Joanna J Sienkiewicz
email: jsienkiewicz@uni-bielefeld.de

Ingrid Tucci

Karolina Barglowski

Thomas Faist

Contrast Groups Based on Spatial Mobility and Social Position for Use in the Qualitative Sample

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

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Abstract This paper provides detailed information about qualitative sampling for the "Transnational Mobility and Social Positions in the European Union" project. The sampling strategy is based on the SOEP-IAB Migration Sample survey. It is part of a sequential research design that uses various quantitative and qualitative methods to study the effect of spatial mobility on social positions and the role of social comparisons in determining how cross-nationally mobile people perceive their social positions. We describe how the quantitative part of the survey was used to create contrast groups that show different intersections of spatial mobility and social position as measured by the Erikson-Goldthorpe-Portocarero (EGP) scheme. In addition, we provide an overview of the main characteristics of these contrast groups. The section on outlook outlines further steps in this project and discusses the strategies used and the challenges faced in this mixed-methods research project.

Project Description: Transnational Mobility and Social Positions in the European Union

Movement across borders is considered to be crucial for an increase in life chances. During the past decade, studies of mobile populations" life chances within the European Union (EU), a space that offers freedom of movement for citizens of its member states, have become a vital field of research. Scholars frequently point out that not all migrants benefit equally from these increased mobility opportunities; instead, differences in life chances proceed along heterogeneities, among which the most important are legal status, gender, ethnicity and class. However, we know little about how mobility patterns and other heterogeneities influence people"s objective and subjective social positions within the transnational social space of the EU. Unexplored are the social mechanisms that underlie how and under what terms migrants who rely on more than one national frame of reference would evaluate their social position according to their spatial mobility trajectory and other heterogeneities.

In the "Transnational Mobility and Social Positions in the European Union" project, funded by the German Research Foundation (DFG), we address these crucial links by pursuing three main objectives:

4

(1) To analyse the spatial mobility trajectories of migrants characterized by multiple heterogeneities;

(2) To link spatial mobility trajectories to social positions, according to the Erikson-Goldthorpe-Portocarero (EGP) scheme, taking into account the perceptions of and evaluations by mobile persons themselves; and

(3) To examine how the mechanisms of social comparison shape people"s subjective evaluation of their social positions.

In this project we are investigating the role played by social comparison (i.e. the comparisons individuals make with reference groups) for evaluating social position and, to a greater extent, social inequality. All these issues are explored by means of a sequential, mixedmethods research design. Data from the SOEP-IAB Migration Sample, a panel survey conducted among migrants and descendants of migrants, are analysed to determine and evaluate typical mobility trajectories and to study the social position of mobile people according to these trajectories and other relevant heterogeneities. Complementary qualitative interviews will be conducted with selected SOEP respondents who have experienced mobility. These interviews will allow us to reveal the interpretations and meanings that individuals attach to spatial mobility and their social position over time. The overall objective of the project is to explore the role of social comparisons as the main social mechanism involved in the nexus of spatial mobility and social positions. The results of the project are expected to help explain how the experience of spatial mobility and the subjective and objective perceptions of social positions interact in social spaces that cross national borders.

Measuring Spatial Mobility Trajectories and Social Positions

In order to analyse the diverse trajectories of mobility in relation to individuals" social positions, as well as the way in which mobile persons interpret these positions, we chose a research design that allows the reconstruction of both "objective" and "subjective" social positions of mobile persons. By "objective" social positions we mean a measurement that indicates someone"s social position within a certain social hierarchy. In particular, we use the standardized indicator developed by Erikson, Goldthorpe and Portocarero (the EGP scheme) [START_REF] Erikson | Intergenerational class mobility in three Western European societies: England, France and Sweden[END_REF] to describe the "objective" dimensions of social positionsthat is, dimensions based on theoretically derived categories of analysis according to internationally recognized measurement criteria for social positions. The "subjective" dimension of social positions relates to evaluations and interpretations derived from the respondents themselves. Both types of dimensions are elements of the concept of social position that we would like to use. By convention, social hierarchies are embedded in national social stratification systems. Thus, migrants have experienced at least two national stratification systems, and this dual experience may also influence their personal assessments of their position as they compare the two systems.

In this paper, we focus on the objective social positions measured by the EGP scheme, with "social position" meaning a concept that includes both social class and social status. Our understanding of social class and social status refers to Weberian thinking by which class and status can be understood as different dimensions of social structure. Class refers to property, commercial and social classes [START_REF] Weber | Economy and society: An outline of interpretive sociology[END_REF][START_REF] Weber | Economy and society: An outline of interpretive sociology[END_REF]), which typically allows for within-class social mobility [START_REF] Swedberg | The Max Weber dictionary: Key words and central concepts[END_REF]. Social status refers to "a quality of social honor or a lack of it, and is in the main conditioned as well as expressed through a specific style of life" [START_REF] Weber | The religion of India: The sociology of Hinduism and Buddhism[END_REF][START_REF] Weber | The religion of India: The sociology of Hinduism and Buddhism[END_REF], p. 39). Although the description of social status typically relates to consumption, the concept of social class, by contrast, emphasizes production [START_REF] Weber | Economy and society: An outline of interpretive sociology[END_REF][START_REF] Weber | Economy and society: An outline of interpretive sociology[END_REF]).

The overlap of both concepts also becomes evident in social indicator research and the wellestablished measurement of social positions. The EGP scheme measures social class, whereas the International Socio-Economic Index of Occupational Status (ISEI) (see [START_REF] Ganzeboom | A standard international socioeconomic index of occupational status[END_REF], for example, measures occupational social status. In any case, both measures are based on the International Labour Organisation"s International Standard Classification of Occupations (ISCO) (see [START_REF] Elias | Occupational classification (ISCO-88): Concepts, methods, reliability, validity and cross-national comparability[END_REF] for occupational groups, although they are operationalized in different ways.

Our previous research indicated that comparisons made by mobile persons often take on a cross-border dimension, because people compare themselves with others (abroad) who are relevant to them in certain aspects (see [START_REF] Faist | Transnational social protection: Migrants" strategies and patterns of inequalities[END_REF]. In transnational social spaces, people may develop and use multiple frames of comparison. Also, heterogeneities, such as legal status, gender, ethnicity or social class, may play a crucial role in shaping migrants" perceptions of their social positions and in making comparisons.

Exploratory findings indicate that the migration experience and transnational comparisons are important for some migrants from Turkey in Germany, such as those who view the emotional experience (e.g. the extent of social support, respect and recognition) as being better in Turkey [START_REF] Sienkiewicz | Social comparisons in migration and inequality studies: A literature review and evidence from a pilot study[END_REF]. Research has also revealed that migrants create "transnational spaces of comparison" [START_REF] Sienkiewicz | The Kazakh-German social space: Decreasing transnational ties and symbolic social protection[END_REF]) in which, for example, informal social protection is evaluated and distributed differently in the national context, meaning that the receiver of protection in the national context may be the provider of protection in transnational contexts. Until now, however, these different realms of comparison have not been studied systemically.

