α	(µΑ s 1/2 β β β β	×10 5 D	Sc
		(Pa.s)	(cm 2 s -1 )		rad -1/2	(cm 2 s -1 )
	Cyphos 110	0.075	9.3	1.065 0.485 0.23	2.785	382
	Cyphos 110/EHUT	0.075	16	1.83	0.299 0.198/	2.55	719
	Cyphos 110	0.085	9.93	1.135 0.320 0.255	3.30	344
	Cyphos 110/EHUT	0.085	15	1.715 0.108 0.212	2.775	618
	Cyphos 110	0.1	9.98	1.14
	[Fc] = 1 mM	″	″	″	0.298	0.246	3.11	367
	[Fc] = 0.5 mM	″	″	″	0.245	0.151	4.25	268
	[Fc] = 0.2 mM	″	″	″	0.0542	0.068	5.04	226
	Cyphos 110/EHUT	0.1	13	1.485 0.0124 0.227	2.97	500
	aph4-cph12	0.03	5.38	0.61	0.203	0.256	2.96	206
	aph4-cph12	0.04	5.5	0.63	0.03	0.275	3.296	191
	aph4-cph12	0.05	6.13	0.7	0.124	0.276	3.31	211

Table 2 :

 2 Fitted parameters values of the EIS diagrams analyzed with the electrical equivalent circuits (a) or (b) of figure7

	Ionic Liquid	Concentration	Fc	k 0		Ceq	Sc
		mol L -1	Concentration	×10 3		µF
			mM	cm s -1	cm -2
	Cyphos 110 (b)	0.075	1	2.37 ±	18.3 ±	160 ±
				0.28		9.2	57
	Cyphos 110/EHUT	0.075	1	1.66		13.6 ±	1550
				±0.50	2.1	±1150
	Cyphos 110 (b)	0.085	1	2.5 ± 12.6 ±6.5 200 ±
				1.2			56
	Cyphos 110/EHUT	0.085	1	1.70	2.3 ± 1.2	-
				±0.38
	Cyphos 110(a)	0.1	0.2	6.04 ± 13.9 ±0.7	286
	(a)		0.5	2.21		12.1 ±	±82
	(b)		1	3.29 ±	4.5	163 ±
				1.07	9.8 ± 2.7	51
				2.9 ±1		249
							±85
	Cyphos 110/EHUT	0.1	1	1.41 ± 6.5 ± 4.3 1240
				0.19			±
							1100
	aph4-cph12	0.03	1	5.49		12.8 210

Acknowledgements

The authors want to acknowledge the financial support of the PHC Tassili (project 13 MDU 893). They also thank S. Catrouillet for supplying them with EHUT.

Light scattering measurements

The dynamic correlation length ξ, measured by dynamic light scattering as a function of the concentration of Cyphos 110 is shown in Figure 10. For a toluene/EHUT (10 g/L) mixture, ξ=4.4 nm which is typical of the semi dilute regime and represents the pseudo mesh size of an entangled network. When Cyphos 110 is added, the dynamic correlation length sharply increases to 12 nm for 0.01 mol L -1 which actually means that the entangled network is broken. By further increasing the Cyphos 110 concentration, ξ decreases evidencing the chain stopper effect of Cyphos anion on the supramolecular structure of EHUT. At 0.075 M of Cyphos 110, ξ=6.5 nm and the viscosity of the mixture is about 1.6 mPa.s which is the signature of the presence of supramolecular aggregates based on EHUT however too short for providing any viscoelastic character to the solutions. ξ values measured for aph4-cph12 RTIL in the concentration range investigated for electrochemical and viscosity measurements are reported in the same Figure 11. By opposition, ξ remains constant and equal to 4 nm indicating that the entangled network is not broken in the presence of this ionic liquid. Therefore, the supramolecular aggregates are entangled and provide a viscoelastic character to the solutions. It can be concluded that aph4-cph12 has a smaller chain stopper effect than Cyphos 110.

< Figure 10 >

Conclusions

This work was intended for evidencing the possible formation of reversible supramolecular structures from EHUT (2, 4-bis (2-ethylhexylureido) toluene) monomer in toluene and assessing the viscoelastic character of this solution in the presence of either of two added ionic liquids known as chain stoppers. These ionic liquids, Cyphos 110 and aph4-cph12, were based on a common phosphonium cation and two different anions, namely hexafluorophosphate and tris(pentafluoroethyl) trifluorophosphate respectively. To this end, electrochemical, rheological and light scattering methods were combined.

Electrochemical methods, based on the analysis of current potential curves and of

Electrochemical Impedance Spectroscopy diagrams were conducted with a rotating disk electrode, a geometry containing an elongational component thus able to trigger viscoelastic effects.

From the analysis of the limiting diffusion plateau, diffusion coefficients of ferrocene in those mixtures could be measured. It was found that the presence of EHUT decreased this value because of the viscosity increase. In the case of the Cyphos 110, the diffusion current followed the Levich law over the whole angular velocity range as for a Newtonian fluid, thus evidencing the absence of any viscoelastic character for these solutions. By opposition, in the presence of aph4-cph12, a departure from the Levich law together with strong fluctuations of the current allowed to assign a viscoelastic character to the solutions.

The electrochemical impedance spectroscopy diagrams showed the presence of an inductive effect revealing an adsorption of the ionic liquid fluctuating with potential and likely due to the anion. The analysis of the diagrams with frequency allowed measuring the heterogeneous rate constant of the Fc/Fc + system in the range of 2 10 -3 cm s -1 for the two ionic liquids, close to a value previously measured in the aph4cph12 at higher concentrations.