Lucile Malard

Jean-François Chastang

Dr Isabelle Niedhammer
email: isabelle.niedhammer@inserm.fr

Changes in psychosocial work factors in the French working population between 2006 and 2010

Keywords: Changes, psychosocial work factors, France

Purpose. The aim of the study was to assess the changes in psychosocial work factors in the French working population between 2006 and 2010, and to examine potential differential changes according to age, occupation, public/private sector, work contract, and self-employed/employee status.

Methods. The study sample included 5600 workers followed up from 2006 to 2010 from the national representative SIP survey. Psychosocial work factors included decision latitude, psychological demands, social support, reward, overcommitment, long working hours, predictability, night and shift work, emotional demands, role conflict, ethical conflict, tensions with the public, job insecurity, and work-life imbalance, and were measured using scores. Linear regressions were used to analyze the change in the scores of these factors adjusted for age and initial score. All analyses were stratified by gender.

Results. Psychosocial work factors worsened between 2006 and 2010: decision latitude, social support, reward, role conflict and work-life imbalance for both genders, and psychological demands, emotional demands, ethical conflict and tensions with the public for women. Differential changes according to age, occupation, public/private sector, work contract and self-employed/employee status were observed suggesting that some groups may be more likely to be exposed to negative changes especially the younger, low and high-skilled and public sector workers.

Conclusion.

Monitoring exposure to psychosocial work factors over time may be crucial, and prevention policies should take into account that deterioration of psychosocial work factors may be sharper among subgroups such as younger, low and high-skilled and public sector workers.

Introduction

Within the last decades, psychosocial work factors have become a major concern in occupational health. The deep changes that have occurred in the labour marketincreased globalization, competition, flexibility, service sector and development of new forms of work organizationmay have increased the prevalence of exposure to psychosocial work factors in the working population. Moreover, in 2007 in the United States, a financial crisis started due the subprime mortgage crisis, and spread all over the world. Consequently, the economic activity has slowed down. For example, in France, between 2006 and2010, the gross domestic product (GDP) per capita decreased by 1.5%, unemployment raised from 8.8% in 2006 to 9.3% in 2010, and public debt increased from 64.0% of GDP in 2006 to 79.2% of GDP in 2010. In this context of changes in the labour market and global economic crisis, the study of changes in exposures to psychosocial work factors may be a crucial topic.

Psychosocial work factors have been mainly studied as risk factors for health outcomes. Indeed, many studies showed that they were associated with a deterioration of mental health [START_REF] Stansfeld | Psychosocial work environment and mental health--a meta-analytic review[END_REF][START_REF] Netterstrøm | The relation between work-related psychosocial factors and the development of depression[END_REF]Bonde 2008), self-reported health [START_REF] Ferrie | Effects of chronic job insecurity and change in job security on self reported health, minor psychiatric morbidity, physiological measures, and health related behaviours in British civil servants: the Whitehall II study[END_REF][START_REF] Niedhammer | Psychosocial factors at work and self reported health: comparative results of cross sectional and prospective analyses of the French GAZEL cohort[END_REF][START_REF] Niedhammer | Effort-reward imbalance model and self-reported health: cross-sectional and prospective findings from the GAZEL cohort[END_REF]), incidence of cardiovascular diseases [START_REF] Lee | Prospective study of job insecurity and coronary heart disease in US women[END_REF]Kivimäki et al. 2006), etc. As psychosocial exposures at work may have adverse effects on health, it might be important to monitor the prevalence of these exposures. To our knowledge, very few studies have focused on the changes over time in the prevalence of exposure to psychosocial work factors.

The rare studies assessing the changes of psychosocial work factors over time were often limited to specific populations or sectors, to some countries or regions and to a small number of psychosocial work factors [START_REF] Tsai | The impact of the 2008 financial crisis on psychological work stress among financial workers and lawyers[END_REF][START_REF] Cheng | Changes in Psychosocial Work Conditions in Taiwanese Employees by Gender and Age from 2001 to 2010[END_REF][START_REF] Houdmont | Psychosocial factors and economic recession: the Stormont Study[END_REF][START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF][START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF][START_REF] Wang | The prevalence of mental disorders in the working population over the period of global economic crisis[END_REF]. In Taiwan, working hours, excessive work, reward, respect from superiors and colleagues, social support, and job promotion prospects improved among lawyers while "supervisor concerned about the welfare", "supervisor pays attention", interruptions and disturbances at work, and trouble sleeping at night worsened among financial workers between 2007 and 2009 according to a prospective study on 135 financial workers and lawyers [START_REF] Tsai | The impact of the 2008 financial crisis on psychological work stress among financial workers and lawyers[END_REF]. A representative Taiwanese periodical cross-sectional study showed that working more than 48 hours a week, working less than 40 hours a week, nonstandard work shift, job control, and job demands deteriorated between 2001 and 2010, and job insecurity increased in 2004 and in 2007 among 64299 Taiwanese employees [START_REF] Cheng | Changes in Psychosocial Work Conditions in Taiwanese Employees by Gender and Age from 2001 to 2010[END_REF]. In a periodical cross-sectional survey in Northern Ireland among 27037 civil servants, work stress increased between 2005 and 2010 as well as exposure to psychosocial work factors such as high job demands, low job control, low peer support, poor relationships, role ambiguity and conflict, and lack of consultation and information about change [START_REF] Houdmont | Psychosocial factors and economic recession: the Stormont Study[END_REF]). An European periodical cross-sectional study found a degradation of decision latitude and job insecurity but an improvement of job promotion, effort, bullying, sexual harassment, long working hours, and work-life imbalance between 2005 and 2010 in a large sample of 56096 European employees [START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF]. In Australia, job insecurity decreased from 2001 to 2007 but increased in 2008 in a prospective representative study including 13182 Australian workers [START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF]. Finally, in a cross-sectional study among 3579 Canadian employees in Alberta, job insecurity increased from the beginning of 2008 to the end of 2009 [START_REF] Wang | The prevalence of mental disorders in the working population over the period of global economic crisis[END_REF]).

Consequently, very few studies were performed to assess changes in psychosocial working conditions using nationally representative prospective data and a large range of psychosocial work factors. Our study is thus an attempt to fill the gap in the knowledge on the changes in psychosocial work factors over time, using prospective national representative data and a wide range of classical and emergent psychosocial work factors. This study also aimed at exploring potential differences in these changes according to age, occupation, public/private sector, work contract and self-employed/employee status.

Population and methods

Sample

The study was based on the data from the prospective and national representative SIP (Santé et Itinéraire Professionnel) survey, performed by the French Ministries of Labour and Health (DARES and DREES), the French Centre for Employment Studies (CEE) and the French National Institute for Statistics and Economic Studies (INSEE). This survey was designed to explore the complex associations between work and health [START_REF] Coutrot | Parcours professionnels et état de santé[END_REF]. In 2006, households were randomly selected from the 1999 census, and one individual aged between 20 to 74 years was randomly selected to be interviewed. Finally, 13648 men and women from the general French population were interviewed by a trained interviewer at respondent's home. The participation rate was 76%. Four years later, they were contacted again for the second wave of the survey, and 11016 individuals (81%) participated. Among them, 2679 men and 2921 women were working in both 2006 and 2010. A study by our team has already been published using these data [START_REF] Murcia | Psychosocial work factors, major depressive and generalised anxiety disorders: results from the French national SIP study[END_REF].