To arrive at a multifaceted picture of social positions, we used a sequential, nested, mixedmethods design (see [START_REF] Creswell | Designing and conducting mixed methods research[END_REF][START_REF] Small | How to conduct a mixed methods study: Recent trends in a rapidly growing literature[END_REF]. The project combines multiple research methods involving quantitative and qualitative approaches [START_REF] Kuckartz | Mixed Methods: Methodologie, Forschungsdesigns und Analyseverfahren[END_REF].

First, the data obtained from the IAB-SOEP Migration Sample (see [START_REF] Brücker | The new IAB-SOEP Migration Sample: An introduction into the methodology and the contents[END_REF] were analysed in order to construct contrast groups of mobile persons. In this paper, we document this first step in our research design. In a subsequent step, these contrast groups will be used for the qualitative sampling.

To identify the trajectories of spatial mobility and the other heterogeneities involved, we used data derived from the IAB-SOEP Migration Sample (2015), a new subsample of the general Socio-Economic Panel (SOEP), which was begun in 1984. The migration sample survey was conducted for the first time in 2013 and included about 5,000 respondents living in 2,700 households in Germany. A supplementary sample was drawn in 2015. As part of the overall SOEP survey, the IAB-SOEP Migration Sample survey contains general information about the life circumstances of the respondents and members of their households. Unlike the other subsamples in the SOEP, the migration sample is unique in that it includes information on the migration biographies of respondents born outside Germany and detailed information about the condition of their arrival in different countries for at least three months before their last immigration to Germany. We used the latest sample wave ( 2015) and added available biographical information for all participants, some of whom were interviewed for the first time in 2013 and 2014.

Overall, 540 respondents (about 13%) have had multiple experiences of mobility, or "staying abroad", either within or outside the EU. Using the information on migration and employment biographies available from the surveys (2013)(2014)(2015), we were able to identify diverse trajectories of spatial mobility and link them with respondents" objective social position using the EGP scheme. For the qualitative sampling, we decided to use the EGP scheme because it is known for its high degree of international comparability and fits our goal of studying migrants" social position, which is shaped by social status and class in different national stratification systems.

Social Position and Mobility Experience as Determinants in Constructing Contrast Groups

For the qualitative sample, having fewer subgroups is desirable. The data can be split into three groups of social position (upper service, lower service and manual worker) and two spatial mobility groups (single and multiple mobility experiences). To be parsimonious while ensuring appropriate variety, we chose a 2 × 3 scheme for the contrast groups to achieve the best matches. One could say that at this stage we simplified the process by basing the qualitative sampling strategy on three "coarse-grained" status groups in order to study the more "fine-grained" perceptions of social position in the qualitative part of the research project.

The EGP Scheme with Three Categories

A broad theoretical literature that goes back to the roots of sociology (Marx) and sociological classics (e.g. Bourdieu) addresses the question of how to study social class. Much research was conducted using quantifiable approaches to systemize people into different classes.

During the development of this research strand, the most popular measurements for objective social positions (social status and social class respectively) became the ISCO-88 classification for occupational groups [START_REF] Elias | Occupational classification (ISCO-88): Concepts, methods, reliability, validity and cross-national comparability[END_REF], the ISEI-Status 88 [START_REF] Ganzeboom | A standard international socioeconomic index of occupational status[END_REF]),

Treiman"s Standard International Occupation Prestige Scale [START_REF] Treiman | Occupational prestige in comparative perspective[END_REF] and the Erikson-Goldthorpe class category [START_REF] Erikson | Intergenerational class mobility in three Western European societies: England, France and Sweden[END_REF]. Some measurements also include prestige measurements, such as Duncan"s Socioeconomic Index (SEI) [START_REF] Duncan | A socioeconomic index for all occupations[END_REF] or the Hauser-Warren index [START_REF] Hauser | Socioeconomic indexes for occupations: A review, update, and critique[END_REF].

Many of these widely known measurements are included in the SOEP Migration Sample.

The EGP class scheme allows differentiation according to the regulation of employment relationships [START_REF] Schunck | Unfair pay and health: The effects of perceived injustice of earnings on physical health[END_REF]. As Gayle and colleagues note: Individuals within a social class are considered to share similar "market situation" (e.g. levels of income, economic security and chances for economic advancement) and "work situation" (e.g. authority and control) […]. Accordingly, those individuals within a social class are thought to hold similar life chances and often lifestyles (Gayle, Connelly, & Lambert, 2015, p. 5).

This quote shows that the class measurements by Goldthorpe and colleagues include, in a Weberian sense, not only social class ("market" and "work situation") but also social status ("life chances" and "lifestyles"). Understood in this way, the measurement serves to capture social positions, and several publications emphasize not only its reliability in predicting individuals" social positions but also its parsimony [START_REF] Parkin | Class inequality and political order: Social stratification in capitalist and communist societies[END_REF][START_REF] Rose | The NS-SEC explained[END_REF]. EGP as an occupation-based socio-economic measure is more stable for describing people"s social class than for describing their earning profiles [START_REF] Goldthorpe | The economic basis of social class[END_REF][START_REF] Rose | The NS-SEC explained[END_REF]. According to a literature review, the EGP is commonly used as a measure of Occupation-based measures can also be used to represent households rather than individuals, because not every household member is employed. In addition, to ascribe an objective social position to household members who are doing domestic work, for example, and are not officially employed, the stratification research offers "individual", "dominance" and "conventional" approaches for social classification (e.g. [START_REF] Erikson | Social class of men, women and families[END_REF]. While the individual approach looks at the current or last occupation, the dominance approach looks at all occupations in the household and for the most part characterizes the household based on the dominant occupational status, which contributes most in monetary terms and in terms of time. The conventional approach uses the head of the household as the main reference for its assessment (see [START_REF] Gayle | A review of occupation-based social classifications for social research[END_REF]. In our case, we will use the individual approach, because the emphasis in analysing the qualitative interviews will be on individuals and their personal social comparisons.

The EGP scheme is based on the ISCO codes and covers eleven groups that represent social class. (For more details about operationalization in the SOEP data, see SOEP, 2012.) In addition, the EGP groups can be combined into more general groups. [START_REF] Erikson | The constant flux: A study of class mobility in industrial societies[END_REF] mention the possibility of applying their scheme in a similar way for seven-, five-and three-class versions. Owing to our research design and limitations in the data, it is appropriate to have a few groups representing big (macro-)groups of social positions. We are not interested in micro-classes or in the general debate about how to construct a good quantitative measurement of social class that serves international comparisons (like [START_REF] Grusky | Are there big social classes?[END_REF][START_REF] Grusky | Does the sociological approach to studying social mobility have a future[END_REF]. Because one of our aims is to connect the concept of transnational social comparison to the academic discussion about (perceived) social position in the nexus of spatial and social mobility, a well-established and more general classification obtained with the EGP scheme provides the best fit.

We decided to construct contrast groups with different patterns of social position and potential (trans)national frames of comparisons. It is preferable to define these different groups ex ante, because we assumed that the social comparisons made would be influenced by different social positions and experiences of mobility. This approach to data grouping allowed us to retain much greater control over the sampling frame than would, for example, cluster analysis, the reliability of which is a matter of controversy in the social sciences because it requires careful interpretation and a deep knowledge of the data (see e.g. [START_REF] Hartmann | Methodische und methodologische Probleme der Lebensstilforschung[END_REF].

Table 1 shows the distribution of the EGP scheme for the 2015 SOEP Migration Sample. Our intention was to use this EGP scheme to create three large groups that would represent three different types of social positions. As mentioned earlier in this strand of literature, a social class scheme cannot be seen as necessarily hierarchical, but it often has an ordinal structure [START_REF] Glass | Social mobility in Britain[END_REF]. Erikson and Goldthorpe themselves published a seven-class, a fiveclass and a three-class version of the EGP scheme. The three-class version distinguishes among non-manual workers, farm workers and manual workers. Because our data do not 10 include farm workers, we adopted some ideas from the more extended five-class and sevenclass versions to create the three EGP groups (Table 2). Note. Adapted from the SOEP Migration Sample 2015.

Non-Manual White-Collar Workers Representing the 'Upper Service Position'

The groups "Upper Service" and "Lower Service" (from the from the EGP scheme with elven classes) were defined as upper white-collar service positions and included engineers, university professors, computer professionals, managers, architects, pharmacists, teachers, lawyers, sales managers and so on.

Routine Non-Manual White-Collar Workers Representing the 'Lower Service Position'

Routine non-manual white-collar workers, such as social work associate professionals, bookkeepers, nursing associate professionals, nursery school teachers, stock clerks, shop salespersons and other office staff, were labelled as "Lower Service Positions".

Manual Skilled and Unskilled Blue-Collar Workers Representing the 'Manual Working Position

Migrants working as skilled workers (e.g. cooks, hairdressers, plumbers, painters, structural metal preparers, machine mechanics) and unskilled workers (e.g. waiters, protective service workers, cleaners, machine operators, drivers) were labelled more generally as "Manual Working Position". Agricultural workers were also included in this group.

Self-Employed Workers

Self-employed workers with and without employees are the most heterogeneous group, and it is difficult to assign them to a particular social position. General managers, IT professionals and secondary school teachers were included in this group, as were drivers, care workers and plumbers. One possible way to integrate this group within the three specified positions would be to split them into manual working, upper service and lower service positions according to the Ganzeboom ISEI social status scale. Research has shown that the average score on this scale is 40, with a standard deviation of 14 for an individual sample [START_REF] Gayle | A review of occupation-based social classifications for social research[END_REF]. Based on this value, we ascribed the self-employed workers to the manual working position if their ISEI score was lower than 26, to the lower service position for scores 26 to 54 and to the upper service position for scores 55 and above. This approach made it possible to differentiate this very heterogeneous group more precisely and according to their objective social position.

Mobility Experience

The operationalization of spatial mobility across borders is necessary in order to determine the potential frames of reference migrants" use when evaluating their social position and how it changes over time. One group includes those with a single mobility experience and thus "dual (trans)national frames of reference for comparison". These are people who were born outside Germany and who migrated once in their lifetimeto Germanyand also include descendants of immigrants to Germany who lived for at least three months in another country and returned to Germany. The other group includes those with multiple mobility experiences and thus potentially "multiple (trans)national frames of reference for comparison", as well as people born outside Germany who migrated to Germany but also lived for at least three months in another country (before or after moving to Germany). This definition also covers a relatively small number of people who lived in four or more countries. Potentially, descendants of immigrants born in Germany who lived in at least two other countries could 12 be in this group as well. Table 3 shows the number of cases according to type of mobility experience and includes only those respondents with valid information on the EGP in 2015:1 We expect that those with more mobility experience will use multiple frames of references (national and transnational) to position themselves. This approach opens the discussion for multiple positions in transnational social spaces that can claim two or more national references and ideas about social positions. A systematic exploration of this neglected area of social comparisons research and transnational (class) studies will be needed to understand social inequalities beyond the nation state, as in the case of the EU. In this way, both assigned and perceived social positions can be combined in a transnational perspective. This perspective should supersede the prevailing ethnic lens and methodological nationalism (see [START_REF] Schiller | Beyond the ethnic lens: Locality, globality, and born-again incorporation[END_REF][START_REF] Schiller | Beyond the ethnic lens: Locality, globality, and born-again incorporation[END_REF][START_REF] Wimmer | Methodological nationalism, the social sciences and the study of migration: An essay in historical epistemology[END_REF]Glick Schiller, 2003, respectively), because the main classifying heterogeneities will then be objective social position and spatial mobility pattern. 13 We found a total of 2,709 respondents who had personal mobility experiences and valid EGP information. Overall, the characteristics of the six contrast groups show similarities, but they also reveal differences (see Table 5), to be described next.

Six Contrast Groups

Gender and Age

Out of the 2,709 respondents 1,418 (52.3%) are male and 1,291 (47.7 %) are female. Notably, women are highly overrepresented in the lower service position with single or multiple mobility experience (about 75% of all respondents in this group). Men are similarly overrepresented in the manual working position with multiple mobility experiences and to a lesser extent when they have only a single mobility experience. In the upper service position, the proportion of women is slightly larger than that of men.

The mean age for all respondents is 38.6 years (s = 10.44), with the youngest respondent being 18 and the oldest 74 years of age. Also, the average age of people in the upper and lower service positions is lower than the general average, and people from the manual working position have a higher mean age (about 40 years). 14

Average Education

We used the CASMIN classification to describe the general tendencies and differences in educational level for the different contrast groups. In this case, a value of "1" indicates a low education level ("inadequately completed") and a value of "9" indicates a higher tertiary education. The mean value for all respondents is 5.1 (s = 2.74), which is the level of intermediate vocational training. The average in the upper service position is around 7, which indicates Abitur (comparable to A-levels in the United Kingdom) and is much higher than the averages in the lower service position (5.1/6.3 = intermediate general qualification/full maturity certificates) and in the manual working position (3.9/4.0 = vocational qualification or intermediate general qualification/vocational qualification). One interesting finding is that in all the social position groups, the more mobile respondents tend to have higher educational achievements.

Legal Status and Average Year of Immigration to Germany

The general description of migrants" legal status upon their arrival in Germany shows a majority of third-country nationals (891 cases) and EU citizens (835). There are also a substantial number of resettlers from Eastern Europe (455) and refugees (204). A comparatively small group comprises Germans who were born or lived abroad (39).

Of interest are the missing values for this variable. The majority of the 285 missing values are distributed in the group with multiple mobility experiences (more than 50% of the values are missing for the upper service and the manual working positions). To determine why respondents were not willing to answer this question regarding legal status, it is necessary to systematically study these missing values in greater detail (especially if the respondents consciously chose not to answer), because the reasons for such a pattern would provide some further insight.

The majority of the migrants in the upper service position are EU citizens, followed by other nationalities outside the EU (for those with a single mobility experience). The largest proportion of third-country migrants can be found in the lower service position. There is also a substantial proportion of EU migrants and resettlers within the single-mobility experience group in the lower service position. The manual working position is dominated by third-country migrants, followed by EU migrants and resettlers. The comparatively largest proportion of refugees can be found in the manual working position with a single mobility experience (115).