Psychosocial work factors

Psychosocial work factors were measured following the classical demand-control-support [START_REF] Karasek | The Job Content Questionnaire (JCQ): an instrument for internationally comparative assessments of psychosocial job characteristics[END_REF] and effort-reward imbalance models [START_REF] Siegrist | The measurement of effort-reward imbalance at work: European comparisons[END_REF]) and emergent concepts. No validated questionnaire was available in the SIP survey, thus proxies were constructed.

Three factors of the demand-control-support model were constructed: decision latitude (2 items: "freedom to decide how to do the work", "use of skills"), psychological demands (3 items: "working under pressure", "too many things to do", "excessive amount of work") and social support (1 item: "good relationships with colleagues").

Two factors of the effort-reward imbalance model were constructed: reward (1 item: "fair feedback on the work done") and overcommitment (1 item: "work still on mind when going to sleep"). Four factors related to working time/hours were measured: long working hours (1 item: "working more than 48 hours a week"), predictability (1 item: "irregular hours difficult to predict"), night work (1 item: "working between midnight and 5 am"), and shift work (1 item: "working on alternating shift").

The other emergent psychosocial work factors included: emotional demands (1 item: "hiding feelings at work"), role conflict (1 item: "not being able to work following best practices"), ethical conflict (1 item: "exposure to unethical situations"), tensions with the public (1 item: "tensions with the public (users, students, patients, customers)"), job insecurity (1 item: "fear of job loss"), and work-life imbalance (1 item: "work in line with family life").

For all items, the responses were "always", "often", "sometimes" or "never" ranging from 1 to 4, the higher the value, the better the situation (if it was not the case, the value order was reversed). Thus, each psychosocial work factor had a score between 1 and 4, except decision latitude and psychological demands which were the addition of 2 and 3 items.

Covariates

The covariates were age, occupation (managers/professionals, associate professionals, clerks and manual workers), public/private sector, work contract (temporary or permanent contract) and self-employed/employee status. Occupation was coded using the French national classification of occupations that is close of the international classification (ISCO). In the analyses, age, occupation, public/private sector, work contract, and self-employed/employee status were those of 2006.

Statistical analyses

To be representative of the French working population of 2006, weights were calculated using marginal To test whether the changes were different according to covariates, regressions models were performed using the same models to which we added successively occupation, private/public sector, work contract and employee/self-employed status. Additional regression models adjusted for the score in 2006 were performed with age to test if the changes were different according to age groups.

As psychosocial work factors differ according to gender, all analyses were performed for men and women separately.

Statistical analyses were carried out using SAS 9.3 software (SAS Institute Inc, Cary, NC).

Results

Table 1 presents the description of the study sample according to covariates in 2006 and 2010. There were few changes in the distribution of occupation, public/private sector and self-employed/employee status between 2006 and 2010, nevertheless 18% of the sample changed occupation in 2010 compared to 2006 (data not shown).

Temporary contract decreased by around 50% for men and women, indeed in 2006 there were 12% and 16% of men and women with temporary contracts while in 2010 there were only 5% and 8%.

Differences in the exposure to psychosocial work factors according to age, occupation, public/private sector, work contract and self-employed/employee status were observed in 2006 (Supplementary Tables S1 to S5). The prevalence of psychosocial work factors was higher among younger individuals, except for long working hours that were more prevalent among older male workers. Differences in the exposure to many factors were observed according to occupation, depending on the factor concerned, the most exposed group was either managers/professionals or manual workers. Differences in the exposure to psychosocial work factors were also found between public/private sector, temporary/permanent contract, and self-employed/employee status, but the number of significant differences was small for temporary/permanent contract.

Among men, five psychosocial work factors worsened significantly between 2006 and 2010 (Table 2). Men reported lower levels of decision latitude, social support, and reward, and higher levels of role conflict and worklife imbalance in 2010 compared to 2006. Among women, two third of the psychosocial work factors (i.e. 10 factors) showed a significant change within the period, and only one of these factors improved. In 2010 compared to 2006, women reported lower levels of decision latitude, social support, and reward, higher levels of psychological demands, emotional demands, role conflict, ethical conflict, tensions with the public, and worklife imbalance. However, women reported higher levels of predictability in 2010.

Differential changes according to age in 2006 were observed as shown in Table 3. Differences in exposure to various psychosocial work factors between age groups in 2006 were intensified between 2006 and 2010 to the detriment of younger workers for low decision latitude (men only), shift work, tensions with the public (men only), and work-life imbalance. Differential changes were also observed for factors for which there was no difference according to age in 2006 leading to differences to the detriment of younger workers for psychological demands, low social support, low predictability, and job insecurity among men, and for role conflict, ethical conflict and tensions with the public among women.

Table 4 presents the differences in changes according to occupation in 2006. The exposure to various factors was higher for low-skilled occupations (manual workers or clerks) in 2006, and the changes led to increase the gaps between occupational groups for low decision latitude, low reward (men), night work (men), shift work, and tensions with the public (men). The exposure to other factors was higher for high-skilled occupations (managers/professionals), and the changes increased the gaps between occupational groups for psychological demands, overcommitment, long working hours (women), emotional demands, tensions with the public (women), and work-life imbalance. For low predictability (men), role conflict (men), and tensions with the public (men), differential changes also intensified the gaps between occupations to the detriment of managers/professionals and clerks. However, differential changes in job insecurity among men reduced the difference observed in 2006 between managers/professionals and clerks.

Changes in psychosocial work factors between 2006 and 2010 were different according to public/private sector in 2006 (Table 5). Existing differences between public and private sector were exacerbated for overcommitment (women), emotional demands (women), role conflict, ethical conflict (women), and tensions with the public to the detriment of the public sector and for long working hours (men), predictability (men) and job insecurity to the detriment of the private sector. Some factors, with no public/private sector differences in 2006, displayed differential changes between 2006 and 2010 to the detriment of the public sector, these factors were decision latitude, psychological demands (women), social support (men), and reward (women).

Decision latitude and role conflict showed differential changes according work contract in 2006 among women to the detriment of temporary contract workers (Supplementary Table S6). In 2006, temporary contract women were more likely to be exposed to low decision latitude than permanent contract women, these differences were reinforced between 2006 and 2010. There was no difference in role conflict according to work status in 2006 among women, but a change in this factor was observed from 2006 to 2010 to the detriment of temporary workers.

Differential changes according to self-employed/employee were found (Supplementary Table S7). The differences in psychosocial work factors observed in 2006 to the detriment of employees were increased between 2006 and 2010 for low decision latitude, low social support (men), shift work, role conflict, and ethical conflict (women). Differences observed to the detriment of self-employed workers were also exacerbated for psychological demands (men), overcommitment (men), long working hours, low predictability, emotional demands (women), and work-life imbalance (men). Psychological demands did not differ according to selfemployed/employee status in 2006, but a change led to a gap between the two groups for this factor among women to the detriment of employees.

Discussion

A substantial number of psychosocial work factors worsened in France between 2006 and 2010 especially among women. These factors were low decision latitude, psychological demands (women), low social support, low reward and emergent factors, emotional demands (women), role conflict, ethical conflict (women), tensions with the public (women), and work-life imbalance. Differential changes according to age, occupation, public/private sector, work contract and self-employed/employee status were observed showing that some groups may be particularly exposed to negative changes, in particular young workers, high and low-skilled workers (clerks and manual workers) and public sector workers.