Although people with one mobility experience tend to have lived in Germany longer (average year of immigration [2002][2003][2004], on average the more mobile ones came later (2006)(2007)(2008)(2009). The data show that employees in the upper service and the manual working positions tend to work more often in full-time positions. The upper service position has a small proportion of respondents who do not work but have worked in Germany at least once during their participation in the SOEP. In the lower service position, we see comparatively low proportions of full-time employment in the single-and multiple-mobility experience groups (43.0% and 37.9% respectively) and strong representation in the group of part-time employment (29.2% and 28.7% respectively). This corresponds to the fact that women are overrepresented in this group, and we know that it is much more likely that women rather than men will be employed part-time, particularly in Germany. The employment arrangements in the manual working position are dominated by full-time employment, with less part-time employment compared with the average.

Employment Status

Outlook

This paper documents the construction of mobility and social-position contrast groups that will serve to elaborate a sampling strategy for the planned qualitative interview phase involving members of these different groups of migrants. In total, we plan to conduct about six interviews with members of all six contrast groups (i.e. a total of about 36 interviews). Respondents will be contacted by means of an invitation letter that offers a small financial incentive to participate. The sampling and recruiting process will be conducted in successive waves, because the wide geographical scope, as well as several logistical obstacles to the collaboration of different institutions, prevents us from contacting all the sampled respondents from the six contrast groups at the same time. The experience of other SOEP-based mixed-methods projects indicates that the response rate is relatively low [START_REF] Legewie | Panel-basierte Mixed-Methods-Studien[END_REF], although the number of respondents who belong to contrast groups with a large number of cases and who are available for a qualitative interview might exceed six, should many respondents agree to participate. In this case, we will adapt our design to accommodate additional interviewees. We plan to begin by sending out invitation letters to a sample of 100 cases in the largest contrast groups and will increase this number if the response rate is lower than expected until we arrive at the required number of interviewees in all contrast groups. As described, our sampling strategy is grounded in theoretical assumptions concerning the classifications of social position groups and aims to achieve gender representation in each group. In addition, we want to understand how people, who are not working outside the home or are registered unemployed position themselves. This is why the initial sample frame of 100 cases in each of the six groups will include similar percentages of women and men and alsoin as much as this is possiblea substantial share (around 20 %) of respondents who are nonworking or registered as unemployed (Table 6). Conducting the interviews will be challenging, because the respondents may reside anywhere in Germany. In order to make this process easier to manage and less costly, we decided to contact migrants in all three contrast groups with a single mobility experience who actually now live in the federal province of North Rhine-Westphalia, which hosts large numbers of migrants and descendants of migrants.

During the interviews, we will also ask our respondents for permission to link their interviews with the data from the SOEP sample (record linkage) in order to match information from the qualitative interviews with the standardized SOEP data. This will allow us to obtain a wide range of information about the whole household setting and potential other dominant earners in the household from the quantitative sample as one factor in addition to many other key social science variables (e.g. gender, age) that may influence the perception of people"s social position. The availability of that information in the SOEP data will make it possible during the qualitative interviews to focus on aspects that are at the core of our research questions but cannot be captured from the survey data.

  social class in social science research involving the SOEP data (Groh-Samberg & Voges, 2014; Lancee & Pardos-Prado, 2013; Schacht, Kristen, & Tucci, 2014).

A

  total of 1,616 (59.7%) respondents are employed full-time, 519 (19.1%) are employed parttime, 93 (3.4%) are receiving vocational training, 270 (10.0%) are employed on a reduced part-time basis (< 25%), 209 (7.7%) are not employed and 2 work in a sheltered workshop for the disabled.

Table 1 . Frequencies of Erikson-Goldthorpe-Portocarero Values (Eleven Groups)

 1 Note. Adapted from the SOEP Migration Sample 2015.

	Total	2,709	100.00

Table 2 . Regrouping of the EGP Values into Three Groups

 2

	EGP (3 Groups)	Freq.	Percent	Cum.
	Upper Service Position	626	23.11	23.11
	Lower Service Position	703	25.95	49.06
	Manual Working Position	1,380	50.94	100.00
	Total	2,709	100.00

Table 3 . Frequencies of Respondents with Single or Multiple Mobility Experiences

 3

	Experience
	of Mobility	Freq.	Percent	Cum.
	Single	2,298	84.83	84.83
	Multiple	411	15.17	100.00
	Total	2,709	100.00
	Note. Adapted from the SOEP Migration Sample 2015.

Table 4 . Cross-Tabulation of Mobility Experience and Three Groups of Social Position (Based on the EGP Classification)

 4

		Experience of
		Mobility
	EGP (3 Groups)	Single	Multiple	Total
	Upper Service Positio	483	143	626
	Lower Service Positio	616	87	703
	Manual Working Positi	1,199	181	1,380
	Total	2,298	411	2,709

Note. Adapted from the SOEP Migration Sample 2015.

Table 5 . Description of the Six Contrast Groups

 5 Adapted from the SOEP Migration Sample 2015.

		Descriptive Analysis	Single Mobility Experi-ence	Multiple Mobility Ex-periences
	Upper Service	Total Cases		483		143
	Position	Gender (m/f)		(258/225) (53.4%/46.6%)		(74/69) (51.8%/48.2%)
		Mean Age		36.6		36.7
		Average Education (Mean of CASMIN 2 )		7.2 (s = 2.40)		7.9 (s = 2.12)
		Legal Status on Arrival
		Resettlers	58	(12.0%)	1	(0.7%)
		Germans (Abroad)	9	(1.9%)	5	(3.5%)
		EU Migrants	193	(40.0%)	39	(27.3%)
		Refugees	18	(3.7%)	2	(1.4%)
		Other Foreigners	176	(36.4%)	21	(14.7%)
		Missing Values	29	(6.0%)	75	(52.5%)
	2 The CASMIN (Comparative Analysis of Social Mobility in Industrial Nations) classification (see König,
	Lüttinger, & Müller, 1988) ranges from 1a ("Inadequately completed general education") to 3b ("Higher
	tertiary education"). In our descriptive analysis, we coded the lowest educational level with "1" and the
	highest with "9" and excluded all respondents who are still in school now. The means indicate the av-
	erage educational level achieved within the different groups and give very general information about
	the educational level in these groups.

Table 6 . Description of the Sampling Plan Single Mobility Experience Multiple Mobility Experiences

 6

	Upper	100 out of 483 respondents pre-	100 out of 143 respondents from all
		dominantly in NRW	over Germany
	Service Position
	Lower	100 out of 616 respondents pre-	All 87 respondents from all over Ger-
		dominantly from NRW	many
	Service Position
	Manual	100 out of 1,199 respondents pre-	100 out of 181 respondents
		dominantly from NRW
	Working Position
	Note. NRW = North Rhine-Westphalia.

In addition, all respondents who came before 1961 (9 in total) were deleted because they could not be considered in terms of mobility within the EU.

The authors wish to thank the German Research Foundation (DFG) for their grant enabling us to study this topic, as well as the anonymous reviewers who supported our application. We also appreciate the support provided by the German Institute for Economic Research (DIW Berlin) in helping us to realize this challenging research design and thus to contribute substantially to mixed-methods research. In addition, we would like to thank Isabell Diekmann and Inka Stock for their support.