Few studies examined the changes in psychosocial work factors over time, and the existing literature often studied specific populations or regions based on periodical cross-sectional surveys and explored a limited number of factors, thus the comparison with our own results may be difficult. A prospective study including 135 financial workers and lawyers in Taiwan showed that psychosocial working conditions deteriorated for financial workers while they improved for lawyers between 2007 and 2009 [START_REF] Tsai | The impact of the 2008 financial crisis on psychological work stress among financial workers and lawyers[END_REF]. As observed in our study, psychological demands increased, and social support and reward decreased between 2007 and 2009 but only for financial workers. Tsai and Chan also found an increase in overcommitment and job insecurity among financial workers. A representative periodical cross-sectional study in Taiwan among 64299 employees [START_REF] Cheng | Changes in Psychosocial Work Conditions in Taiwanese Employees by Gender and Age from 2001 to 2010[END_REF] Wang et al. found that job insecurity was higher in 2009 compared to the beginning of 2008 in a cross-sectional study among 3579 employees in Alberta, Canada [START_REF] Wang | The prevalence of mental disorders in the working population over the period of global economic crisis[END_REF]). In our study, no worsening of job insecurity was found. Finally, a Danish study, using a split panel design of 6067, 5454 and 5404 employees representative of the labor force in 1990, 1995 and 2000, assessed the changes in job control and job insecurity between 1990 and 2000. The study period was different from ours and did not include the economic crisis of 2008 but in this period the Nordic countries were hit by an economic crisis in the early 90's. They found an improvement in job insecurity between 1990 and 1995 and stabilization between 1995 and 2000, and there was no change in low job control [START_REF] Burr | Trends in the Danish work environment in 1990-2000 and their associations with labor-force changes[END_REF].

The differential changes according to age, occupation, public/private sector, work contract and selfemployed/employee status have almost never been studied before. In the Taiwanese study by Cheng and al., analyses were stratified on age but no test was performed to assess whether the changes were different according to age [START_REF] Cheng | Changes in Psychosocial Work Conditions in Taiwanese Employees by Gender and Age from 2001 to 2010[END_REF]. In line with our study, they found that job control and psychological demands seemed to deteriorate more for younger and middle age workers. In the European study [START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF], decision latitude was more likely to deteriorate among manual workers, which is in agreement with our results. Finally, in the Australian study [START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF]), the authors found that inequalities in job control narrowed among young workers compared with older groups and for casual, fixed-term and self-employed compared with permanent workers from 2001 to 2008. They also observed a slight narrowing of disparities over time in job security between genders, age, employment arrangement and occupational skill level groups. The trends observed in the Australian study were very different compared with our results, as most of our differential changes led to increase the gaps between subgroups of the population. These discrepancies may be explained at least partly by a better economic situation of Australia over 2001-2008compared with France over 2006-2010. . It may be difficult to attribute these negative changes in psychosocial work factors that were found in our study to the 2008 economic crisis that occurred in the middle of the period 2006-2010. Nevertheless, these results seemed to be consistent with what may be expected in such a period of decreased economic activity with a rise in unemployment: less decision latitude, more psychological demands, less reward, more role stressors, more tensions with the public, etc. In such a difficult period, changes might have been introduced by companies such as technological and organizational changes. In additional analyses (not showed), technological and organizational changes that occurred within the study period were found to have an impact on changes in psychosocial work factors. Indeed, workers who were exposed to technological or organizational changes between 2006 and 2010 experienced a stronger deterioration of many psychosocial work factors, especially among women, compared to those who were not exposed. Thus, we may assume that technological and organizational changes might be factors that might contribute to explain the degradation of the psychosocial work environment. Competing explanations may be considered such as trends in psychosocial work factors that would have been observed even without the 2008 crisis. Only few studies explored the changes in psychosocial work factors in the period before the crisis. A French report among employees from the private sector showed a deterioration of psychological demands between 1994 and 2003 [START_REF] Arnaudo | L'évolution des risques professionnels dans le secteur privé entre 1994 et 2010 : premiers résultats de l'enquête SUMER. DARES Analyses 23: Bonde JPE[END_REF]. A Belgian study reported a deterioration in psychological demands and job insecurity but an improvement in decision latitude and social support from 1994 and 2002 [START_REF] Clays | Long-term changes in the perception of job characteristics: results from the Belstress II--study[END_REF]. Comparison of the deterioration strength of psychological demands with our study was not possible, however decision latitude improved before the crisis, and deteriorated in our study, which may be in favor of an effect of the economic crisis. Moreover, in our European study, differential changes were found according to country, countries less affected by the crisis showed more positive changes than the European mean while countries more affected by the crisis showed more negative changes than the European mean [START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF]). These differential changes may also be in favor of a potential effect of the economic crisis on psychosocial work factors. The fact that job insecurity did not worsen in our study might seem surprising as this result was found in other studies [START_REF] Wang | The prevalence of mental disorders in the working population over the period of global economic crisis[END_REF][START_REF] Tsai | The impact of the 2008 financial crisis on psychological work stress among financial workers and lawyers[END_REF][START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF]). However, this result might be explained at least in part by the fact that the rate of unemployment in France was already high in 2006 (8.8%), and given the study design and studied sample, people were working in both 2006 and 2010, and more than 80% of them did not change of employer within the period. Consequently, our sample in 2010 may have a longer seniority and a more stable working situation (something that is confirmed by the reduction of the prevalence of temporary work contract from 2006 to 2010, in Table 1). Using a complementary sample of workers in 2010, we were able to estimate job insecurity in representative samples in 2006 and 2010 and found no differences among men and women (not showed). Therefore, even if we may assume that our study design may result in an underestimation of change in job insecurity, the additional analyses suggest that job insecurity may have not changed in France between 2006 and 2010 substantially.

Reward showed the strongest deterioration for both men and women, it may be difficult to explain this result, and there has been no previous study exploring reward change. Reward may be viewed as a combination of different psychosocial work aspects (salary, job (in)security, esteem or social support, job promotion, etc.), thus it may also have been more sensitive to deterioration.

The main asset of the study was to be the first, to our knowledge, to explore the changes in psychosocial work factors over time in a nationally representative prospective sample allowing generalization to the French working population, and the assessment of the changes in a large number of psychosocial work factors and the differential changes according to several subgroups of the population. Indeed, only two previous studies were prospective [START_REF] Tsai | The impact of the 2008 financial crisis on psychological work stress among financial workers and lawyers[END_REF][START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF]), and among these two studies, only one was based on a representative sample at national level [START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF]. Furthermore, the response rate to the SIP survey in 2006 was satisfactory (76%). The results may be extrapolated to the French working population of 2006, as weights were taken into account in all statistical analyses. The analyses were powerful enough to allow stratification by gender something that may be considered fundamental [START_REF] Niedhammer | How is sex considered in recent epidemiological publications on occupational risks?[END_REF], and to observe differential changes according to several covariates. To date, only three previous studies explored the differential changes in psychosocial work factors according to age [START_REF] Cheng | Changes in Psychosocial Work Conditions in Taiwanese Employees by Gender and Age from 2001 to 2010[END_REF], occupation [START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF], and gender, age, occupational skill level and employment arrangements (a combination of work contract, selfemployed status and working time) but only for job control and job security [START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF].

Moreover, a large range of psychosocial work factors were studied, both classical factors from demand-controlsupport and effort-reward models, and emergent factors such as long working hours, predictability, emotional demands, role conflict, ethical conflict, tensions with the public, job insecurity, and work-life imbalance.

Nevertheless, some limitations deserve to be mentioned. A part (19%) of the initial sample did not participate in 2010 which might lead to a loss in statistical power and a potential selection bias. Weights were included in the analyses to reduce this potential bias. Another limitation was the floor or ceiling effect, for example a worker reporting 'never' or 'always' to one item in 2006 was not able to provide worse or better responses in 2010, even if the situation deteriorated or improved. To address this issue, statistical analyses were adjusted for baseline score of each factor. Psychosocial work factors were measured using theoretical models and emergent concepts but no validated questionnaires were available in the SIP survey leading to a potential imprecision in the measurement of the factors. However, previous studies showed the interest and validity of constructing proxies [START_REF] Karasek | Testing two methods to create comparable scale scores between the Job Content Questionnaire (JCQ) and JCQ-like questionnaires in the European JACE Study[END_REF]. A potential selection bias should be considered, individuals in employment in 2006 but who lost their job and were not working any longer in 2010 might be a particular subgroup who might have been exposed to a stronger deterioration of their psychosocial work environment before losing their job.

Consequently, this might contribute to a slight underestimation of the degradation of psychosocial work environment in our study (the number of people who become unemployed in 2010 was small, N=277). Some people also changed jobs within the study period, and part of them might have done so because of good opportunities, leading also to an underestimation of the degradation of psychosocial work factors. Finally, as the study was based on two data collections in 2006 and 2010, this prospective design might not capture all the changes in psychosocial work factors that might have occurred within the study period. For example, with only two points of data collection, our study could not be as accurate as the 8-wave Australian study and the fluctuations in job insecurity observed in this recent study may explain our non-significant results about this factor [START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF]. Psychological demands and work-life imbalance presented more missing data than other factors. Psychological demands was measured using three items, we performed additional analyses and imputed missing values by the weighted score using two items among the three items that were not missing.

The results slightly changed, the deterioration was stronger for both genders, therefore, we may assume that our results may be cautious and may underestimate the actual deterioration of psychological demands. People who did not respond to the item of work-life imbalance were more likely to live alone and without children. Thus, we may assume that most of those who did not respond to the question about work-life imbalance did not feel concerned by the question because they had "no family". Additional analyses, considering those who did not respond to the item as non-exposed to work-life imbalance, were performed and the results were unchanged.

Additional analyses were performed to study the potential biases mentioned above. First, to study the potential bias due to attrition, the subsample of those who were interviewed in 2010 and the subsample of those who were not were compared using the data in 2006. Individuals who did not participate in 2010 were more likely to be younger, to work with a temporary contract, and non-respondent women in 2010 were more likely to work in the private sector in 2006 than women participating in 2010. Psychosocial work exposures were different between the two subsamples only among men; men who did not participate in 2010 were more likely to be exposed to low predictability, emotional demands, tensions with the public, and job insecurity. Secondly, additional analyses were performed to study the potential bias induced by workers in 2006 who lost their job during the study period. Unemployed people and workers in 2010 were compared using the data collected in 2006.

Individuals who were unemployed in 2010 were more likely to be older (men), employees, and manual workers, and to have temporary contracts. They were also more likely to be exposed to low decision latitude and job insecurity, but less likely to be exposed to long working hours and tensions with the public in 2006 compared to those who were working in both 2006 and 2010. Finally, additional analyses showed that the degradation of psychosocial work factors was stronger among those who did not experience job change (change in employer, occupation, or sector/economic activity). Thus, it may be assumed that the deterioration of psychosocial work factors might be stronger if the sample was restricted to people who did not experience any job change.

To conclude, this study showed that psychosocial work factors deteriorated between 2006 and 2010 in the French working population, and that these changes were different according to age, occupation, public/private sector, work contract, and self-employed/employee status. Therefore, as psychosocial work factors are known to have an impact on health and also to play a role in social inequalities in health, monitoring exposure to psychosocial work factors over time might be crucial, and prevention policies should take into account that deterioration of psychosocial work factors might be sharper among subgroups of the population such as younger workers, low and high-skilled workers and public sector workers.

  calibration and inverse probability weighting to control for the biases due to non-response in 2006 and to attrition in 2010 (De Riccardis 2012). A marginal calibration on age, work status (working/unemployed/nonworking)*age, urban area, size of household, occupation and economic activity (NAF) was performed on the sample in 2006. Homogeneous response groups were formed based on characteristics in 2006 (work status, urban area, age, level of education, gender and self-reported health), and the probability of being interviewed in 2010 was calculated for each group. Weights calculated by marginal calibration (for non-response in 2006) were multiplied by the inverse probability of being interviewed in 2010. Finally, a second marginal calibration on territorial unit, urban area, age*gender, education, nationality, and size of household was performed on the sample of individuals interviewed in 2006 and 2010 to be representative of the population of 2006. Weights were included in all statistical analyses. Descriptive statistics were preformed to present the study sample in 2006 and 2010. To assess the changes in psychosocial work factors, the variation of score between 2006 and 2010 (score 2010score 2006) was calculated for each factor. A positive variation of score meant improvement in psychosocial work conditions while a negative variation meant deterioration. Regression models were used to estimate the variation of score between 2006 and 2010 adjusted for the score in 2006 and age. The mean variation of score was calculated based on these regressions as the prediction for the mean age and the distribution of the score in 2006 in the sample.

  assessed the changes in psychosocial work factors from 2001 to 2010 and found a worsening in decision latitude, psychological demands and nonstandard work shifts which were in line with our results. They also found a deterioration in long working hours and job insecurity. In a periodical cross-sectional survey of 27037 civil servants in Northern Ireland, Houdmont et al. found a degradation of decision latitude, psychological demands, and social support[START_REF] Houdmont | Psychosocial factors and economic recession: the Stormont Study[END_REF], which is in agreement with our study. Using a large representative sample of 56096 employees working in 30 European countries from a cross-sectional periodical survey, in line with our results, decision latitude and skill discretion deteriorated between 2005 and 2010[START_REF] Malard | Changes in Psychosocial Work Exposures Among Employees Between 2005 and 2010 in 30 Countries in Europe[END_REF]). This study also showed opposite trends, such as an increase of job promotion (one dimension of reward) and a decrease of work-life imbalance. Other results from this European study were an increase of job insecurity, and a decrease of effort, long working hours, bullying, and sexual harassment. An 8wave prospective study in Australia found that there was a slight decrease of job insecurity from 2001 to 2007 and then a rise in 2008 among a nationally representative sample of 13182 workers[START_REF] Lamontagne | Psychosocial working conditions in a representative sample of working Australians 2001-2008: an analysis of changes in inequalities over time[END_REF]).

  score in 2006 according to public/private sector, the lower the score, the higher the exposure b Difference of change in score compared to private sector from linear regression model adjusted for age and score of factor in 2006; Positive beta meant improvement of the factor, negative beta deterioration of the factor compared to reference group c Global p-value for differences in score in 2006 according to public/private sector d Global p-value for differences in change in score between 2006 and 2010 according to public/private sector *p<0.05 ; **p<0.01 ; ***p<0.001 Only the factors with significant differences according to public/private sector are presented

Table 1 Description of the study sample in 2006 and 2010 according to covariates

 1

		Men					Women
	2006		2010			2006		2010
	N a	% b	N a	% b	N a	% b	N a	% b

Table 2 Mean changes in psychosocial work factors: results from linear regression models adjusted for age in 2006 and score of factor in 2006

 2

	Men

Table 3 Differential changes according to age in 2006: results from linear regression models adjusted for score of factor in 2006