Gabin Gbabode

Philippe Négrier

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Miquel Àngel Cuevas-Diarte

Philippe Negrier

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Structures of the High-Temperature Solid Phases of the Odd-Numbered Fatty Acids from Tridecanoic Acid to Tricosanoic Acid

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

Introduction

Higher fatty acids of the formula C n H 2nÀ1 OOH are com posed of long, saturated aliphatic chains with a carboxyl group at one of their extremities. It is well known that long chain aliphatic compounds adopt several solid forms, with different configurations of the packing of the molecules in and between the layers. [1 5] Typically, the A', B', C', C'', and D' forms [6 9] are adopted by the saturated fatty acids with an odd number of carbon atoms, whereas the A, B, C, and E forms [6 10] are adopted by those with an even number of carbon atoms. All of these fatty acids exhibit at least one solid solid transition prior to melting, [7 9] and we usually dis tinguish the high temperature phase that is stable just below the melting point from the low temperature phase observa ble at lower temperatures. For odd numbered fatty acids, the high temperature phase may be the C' or the C'' form. [6] For years, only the structure of the C' form of hendecanoic acid (C 11 H 21 OOH) had been reported, [11] and, moreover, it had not been fully resolved (two dimensional (2D) struc ture). Recently, Bond solved the crystal structures of the high temperature solid phases of all fatty acids from hexano ic acid (C 6 H 11 OOH) to pentadecanoic acid (C 15 H 29 OOH) from single crystals. [6] The results obtained for the odd num bered fatty acids showed that, just below their respective melting points, the fatty acids with chain length from n = 7 to n = 11 adopt the C' form, whereas tridecanoic acid and pentadecanoic acid adopt the C'' form.

In the present article, we focus on longer chain odd num bered fatty acids, specifically those with 13 to 23 carbon atoms. These compounds have high enthalpies of melting and they are also thermo adjustable by means of their chain length. These fatty acids, as well as their mixed samples, could therefore be potential candidates for applications in the field of energy storage or thermal protection, as has been demonstrated for alkanes [12,13] and alkanols. [14,15] In this context, it is important to know the crystal structures of the high temperature solid phases, as it is these that are in volved in the melting process.

Crystal structure determination of the high temperature phases of odd numbered fatty acids is not an easy task. These solid forms are only stable in a narrow temperature range just below the melting point, and this temperature in terval becomes narrower with increasing chain length. [16,17] Abstract: Crystal structures of the high temperature phases of odd num bered fatty acids (C n H 2nÀ1 OOH) from tridecanoic acid (C 13 H 25 OOH) to trico sanoic acid (C 23 H 45 OOH) are present ed in this article. They have been deter mined from high quality X ray powder diffraction patterns. Two types of high temperature phases are adopted: one monoclinic A2/a with Z = 8 for the fatty acids with n = 13 and n = 15, de noted as C'', and one monoclinic P2 1 /a with Z = 4 for the longer chain fatty acids, denoted as C'. It appears that the packing arrangement of the alkyl chains and of the carboxyl groups is similar in all of the structures. Howev er, the arrangement at the methyl group interface differs between the C' and C'' forms. A survey of the intermo lecular interactions involved in these polymorphs coupled with a study of the effects of temperature on the struc tures have led us to a better under standing of the arrangement of the molecules within the high temperature solid phases of odd numbered fatty acids.

Keywords: bilayers • hydrogen bonds • polymorphism • thermal motion • van der Waals interactions

[a] Dr. G. Gbabode The growth of single crystals is therefore very complicated, and the degree of difficulty goes on increasing for the longer acids. Some attempts have been made to grow such crystals, but without success. As a consequence, we have now determined their crystal structures from X ray powder diffraction patterns measured at the appropriate tempera tures. The module POWDER SOLVE [18] of the MATERI AL STUDIO application [START_REF]Material Studio) version 3.0[END_REF] has been used to resolve the crystal structures.

In the first part of this paper, the polymorphism of the fatty acids from C 13 H 25 OOH to C 23 H 45 OOH is briefly de scribed. Data from both calorimetric and X ray powder dif fraction measurements are presented. A detailed analysis of the X ray powder diffraction patterns of the high tempera ture solid forms is then described. Their crystal structures are presented and the packing arrangement of the molecules throughout the studied series is discussed. In particular, the results obtained for tridecanoic acid and pentadecanoic acid are compared with those obtained by Bond. Finally, the ef fects of temperature are analysed and related to the packing arrangement of the molecules.

Results

Calorimetric analysis: The DSC traces obtained for the six fatty acids were, in each case, indicative of the occurrence of a solid solid transition before melting (Figure 1). The tem perature interval between the two transitions diminishes with increasing chain length (at least up to C 19 H 37 OOH; this temperature interval is a little wider for C 21 H 41 OOH and C 23 H 45 OOH than for C 19 H 37 OOH).

The various transitions observed for these materials have been characterised by both X ray diffraction and thermal analysis. The measured temperatures, entropies, and enthal pies are displayed in Table 1. As mentioned in the litera ture, [7 9] C 13 H 25 OOH adopts the A' form at room tempera ture. A low energy reversible transition was observed at 287.7 K, which we attribute to an A' l (l for low)!A' h (h for high) transition. Such a transition has been previously ob served by Kaneko et al. [START_REF] Kaneko | [END_REF] for pentadecanoic acid. All of the other acids adopt the B' form at room temperature, as pre dicted by many authors. [8,9] However, we have also observed A' l and A' h solid phases for samples of C 15 H 29 OOH. The temperature of the A' h !C'' transition is lower than that of the B'!C'' transition (Table 1). Therefore, B' is more stable than A' in the vicinity of the transition point for pentadeca noic acid. Irrespective of the low temperature phases, the high temperature phases are the C'' form for C 13 H 25 OOH and C 15 H 29 OOH and the C' form for the four other acids.

The evolution of the solid solid transition temperatures and the melting points shown in Figure 2 is in agreement with the work of von Sydow and Stenhagen, [16] in which these parameters were plotted for the odd numbered acids from n = 13 to n = 29.

The enthalpies and entropies of melting increase almost linearly with increasing chain length. These trends reflect the regular incremental lengthening of the hydrocarbon chain by the addition of two CH 2 groups on going from one acid to the next.

Indexing of the X-ray powder-diffraction patterns: Taking into account the temperatures of the transitions determined by thermal analysis, X ray powder diffraction patterns of the high temperature phases were recorded at 313.0, 324.0, 333.0, 340.0, 346. culated powder patterns (Pawley refinement [21] ) of C 13 H 25 OOH and C 23 H 45 OOH are shown superimposed in Figure 3.

For the fatty acids from C 17 H 33 OOH to C 23 H 45 OOH, the hypothetical cell parameters of the A2/a C'' forms have also been calculated by analogy with the cell parameters of C 13 H 25 OOH and C 15 H 29 OOH by using the Win CELREF and Win CRISDR programs. [22] Figure 4 shows the Pawley fits for C 17 H 33 OOH and C 19 H 37 OOH obtained for the P2 1 /a and A2/a arrangements in the 2q domain (25 328), which ex hibits the most marked differences between the two ar rangements for each compound. Trial assignments of the A2/a phase for the fatty acids from C 17 H 33 OOH to C 23 H 45 OOH invariably gave worse agreement of the experi mental and calculated X ray diffraction patterns. As an ex ample, the relatively strong reflection at around 298 is never taken into account in the A2/a lattice, whereas it corre sponds to the 2 ¯11 reflection in the P2 1 /a lattice for the four fatty acids. All reflections are indexed with the P2 1 /a lattice of the C' form for the fatty acids from C 19 H 37 OOH to C 23 H 45 OOH, whereas this is not quite the case for C 17 H 33 OOH. Indeed, it is evident from Figure 4a that the weak reflection at 29.58 is not possible with the P2 1 /a lattice, whereas it is with the A2/a lattice. It may be assumed that this sample also contains a small amount of the C'' form, as this fatty acid is at the limit between the occurrence of the C' and C'' forms in the series.

The cell parameters, the space groups, and the calculated densities determined for the high temperature solid forms of the six fatty acids are displayed in Table 2. The agreement factor, Rwp, obtained after Pawley refinement, is also given for each acid. In addition, the crystallographic data deter mined by von Sydow [11] for the C' form of C 11 H 21 OOH and by Bond [6] atoms increases, following a regular curve (Figure 5) from C 11 H 21 OOH to C 23 H 45 OOH. Furthermore, the b parameter is nearly constant for all of these acids.

The density decreases with increasing chain length. Indeed, the temperature of acquisition increases with in creasing chain length and so does the thermal motion, which tends to increase the volume of the crystal lattice. The den sities calculated for the high temperature phases are all around 0.99 g cm À3 , whereas they are a little higher, around 1.02 g cm À3 , for the low temperature phases. [23,24] As a conclusion of the two previous sections, it can be stated that the evolution with increasing chain length of sev eral measured quantities (transition temperature, enthalpy, a parameter) are described by continuous curves from The crystal structures show al ternating methyl and carbox yl group interfaces along the c axis, as is visible in Figure 6. The A2/a structure is a twofold version of the P2 1 /a structure. The two types of structures are centrosymmetric and the hy drogen bonds bridge the car boxyl groups of molecules re lated by inversion centres. In these representations, it can be seen that the molecules are not situated in the same posi tions in the A2/a lattice and the P2 1 /a lattice, which clearly indicates that these two types of structure are different.

The values of the final agreement factor, Rwp, range be tween 4.0 and 5.5 % for the structures solved (Table 3), indi cating a very good agreement between the calculated and experimental X ray diffraction patterns. Besides, they do not differ markedly from the values obtained after Pawley refinement (Table 2), which did not take into account the Table 2. Crystallographic data determined for the high temperature solid forms of the odd numbered fatty acids from C 13 H 25 OOH to C 23 H 45 OOH, together with those found in the literature. The non standard space groups settings A2/a and P2 1 /a have been chosen for convenience, so that the chain axis is almost parallel to the c axis.

Ref. T [K]

Rwp Density [g cm 3 ]

Space group

Z a [] b [] c [] b [8]
C agreement between the calculated and measured intensities of the various reflections. Table 3 also contains selected structural data that serve to describe the packing arrange ment of the fatty acids within (alkyl chains, carboxyl groups) and between (methyl groups) the layers, and that have been determined from this work and from the C'' structures of C 13 H 25 OOH and C 15 H 29 OOH solved by Bond.

Description of the C'' structures and comparison with the single-crystal data: [6] The alkyl chains are packed in the or thorhombic packing arrangement O ? , as described long ago by Bunn, [1] in accordance with the single crystal struc tures. This motif is very common in long chain aliphatic compounds. [START_REF] Hernqvist | Crystallization and Polymorphism of Fats and Fatty Acids[END_REF][START_REF] Yano | [END_REF] The chains are almost parallel and the zigzag planes of neighbouring molecules are perpendicular to one another (Figure 7). Moreover, the alkyl chains are tilted from the (a,b) plane. The angles of tilt of the chain axis with respect to the a and b axes have been evaluated and are dis played in [23 26] ) as opposed to much shorter distances in our study. The uncertainties in our values have been assessed by estimat ing the uncertainties in the po sitions of the oxygen atoms, as these were not available from the refinement program. Our measurements are much less precise (average deviation of 0.06 , taking into account the values obtained for the C' structures) than those based on the single crystal data (precision of around 0.01 ). This lack of accuracy of the O•••O distances is directly related to the method used for the crystal structure determination as the final structure is a compromise between the agreement of the measured and calculated X ray powder diffraction patterns and the energy minimisation. However, taking into account the evaluated uncertainties, the O•••O distances de Table 3. Selected structural data determined from the crystal structures of the C'' (this work and Bonds [6] ) and C' forms of the six fatty acids.

Angle of tilt of the alkyl chain [8] Packing arrangement of the carboxyl groups termined from the powder data are almost consistent with those obtained from the single crystal data. At the methyl group interface, the packing arrangement is also similar for the C'' structures determined by the two different techniques. A given methyl group, denoted as (0), just below the (a,b) plane has three closest neighbouring methyl groups just above the (a,b) plane, denoted as (1), (2), and (3) (see Figure 8). ( 1) and ( 2 3) are consistent between the two sets of data (Table 3). On the other hand, the C C C O torsion angle is close to 1808 for the C'' structures solved by Bond, which corre sponds to a cis conformation of the carboxyl groups. In the latter case, however, the C O and C=O distances are very close (1.291(5) and 1.233(5) for C 13 H 25 OOH; 1.280(6) and 1.237 (7) for C 15 H 29 OOH). Thus, it may well be the case that these structures exhibit both conformations, as Hayashi and Umemura have ascertained for several fatty acids from C 3 H 5 OOH to C 20 H 39 OOH by means of polarized infrared spectroscopy. [27] In the present work, structures with a cis conformation of the carboxyl group, that is, with the C C C O torsion angle equal to 1808, have also been tested. These structures were invariably found to be less energetically fa vourable than those featuring a trans conformation of the carboxyl groups. Although this result does not disprove that the actual structures might ex hibit both conformations, it nevertheless indicates that the trans conformation must be the dominant one for the structures we have solved. The crucial differences be tween the C' and C'' structures lie in the packing arrange ments at the methyl group in terface. Figure 8 shows the packing arrangements of the methyl groups in the (a,b) plane for the C'' form of C 15 H 29 OOH and the C' form of C 19 H 37 OOH. The methyl groups of the molecules above the plane are shaded black, whereas those situated just below the plane are in grey. (0) has three closest neighbours above the methyl group inter face, (1), ( 2) and (3), which are situated at similar positions relative to (0) in both the C' and C'' structures. However, (1), ( 2) and (3) are differently related to (0) in terms of the symmetry elements involved, and hence according to the space groups. In the A2/a structures (C'' form), ( 1) and ( 2) are related to (0) through inversion centres, whereas they are related by a 2 1 axis in the P2 1 /a structures (C' form). Thus, (1) and ( 2) are equidistant from (0) in the P2 1 /a struc tures, whereas in the A2/a structures the relative positions of ( 1) and ( 2) with respect to (0) depend on the relative po sition of (0) with respect to the inversion centres. ( 3) is relat ed to (0) by a 2 axis in the A2/a structures, whereas it is re lated by an inversion centre in the P2 1 /a structures. The shortest H•••H distances measured between (0) and its three closest neighbours exceed 2.4 (sum of the van der Waals radii of two hydrogen atoms) in each of the six structures (Table 3). It may also be noted that the distances between the hydrogen atoms of (0) and (3) increase with increasing chain length. This trend can be attributed to the increased thermal motion, as the temperature of measurement also in creases with increasing chain length. Actually, the C' and C'' forms contain identical 2D layers: the methyl group ar rangements in both the above and below layers (in black and grey, respectively, in Figure 8) are the same for the P2 1 / a and A2/a structures. The difference between these struc tures lies in the way in which these layers are stacked. It can clearly be seen in Figure 8 that when (1), ( 2) and (3) are dis placed along the 1/2a + 1/2b vector in the P2 1 /a structure (or A2/a structure), they become related to (0) with the symme try elements involved in the A2/a arrangement (or P2 1 /a ar rangement).