 3 Mean score in 2006 according to age group, the lower the score, the higher the exposure b Difference of change in score compared to +50y from linear regression model adjusted for score of factor in 2006; Positive beta meant improvement of the factor, negative beta deterioration of the factor compared to reference group c Global p-value for differences in score in 2006 according to age d Global p-value for differences in change in score between 2006 and 2010 according to age *p<0.05 ; **p<0.01 ; ***p<0.001 Only the factors showing significant changes according to age are presented

			20-30 y			30-40 y			40-50 y		+50 y (ref.)	p c	p d
		Mean score 2006 a	Beta b	95% CI	Mean score 2006 a	Beta b	95% CI	Mean score 2006 a	Beta b	95% CI	Mean score 2006 a
	Men
	Low decision latitude	6.45	-0.41***	[-0.61 ; -0.20]	6.80	-0.19*	[-0.35 ; -0.04]	6.86	-0.23**	[-0.37 ; -0.08]	6.87	**	***
	Psychological demands	8.62	-0.68***	[-1.04 ; -0.31]	8.54	-0.49***	[-0.77 ; -0.21]	8.61	-0.29*	[-0.56 ; -0.02]	8.73	ns	***
	Low social support	3.69	-0.08	[-0.17 ; 0.00]	3.65	-0.16***	[-0.23 ; -0.09]	3.69	-0.12***	[-0.19 ; -0.05]	3.70	ns	***
	Low predictability	3.28	-0.27***	[-0.41 ; -0.12]	3.35	-0.11*	[-0.21 ; -0.01]	3.40	-0.11*	[-0.21 ; -0.01]	3.47	ns	**
	Shift work	3.39	-0.12	[-0.26 ; 0.01]	3.48	-0.17***	[-0.27 ; -0.07]	3.55	-0.11*	[-0.19 ; -0.03]	3.74	***	**
	Tensions with the public	3.44	-0.15**	[-0.25 ; -0.04]	3.38	-0.05	[-0.13 ; 0.04]	3.46	-0.01	[-0.09 ; 0.07]	3.56	**	*
	Job insecurity	3.62	-0.20***	[-0.30 ; -0.09]	3.64	-0.17***	[-0.24 ; -0.09]	3.66	-0.12***	[-0.18 ; -0.05]	3.68	ns	***
	Work-life imbalance	3.40	-0.18**	[-0.32 ; -0.04]	3.39	-0.14*	[-0.24 ; -0.03]	3.46	0.00	[-0.10 ; 0.10]	3.56	*	**
	Women
	Shift work	3.31	-0.18**	[-0.31 ; -0.06]	3.59	-0.05	[-0.13 ; 0.03]	3.67	0.00	[-0.07 ; 0.07]	3.72	***	*
	Role conflict	3.33	-0.18**	[-0.30 ; -0.05]	3.32	-0.09	[-0.19 ; 0.00]	3.31	-0.09*	[-0.17 ; 0.00]	3.39	ns	*
	Ethical conflict	3.52	-0.17***	[-0.27 ; -0.07]	3.65	-0.12**	[-0.19 ; -0.05]	3.64	-0.05	[-0.11 ; 0.02]	3.65	ns	***
	Tensions with the public	3.28	-0.23***	[-0.34 ; -0.12]	3.38	-0.12**	[-0.21 ; -0.04]	3.42	-0.05	[-0.13 ; 0.02]	3.43	ns	***
	Work-life imbalance	3.42	-0.20**	[-0.33 ; -0.06]	3.39	-0.14**	[-0.24 ; -0.04]	3.53	-0.06	[-0.15 ; 0.03]	3.66	***	**
	a

Table 4 Differential changes according to occupation in 2006: results from linear regression models adjusted for age in 2006 and score of factor in 2006

 4 Mean score in 2006 according to occupation group, the lower the score, the higher the exposure b Difference of change in score compared to manual workers from linear regression model adjusted for age and score of factor in 2006; Positive beta meant improvement of the factor, negative beta deterioration of the factor compared to reference group c Global p-value for differences in score in 2006 according to occupation d Global p-value for differences in change in score between 2006 and 2010 according to occupation *p<0.05 ; **p<0.01 ; ***p<0.001 Only the factors showing significant changes according to occupation are presented

			Managers/professionals		Associate professionals		Clerks	Manual workers (ref.)	p c	p d
		Mean score 2006 a	Beta b	95% CI	Mean score 2006 a	Beta b	95% CI	Mean score 2006 a	Beta b	95% CI	Mean score 2006 a
	Men
	Low decision latitude	7.20 0.28**	[0.11 ; 0.44]	6.86	0.22**	[0.07 ; 0.38]	6.66	0.02	[-0.16 ; 0.19]	6.54	*** **
	Psychological demands	7.80 -0.39*	[-0.69 ; -0.09]	8.11	-0.38**	[-0.65 ; -0.12]	8.80	-0.27	[-0.58 ; 0.04]	9.29	***	*
	Low reward	3.14 0.26***	[0.14 ; 0.39]	2.92	0.09	[-0.02 ; 0.21]	2.80	-0.06	[-0.19 ; 0.08]	2.92	*** ***
	Overcommitment	2.61 -0.22***	[-0.34 ; -0.10]	2.83	-0.20***	[-0.30 ; -0.10]	2.96	-0.17**	[-0.29 ; -0.05]	3.23	*** ***
	Long working hours	2.90 -0.17**	[-0.29 ; -0.05]	3.25	-0.05	[-0.15 ; 0.06]	2.92	-0.10*	[-0.21 ; 0.00]	3.52	***	*
	Low predictability	3.30 -0.12*	[-0.24 ; -0.01]	3.41	-0.13*	[-0.23 ; -0.03]	3.27	-0.19**	[-0.31 ; -0.07]	3.46	*	**
	Night work	3.81 0.19***	[0.11 ; 0.28]	3.70	0.14**	[0.05 ; 0.23]	3.39	-0.02	[-0.13 ; 0.09]	3.39	*** ***
	Shift work	3.93 0.33***	[0.25 ; 0.42]	3.68	0.22***	[0.12 ; 0.32]	3.39	0.18**	[0.05 ; 0.31]	3.30	*** ***
	Emotional demands	2.59 -0.30***	[-0.43 ; -0.16]	2.78	-0.13*	[-0.25 ; -0.02]	2.69	-0.23**	[-0.37 ; -0.09]	3.31	*** ***
	Role conflict	3.36 -0.11*	[-0.21 ; -0.01]	3.27	-0.08	[-0.16 ; 0.01]	3.36	-0.15**	[-0.25 ; -0.05]	3.41	*	*
	Tensions with the public	3.28 -0.16**	[-0.26 ; -0.06]	3.39	-0.18***	[-0.26 ; -0.10]	3.27	-0.18***	[-0.27 ; -0.09]	3.70	*** ***
	Job insecurity	3.67 0.08*	[0.01 ; 0.16]	3.65	0.02	[-0.05 ; 0.10]	3.73	-0.08	[-0.18 ; 0.03]	3.57	**	*
	Work-life imbalance	3.26 -0.26***	[-0.37 ; -0.15]	3.43	-0.15**	[-0.25 ; -0.06]	3.35	-0.12*	[-0.23 ; -0.01]	3.62	*** ***
	Women
	Low decision latitude	7.02 0.38**	[0.09 ; 0.67]	6.97	0.17	[-0.10 ; 0.45]	6.79	0.14	[-0.13 ; 0.41]	6.10	*** **
	Psychological demands	7.93 -1.06***	[-1.59 ; -0.53]	8.32	-0.94***	[-1.43 ; -0.46]	9.38	-0.55*	[-1.02 ; -0.09]	9.16	*** ***
	Overcommitment	2.47 -0.34***	[-0.54 ; -0.15]	2.68	-0.24*	[-0.42 ; -0.05]	3.10	-0.15	[-0.33 ; 0.02]	3.14	*** **
	Long working hours	3.25 -0.24***	[-0.38 ; -0.11]	3.61	-0.19***	[-0.30 ; -0.09]	3.70	-0.08	[-0.17 ; 0.01]	3.78	*** ***
	Shift work	3.96 0.31***	[0.15 ; 0.48]	3.55	0.22*	[0.04 ; 0.40]	3.61	0.15	[-0.03 ; 0.33]	3.13	*** ***
	Emotional demands	2.30 -0.32**	[-0.54 ; -0.11]	2.36	-0.35***	[-0.56 ; -0.15]	2.59	-0.27**	[-0.46 ; -0.08]	3.05	*** **
	Tensions with the public	3.30 -0.29***	[-0.41 ; -0.16]	3.17	-0.30***	[-0.42 ; -0.18]	3.43	-0.23***	[-0.34 ; -0.13]	3.80	*** ***
	Work-life imbalance	3.23 -0.23*	[-0.41 ; -0.05]	3.40	-0.08	[-0.23 ; 0.08]	3.59	0.00	[-0.15 ; 0.14]	3.59	*** **

a

Table 5 Differential changes according to public/private sector in 2006: results from linear regression models adjusted for age in 2006 and score of factor in 2006

 5

			Public		Private (ref.)	p c	p d
		Mean score 2006 a	Beta b	95% CI	Mean score 2006 a
	Men
	Low decision latitude	6.76	-0.28***	[-0.43 ; -0.12]	6.77	ns	***
	Low social support	3.66	-0.10**	[-0.18 ; -0.03]	3.68	ns	**
	Long working hours	3.48	0.16***	[0.08 ; 0.24]	3.14	***	***
	Low predictability	3.47	0.12**	[0.03 ; 0.21]	3.35	*	**
	Role conflict	3.21	-0.26***	[-0.34 ; -0.17]	3.38	***	***
	Tensions with the public	3.22	-0.20***	[-0.28 ; -0.11]	3.50	***	***
	Job insecurity	3.87	0.16***	[0.10 ; 0.21]	3.59	***	***
	Women
	Low decision latitude	6.80	-0.13*	[-0.25 ; -0.01]	6.80	ns	*
	Psychological demands	8.75	-0.50***	[-0.71 ; -0.29]	8.98	ns	***
	Low reward	2.86	-0.13**	[-0.22 ; -0.05]	2.95	ns	**
	Overcommitment	2.83	-0.16***	[-0.24 ; -0.07]	2.96	**	***
	Emotional demands	2.43	-0.14**	[-0.24 ; -0.05]	2.59	**	**
	Role conflict	3.19	-0.14***	[-0.21 ; -0.06]	3.40	***	***
	Ethical conflict	3.57	-0.08**	[-0.14 ; -0.02]	3.64	*	**
	Tensions with the public	3.22	-0.19***	[-0.26 ; -0.12]	3.45	***	***
	Job insecurity	3.83	0.16***	[0.11 ; 0.21]	3.60	***	***
	a Mean

Acknowledgements

The authors thank Nicolas de Riccardis and the work group of the DREES and DARES for their help and advice with the SIP dataset.

Funding

French Ministry of Labour (DARES, Grant No 2200727156) and Université de Versailles Saint-Quentin (Lucile Malard's PhD thesis).

Conflict of interest

The authors declare that they have no conflict of interest.


E Wandersman
email: elie.wandersman@upmc.fr

Y Chushkin
email: chushkin@esrf.fr

E Dubois

V Dupuis

A Robert

R Perzynski

Field induced anisotropic cooperativity in a magnetic colloidal glass

The translational dynamics in a repulsive colloidal glass-former is probed by time-resolved Xray Photon Correlation Spectroscopy. In this dense dispersion of charge-stabilized and magnetic nanoparticles, the interaction potential can be tuned, from quasi-isotropic to anisotropic by applying an external magnetic field. Structural and dynamical anisotropies are reported on interparticle lengthscales associated with highly anisotropic cooperativity, almost two orders of magnitude larger in the field direction than in the perpendicular direction and in zero field.

In many classes of disordered systems, the transition from the fluid state to the solid state remains puzzling : when decreasing the temperature, or increasing the density, the dynamics slows down by several orders of magnitude, whereas static structural properties are weakly affected. This abrupt slowing-down, referred to as the glass transition, is observed in numerous disordered systems [1,2], from frustrated magnets, to molecular glasses, colloidal glasses and granular systems. It is widely accepted that the divergence of the relaxation time is accompanied by a growing length scale resulting in dynamical heterogeneities [3][4][5][6]. The structural relaxations occur through cooperative rearrangements of clusters of mobile particles. The size of these dynamically correlated clusters can be evaluated, through the computation of dynamical susceptibilities [5,7], χ 4 ∝ N ( F 2 (t) -F (t)

2 ), with N the number of dynamically correlated particles and F , a time-dependent correlator, for example the intermediate scattering function [7]. For hard-sphere systems, the Mode Coupling Theory (MCT) predicts scaling laws [5,6], both for the divergence of the relaxation time and the dynamical susceptibility.

Several recent experimental works have therefore been dedicated to the extraction of the size of dynamically heterogeneous regions : in molecular and magnetic systems, the measurement of the dynamical susceptibility is delicate and requires an indirect evaluation through nonlinear response measurements [8][9][10][11]. An increase of χ 4 is observed as temperature is lowered. In colloidal systems, experiments using confocal microscopy [4,12] or scattering techniques [13,14] provide an easier access to space and time resolved dynamics, and thus to χ 4 . In [6] the growth of the dynamical susceptibility with the packing fraction Φ in colloidal hard sphere glasses is observed. χ 4 diverges at Φ ≈ 64%, but MCT predictions do not fit the data over the whole Φ range. However, fine variations and determinations of Φ are difficult to perform experi-mentally in concentrated samples and require many independent experiments. In addition, the relevance of such an averaged macroscopic quantity to characterize the nature of local structural relaxations is questionable [15]. An external parameter allowing to perturbate the local structure at constant Φ while measuring its dynamical consequences would be of great interest experimentally. Precisely to unravel the relationship between the local structure, local dynamics and mechanical properties, micro-rheological experiments and simulations have recently been performed [16][17][18]. In [18] the authors consider a single particle driven by a constant force in a glassforming system. They show that beyond the linear response regime, an anomalous -superdiffusive -dynamics takes place in the parallel direction to the force, while it remains diffusive in the perpendicular direction. Interestingly, this superdiffusive anisotropic dynamics is associated with wide tails in the distribution of displacements. These features are in agreement with biased trap models [19] that consider the dynamics of a particle in an anisotropic free energy landscape. Experimental measurements of the dynamical susceptibility would help to understand this anomalous dynamics in biased energy landscapes or in driven systems.

In this Letter, we report experiments on a colloidal glass based on magnetic nanoparticles and we study the effect of an external magnetic field on both structural and dynamical properties. We show that if structural anisotropy is weak under field, the dynamics is accelerated and strongly anisotropic : in the direction parallel to the field, we observe giant dynamical susceptibilities associated with shorter relaxation times. We discuss these effects considering the fluctuations induced by local magnetization inhomogeneities along the field direction as an external source of energy.