Discussion

According to the crystal structures of the high temperature phases of odd numbered fatty acids determined in the pres ent work and in that of Bond, [6] the C'' form is only seen for C 13 H 25 OOH and C 15 H 33 OOH in the series from C 7 H 13 OOH to C 23 H 45 OOH. The question then arises as to why this solid phase is only adopted by these two fatty acids. In the follow ing, we propose an explanation based on a survey of the en ergetic contributions that are operative in the packing ar rangements of the molecules within the C' and C'' crystal structures.

Two major intermolecular interactions are involved in the cohesion of the structures of the high temperature phases of fatty acids, namely hydrogen bonds and van der Waals inter actions. The former influence the packing arrangement of the carboxyl groups, whereas the latter relate more to the interactions between the atoms of the hydrocarbon chains. These two interactions are evaluated in the potential energy descriptions of the structures through van der Waals and electrostatic contributions. The overall potential energies of the structures and the potential energies of the latter two contributions are listed in Table 4 for the six structures in vestigated, together with those determined from the crystal structures of the high temperature phases of the odd num bered fatty acids solved by Bond (from C 7 H 13 OOH to C 15 H 29 OOH). The energy values are given in kJ mol À1 per molecule, so that they can be compared for all of the struc tures.

The electrostatic potential energy is practically constant for all of the structures (around 160 kJ mol À1 ), whether de termined from the powder or single crystal data. This is con sistent with the similar packing of the carboxyl groups within the dimers established for the six structures investi gated. However, the values obtained for the C'' structures do differ a little between our work and that of Bond. This may be related to the discrepancy between the O•••O distan ces mentioned in the previous section (2.54 and 2.55 for our structures, as compared to 2.63 for Bonds structures). The potential energy of the hydrogen bonds is higher than the van der Waals potential energy for each structure. This confirms the predominant role of the hydrogen bonds in the cohesion of these crystal structures. However, the van der Waals forces increase with increasing chain length, and in the case of C 23 H 45 OOH the potential energies of the two in teractions are almost equal. The evolution of the total energy of the structures of the high temperature phases with increasing chain length produces a straight line from C 7 H 13 OOH to C 23 H 45 OOH (Figure 9), irrespective of the solid phase considered. This linear trend confirms the simi larity of the molecular arrangements in the C' and C'' phases. It also implies that the energy barrier between the two solid forms must be very low.

A third contribution, which has already been invoked sev eral times in this paper, also exerts an influence on the pack ing arrangement of the molecules, namely that of thermal motion. Indeed, the high temperature phases are only stable in a narrow temperature range below the melting points, this range narrowing with increasing chain length, as the temperatures of transition to C' or C'' and of melting in crease. Thus, the effect of thermal motion has to be studied if we want to thoroughly understand the packing arrange ment of the molecules in these particular solid forms.

When considering the equivalent temperature factors, U eq , of the non hydrogen atoms of the odd numbered fatty acids Table 4. Potential energies (per molecule) calculated from the crystal structures of the high temperature solid forms of odd numbered fatty acids solved in this work and in that of Bond. [6] Intermolecuar interactions Total energy [kJ mol the structures solved by Bond. [6] from C 7 H 13 OOH to C 15 H 29 OOH determined from the single crystal data, [6] it appears that thermal agitation exerts a greater effect on the last few carbon atoms of the chains, that is, on those close to the terminal methyl group for each compound. These temperature factors are represented in Figure 10 for the non hydrogen atoms of these five acids.

The atoms are labelled from 1 to n+2 (in which n is the total number of carbon atoms), 1 and 2 denoting the two oxygen atoms and the integers from 3 to n+2 denoting the carbon atoms of the hydrocarbon chains from the carboxyl group to the methyl group. It can be seen from this repre sentation that, for the five acids, the temperature factors are much higher for the atoms near the methyl group than for the others. It can be assumed that the strong hydrogen bonds counteract the thermal agitation and limit the motion of the atoms near the carboxyl group. Thus, for a given mol ecule, the further the atoms are from the carboxyl group, the weaker the effect of the hydrogen bonds and the more prone they will be to the effect of thermal agitation. This trend is clearly apparent in Figure 10.

As the structures of the fatty acids from C 17 H 33 OOH to C 23 H 45 OOH were solved by assuming the molecules to be rigid bodies, a global isotropic temperature factor was deter mined for each structure, which accounts for the mean ther mal agitation within the structure. Our aim was to investi gate the evolution of the thermal agitation for the high tem perature solid forms of the odd numbered fatty acids from C 7 H 13 OOH to C 23 H 45 OOH. For C 7 H 13 OOH, C 9 H 17 OOH, and C 11 H 21 OOH, we summed the values of the equivalent temperature factors of the non hydrogen atoms and divided the result by the number of atoms considered. Thereby, we obtained mean temperature factors that could be compared with the global isotropic factors determined for the six longer fatty acids. All of these temperature factors are gath ered in Table 5. In addition, the temperature at which the measurement was undertaken as well as the melting point are also indicated in each case.

It is noteworthy that the values obtained for the mean temperature factors are not very accurate because they can be affected by systematic errors in the measured intensities. Moreover, the X ray diffraction measurements were per formed close to the melting points (within about 1 K) for all of the acids except C 7 H 13 OOH and C 9 H 17 OOH (around 35 and 15 K below their melting points, respectively), which in troduces further uncertainty in the values. However, we are more interested here in the evolution of these values across the series than in the values themselves. Considering that the measurements were made under approximately the same conditions for all of the fatty acids, it can be assumed that all of the temperature factors can be compared. Their evolution in relation to the chain length is plotted in Figure 11. It appears that they increase up to C 13 H 25 OOH and then decrease once more.

The particular evolution obtained may be explained in terms of the competitive effects of van der Waals forces and thermal agitation, both of which increase with increasing chain length, whereas the hydrogen bonds remain approxi mately constant for all of the structures. The ascending part of the curve may be related to a predominance of the effect of thermal agitation, whereas for the descending part the van der Waals forces should prevail. In this representation, it is also apparent that the displacements due to tempera ture are, on average, more significant for C 13 H 25 OOH and C 15 H 29 OOH. As can be seen in Figure 10, the greatest dis placements are certainly located near the methyl group. Moreover, according to van de Streek et al., [28] who studied the influence of thermal motion on the crystal structures of n alkanes, they should be mostly oriented perpendicular to the chain axis, approximately in the (a,b) plane in our case. Keeping in mind that the C' and C'' arrangements are mutu ally related by a translation of a layer in the (a,b) plane and also that the energy barrier between the two solid forms is certainly very low, notably in the cases of C 13 H 25 OOH and C 15 H 29 OOH, the competitive effects of van der Waals forces and thermal motion are more conducive to adoption of the C'' form. A similar conclusion was reached by van de Streek and co workers concerning the relative stabilities of the tri clinic and monoclinic polymorphs of even numbered n alka nes with increasing chain length. For the other acids, we sur mise that the effect of thermal agitation is not strong enough since, on the one hand, for the shorter acids the transition temperatures are not very high (and consequently nor is the thermal motion), while, on the other hand, the van der Waals forces become stronger for the longer acids. This may explain why, as far as we are aware, the C'' form is only adopted by C 13 H 25 OOH and C 15 H 29 OOH.