The investigated system is a repulsive colloidal glass consisting of charged nanoparticles (NP) of maghemite γ -F e 2 O 3 (diameter d ≈10 nm) dispersed in water. The interparticle repulsion due to the surface charge of these particles dominates and can be tuned with the ionic strength. The glassy sample is prepared from a fluid sample using an osmotic stress technique [20]. This allows to set the ionic strength and to increase Φ slowly enough to control the state of interaction of the system [21]. Each NP is also a nanomagnet with a magnetic moment µ ∼ 10 4 µ B . In absence of magnetic field H, the magnetic moments of the NPs are randomly oriented. The magnetic dipolar interaction contribution, attractive on average, remains small (U dd ∼ 0.7 k B T ) with respect to the electrostatic repulsion (U elec ∼ 10 k B T ). The interaction potential is dominated by electrostatic repulsion [22] and in good approximation isotropic. We report here on systems in similar conditions to those of [23] which display slow dynamics and aging above Φ = 25%.

The translational dynamics is probed using X-ray Photon Correlation Spectroscopy (XPCS) at the ID10C beamline of the ESRF (Grenoble, France). The energy of the partially coherent incident beam (40 × 40 µm 2 ) is set to 7.03 keV to minimize sample X-ray absorption. The coherently scattered X-rays form speckle patterns on a Charge Coupled Device (CCD) detector (Princeton Instrument), located 3.3 m from the sample. In this configuration, the range of accessible wavevectors (0.02 < Q < 0.05 Å-1 ) covers the interparticle lengthscales. Depending on the signal, a speckle pattern is collected every 8 to 15 s to get sufficient statistics. A more precise measure of the static structure (with complementary Small Angle X-ray Scattering, SAXS) is performed at the ID02 beamline of the ESRF at 12 keV. Both experiments are performed with and without an applied field. A thin sample layer (∼ 100 µm) is deposited on the wall of a quartz capillary, previously filled with dodecane to avoid water evaporation during the experiment. The sample age t w is initiated as soon as the capillary is placed in measuring conditions and no more subjected to any external mechanical stress. To apply the external permanent magnetic field H (320 kA/m corresponding to 90% of dipole alignment), a set of magnets is added to the setup, perpendicularly to the beam direction, in the horizontal plane. They are removed for H=0 experiments, to suppress any residual field. Note that the colloidal dispersion remains monophasic in presence of a H field [20]. Last, under-field the scattering pattern is anisotropic. The intensity is thus analyzed over angular sectors of 20˚both along or perpendicularly to the field direction.

We investigated the dynamics of a sample with a volume fraction Φ = 30%. It is a freshly prepared glassformer [24] chosen for its slow dynamics, lying in the accessible time window of XPCS. We do not observe any noticeable evolution of its static structure on this time window. The structure factor S(Q) without field (Fig. 1) determined by SAXS is characteristic of repulsive inter-actions, with a low compressibility of 0.04 and a mean distance of ∼ 12 nm between the NPs. Each NP can be seen as an effective sphere of diameter d + 2κ -1 ≈ 12.5 nm, where d is the solid diameter of the NP and κ -1 ≈ 1.2 nm, the effective screening length of the potential. This latter is evaluated by adjusting the Φ-dependence of the compressibility, using the Carnahan-Starling formalism [25]. For the studied sample at Φ = 30%, the mean interparticle distance is comparable to the size of the effective spheres. They are sligthly interpenetrated, giving rise to the glassy behavior of the sample.

When applying a magnetic field (H=320 kA/m), the magnetic dipoles align along H. Since interparticle repulsion is dominant, the solid bodies of the NPs remain well apart from each other and there is no signs of selfassembled anisotropic structures. However the interaction potential becomes slightly anisotropic, inducing a slightly anisotropic structure illustrated here by the anisotropy of the scattered intensity and S(Q) (Fig. 1). The largest anisotropy, observed on the scale of the interparticle distance, i.e. on the peak of S(Q), is quantified by its maximum S max and similar to the behavior in ferrofluids in the fluid state. S max increases in the perpendicular direction, due to the increase of interparticle repulsion under magnetic dipolar interaction. S max decreases in the parallel direction due to the effect of dipolar interaction combined with NPs fluctuations along the field direction around their most probable position [20,26]. Only a small shift of its position Q max occurs while, on larger scales, the compressibility remains almost isotropic.

We already have investigated the anisotropy of the local structure over the whole Φ range in a recent paper [25], showing that the NPs are trapped in an anisotropic cage formed by their first neighbors. The structural anisotropy is interpreted by a model of magnetostriction, lying on the under-field deformation of anisotropic cages formed by neighboring NPs. This model relies on the elastic deformation of the cage at constant volume under the applied field and catches the Q max and S max anisotropies. It provides a measure of the elastic modulus of the magnetic fluid. In this model the anisotropy of the cage writes [25] :

α = d ⊥ -d // d 0 = 9 4π µ 0 M 2 M F (H)σ 2 H k B T (1)
where d ⊥ (resp. d // ) is the dimension of the cage in the perpendicular (resp. parallel) direction of the field, d 0 its dimension in absence of field, M M F (H) the magnetization of the magnetic fluid and σ 2 H the mean squared displacement of the NP (assumed isotropic in the model). The anisotropy of the cage is found to be moderate α ≈ 8% [25] but means that the interpenetration of the effective spheres under an H field is slightly anisotropic. This anisotropic interpenetration could carry dynamical consequences. Interestingly, the widening of S(Q) in the parallel direction suggest σ 2

H to be anisotropic with σ ⊥ < σ . Only XPCS dynamical study can shed some light on this question.

From the XPCS measurements we compute the degree of temporal correlation between two speckle patterns, separated by a lag-time τ , at a time t [13,27] :

c I (Q, τ, t) = I p (Q, t)I p (Q, t + τ ) Q I p (Q, t) Q I p (Q, t + τ ) Q -1 (2)
where I p (Q, t) is the scattered intensity at pixel p and time t, . . . Q denotes an ensemble average over pixels in a ring of iso-wavevectors Q (for isotropic patterns). Under field, the scattered intensity is anisotropic, thus the average in Eq.( 2) is restricted to the same angular sectors as for S(q) along and perpendicular to the field direction. We also observe that for zero field (i.e. isotropic case) this average on a reduced azimutal area does not influence the obtained results. The time average of c I provides the usual intensity autocorrelation function :

g (2) (Q, τ, t w ) = c I (Q, t, τ ) tw + 1 (3)
where the brackets . . . tw denote a time average (over 200 frames) centered on age t w [28]. In addition, we compute the temporal variance of c I , normalized as described in [21,29]. It is related to the dynamical susceptibility χ 4 , the volume integral of a 4-point correlator [3,5,9,29]. This dynamical susceptibility, hereafter referred to as χ(τ ) is calculated at all accessible Q's and provides information on the heterogeneous nature of the dynamics.

The intensity autocorrelation functions at Q=0.048 Å-1 and t w =5622 ±375 s, are plotted in Fig. 2 with and without applied field. The observed decay of g (2) is faster when a field is applied, this effect being stronger along the field direction and associated to a smaller nonergodicity factor (defined here as g (2) at short times τ ). Figure 2. Intensity autocorrelation function g (2) (Q, τ, tW ) as a function of τ for Q=0.048 Å-1 and tw=5622 s. Solid lines are compressed exponential fits, g (2) -1 ∝ exp -2 (Γt) β , with β > 1. Inset : Q-dependence of Γ, at tw=5622 s. Full lines are linear fits at low Q's, for H=0 and in the parallel direction. For the perpendicular direction, the full line is a power law fit Γ = 0.025 Q 0.66 .

These features are observed on all probed Q's and t w 's. The g (2) 's can be modelled by compressed exponentials [23] and the inverse characteristic time Γ = τ -1 c increases linearly with Q for H=0, as observed on many glassy systems [29]. In presence of a H field this ballistic-like behavior is only observed in the perpendicular direction (see inset of Fig. 2). In the parallel direction, we observe a non linear Γ(Q) relationship, better noticeable at high Q's. This behavior is reminiscent of de Gennes' narrowing, occuring at lengthscales close the structure factor peak [30]. This non linearity is also comparable to the superballistic behavior evidenced in [31] with Γ ∼ Q 2/3 (inset of Fig. 2). However, given the limited Q range of our XPCS experiment we cannot properly conclude on the origin of this non linearity. Interestingly however, such an anomalous dynamics in the direction of the field is reported in theoretical works that consider the anisotropic dynamics of a single particle either driven by a constant force in a glass-forming system [18] or evolving in a biased potential energy landscape [19]. For moderate values of the driving force, the dynamics in the parallel direction to the force is superdiffusive -whereas it remains diffusive in the perpendicular direction -and this behavior is associated to a wide-tail distribution of displacements. In our system, the application of a H field tends to reduce the energy barriers in the direction of the field, due to dipolar interactions. This biased and anisotropic energy landscape could thus be at the origin of such an anomalous τ (Q) relationship in the parallel direction. If so, one would expect large temporal fluctuations of the dynamics in the parallel direction and thus a possible signature of it in the dynamical susceptibilities.

The dynamical susceptibility χ(τ ) without and with magnetic field is plotted in Fig. 3 for Q=0.048 Å-1 . When a dynamical cluster of NPs relaxes in the sample, it induces a drop of the correlator c I . χ(τ ) is then maximum on the timescale of these relaxation processes and its maximum χ * is a measure of the degree of cooperativity of the dynamics [21,29]. Therefore the peak position corresponds to the characteristic time τ c of g (2) and reproduces the anisotropy seen in Figure 2. The χ * values are also highly anisotropic being almost two orders of magnitude larger in the parallel direction than in perpendicular one. Assuming that χ * is proportionnal to the cube the size of the dynamic clusters [29], it gives dynamically correlated clusters elongated along the field with an anisotropy ratio of the order of 4 to 5.

The Q-dependence of χ * is presented in the inset of figure 3. When H = 0, χ * is nearly constant with Q, in agreement with previous results of [21]. Under field, χ * in the perpendicular direction is even smaller than for H = 0, and characterizing its Q-dependence is difficult. In the parallel direction χ * grows linearly with Q, providing evidence that the cooperative process takes place on local length-scales. The faster dynamics in the parallel direction appears to be driven by cooperative events taking place at short time/lengthscales.

The application of a magnetic field on this repulsive and magnetic colloidal glass has both structural and dynamical consequences. We can first interpret the field effect as a simple geometrical perturbation of the zero field situation. Since the magnetic dipolar interactions reduce the repulsion between particles in the direction of the field, the system can still be considered as effective spheres -soft and interpenetrated -but trapped in anisotropic cages and coupled to both an external magnetic field and to a thermal bath. There is a growing interest to consider the dynamics of anisotropic systems, such as hard ellipsoids [32] or dumbbells [33]. For instance, Zheng et al. measure the dynamics of concentrated hard ellipsoids dispersions [32]. They show that at a given Φ, the cooperative nature of the translational dynamics is anisotropic. However, the situation we consider here is different in essence, since the anisotropy of the interaction is due to a global coupling to the H field rather than set by a local anisotropic range of interaction as for hard ellipsoids. The coupling to the field modulates the local fluctuations of position of the NPs. These fluctuations are anisotropic, being larger along the field direction and are hindered by the cages inside which the NPs are confined. They are then the "motors" of coherent fluctuations of adjacent cages in the direction of the field, increasing the cooperativity and decreasing the non-ergodicity factor on the scale of a few interparticle distances.

Consequently, we can deduce that in presence of the field, the complex energetic landscape in which the system evolves is anisotropic. Due to the reduced repulsion along the field direction, the time scale of barrier-crossing Figure 3. Dynamical susceptibilities χ(τ ) at Q = 0.048 Å-1 , at 0 and 320 kA/m, parallel or perpendicular to the field direction. Inset : maximum of χ(τ ) as a function of Q is lower and the relaxation is faster. In qualitative agreement with [18,19] we report an anomalous dynamics τ (Q) in the parallel direction to the field, together with highly cooperative dynamics, due to the field-driven fluctuations of position of the NPs. This enhanced cooperativity in the direction of reduced repulsion can be compared to simulations of hard spheres where the interaction potential is tuned [34,35]. By computing numericallly χ 4 in (isotropic) colloidal hard sphere glasses and gels, Coniglio et al. show that in glasses χ 4 is peaked in time, traducing the transcient nature of cooperative process, whereas in gels χ 4 reaches a plateau, traducing the persistent presence of relaxing clusters containing a large number of particles. In our case, in the parallel direction to H, the system is not made of permanent structures at contact, the rearrangements of which lead to a giant cooperativity on long timescales. On the contrary, χ(τ ) we report on seems to plateau at short times, the dynamical fluctuations being driven by short timescales field induced fluctuations. In the perpendicular direction, the dynamics is slower and less cooperative. This is in contradiction with the picture of growing cooperative domains, which usually explains the slowing down of the dynamics in glasses. However, the reduced particle displacements in very dense suspensions tends to decrease χ * despite of the growing size of the cooperative clusters [29]. It leads to a nonmonotonic Φ-dependence of χ * , with a maximum at a volume fraction Φ c and a decay for higher Φ's. A similar scenario could take place here, supported by the observed reduced mean squared displacements in the perpendicular direction σ ⊥ < σ 0 < σ [25], along with the widening of S(Q) around Q max in the parallel direction.

In conclusion, using XPCS experiments, we have pro-bed the translational dynamics of a repulsive colloidal glass made of magnetic nanoparticles. Under the application of a H field the dynamics of the system is faster than in zero field. The dynamics is anisotropic, being faster along the field than in the perpendicular direction. In the parallel direction an anomalous dynamics τ (Q) is observed, associated to a huge increase of the dynamical susceptibility, in qualitative agreement with biased trap models [19] and recent numerical simulations [18]. All these features are qualitatively recovered at any ages of the sample. The field intensity could thus be used as a way to tune the dynamical cooperativity, and thus to study its eventual divergence in the parallel direction. This system, which catches the general features of the glass transition, have through the magnetic field a powerful control parameter. Conjugating experiments on glassy samples at various Φ probed at various H is a promising route to understand how the dynamical heterogeneities vary at the approach of the glass transition.

We acknowledge P. Panine for his support on ID02 beamline in ESRF for SAXS measurements and Fédération F21 UPMC-Paris 6 for financial support.

Figure 1 .

 1 Figure 1. Static structure factor S(Q) obtained by SAXS, for H=0 (circles) and H=320 kA/m (triangles). Inset : speckle pattern of a quadrant of the scattered intensity for H=320 kA/m. The direction of H is indicated by the arrow.