Conclusion

The crystal structures of the high temperature solid forms of the odd numbered fatty acids from C 13 H 25 OOH to C 23 H 45 OOH have been determined from X ray powder dif fraction patterns. C 13 H 25 OOH and C 15 H 29 OOH have been found to adopt the C'' form at high temperatures, as also shown by Bond. [6] However, we have proved that the C' form is adopted by the longer fatty acids, as is also the case for the shorter fatty acids from C 7 H 13 OOH to C 11 H 21 OOH according to Bond. [6] Thus, C'' is only observed for C 13 H 25 OOH and C 15 H 29 OOH. The C'' and C' forms are both monoclinic, but the former has the space group A2/a with Z = 8, whereas the latter has the space group P2 1 /a with Z = 4. Both of their structures consist of bilayers of molecules held together by hydrogen bonds between their carboxyl groups. The packing arrangement in the two types of struc tures is very similar. The major differences lie at the methyl group interface. It has been shown that the packing arrange ments of the molecules in these high temperature solid forms of odd numbered fatty acids are determined by the balance of the competitive effects due, on the one hand, to hydrogen bonds and van der Waals interactions, which serve to hold the structure together, and, on the other hand, ther mal motion, which tends to push the molecules apart. Lastly, this article proves the validity of the technique that we have used to solve crystal structures from X ray powder diffraction data, as the results obtained for the C'' forms of C 13 H 25 OOH and C 15 H 29 OOH compare well with those obtained from single crystals. However, some im provements have to be made regarding the assessment of the hydrogen bonds, considering in particular the low preci sion of the O Thermal analysis: Transition temperatures as well as enthalpy changes were determined by using a Perkin Elmer DSC 7 instrument equipped with a cooling accessory, which allowed the temperature to be increased from 110 to 950 K. A heating rate of 2 K min 1 was typically used. Meas urements at lower heating rates (0.5, 0.2 K min 1 ) were also performed in order to better resolve transitions occurring at close temperatures. Sam ples (about 4 mg) were placed in aluminium pans and weighed before and after each experiment in order to determine the mass loss. At least six measurements were performed on each compound to enable the cal culation of accurate values of the various thermodynamic quantities. The uncertainties in the temperatures and enthalpies were determined by using Students method [START_REF] Linnink | La MØthode des Moindres CarrØs[END_REF] with a 95 % threshold of reliability. To this value was added the systematic error arising from the calibration of the apparatus, which was set at AE 0.2 K for the temperatures and AE 1 % for the enthalpies.

X-ray powder diffraction: An Inel CPS 120 X ray powder diffractometer was used to obtain high quality powder diffraction patterns of the high temperature solid forms. Cu Ka radiation was selected for the incident beam. The diffractometer was equipped with an Oxford Cryosystems N 2 cryostream to facilitate the performance of isothermal experiments at dif ferent selected temperatures. The Inel CPS 120 diffractometer operates with Debye Scherrer transmission geometry and the diffracted beams are collected on a 1208 curved counter by gas ionisation (argon + C 2 H 6 ). The sample is introduced in a 0.5 mm diameter Lindemann glass capilla ry. The latter is rotated about its axis during the experiment in order to minimise preferential orientations of the crystallites. The acquisition time was set at six hours in order to obtain reflections with exploitable intensi ties. The relative heights of the strongest reflections at the start of each measurement were compared with those obtained for the X ray powder diffraction pattern of the B' form of C 17 H 33 OOH, which was calculated from the structure published by Goto and Asada [23] based on a study car ried out on single crystals. Then, we chose the samples for which the agreement was best, assuming that the intensities in the calculated X ray powder diffraction pattern of the B' form of C 17 H 33 OOH were free from any preferential orientation effect. As recommended, [START_REF] Evain | [END_REF] external calibra tion to convert the measured 4096 channels to 2q degrees was applied by means of cubic spline fittings using cubic Na 2 Ca 2 Al 2 F 4 . The latter was combined with a low angle calibration using silver behenate, [31] a material that exhibits several reflections in the 2q range of 1.5 208.

Determination of cell parameters and space groups:

The peak positions were determined after pseudo Voigt fitting using DIFFRACTINEL soft ware. Potential solutions of cell parameters and space groups were ob tained using X CELL software [32] available in the module POWDER IN DEXING of MATERIAL STUDIO. The cell parameters and space group that best corresponded to the experimental X ray diffraction pat tern of the solid form under investigation were finally determined using a Pawley profile fitting procedure. [21] The latter provided the refinement of the cell parameters, the peak profile parameters (function of profile, FWHM, asymmetry), the background, and the zero shift.

Determination of the crystal structures:

The molecule to be studied was drawn in a 3D worksheet and was minimised in energy by means of ge ometry optimisation using the COMPASS force field [33] to obtain the rel evant distances, angles, and dihedral angles for its various bonds. This molecule was then set as a rigid body, but with the dihedral angle of the carboxyl group allowed to adjust freely, as this determines the good es tablishment of the hydrogen bonds. The rigid body was introduced in the cell whose dimensions had been previously found, together with its ho mologues related to the space group. The whole system was moved in the cell according to the seven degrees of freedom (three translations, three rotations, and the dihedral angle of the carboxyl group) by using a Monte Carlo type simulation [18] over several cycles to obtain the best re production of the experimental X ray powder diffraction pattern by the calculated one. The final structure was then obtained after repeated alter nating application of Rietveld refinement [34] and geometry optimisation by energy minimisation in order to reach the best agreement between X ray powder diffraction and molecular interactions. The Rietveld proce dure includes refinement of the translations, rotations, and dihedral angle of the molecule, the isotropic temperature factors, and the preferred ori entations, also with the parameters previously refined in the Pawley pro cedure. The total energy determined for the structures corresponds to a survey of the intra and intermolecular interactions involved. Its entire expression is given in an article by Sun. [33] CCDC 612518 to CCDC 612523 contain the supplementary crystallo graphic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data request/cif.

  for the C' form of C 11 H 21 OOH and the C'' forms of C 13 H 25 OOH and C 15 H 29 OOH are also included. The cell parameters determined for C 13 H 25 OOH and C 15 H 29 OOH are in good agreement with those obtained by Bond. The a parameter decreases as the number of carbon

Figure 2 .

 2 Figure 2. Evolution of some thermodynamic quantities with increasing chain length: a) temperatures of solid solid transition (T trs ) and of melt ing (T fus ), b) enthalpies of melting, and c) entropies of melting.

Figure 3 .

 3 Figure 3. Superimposition of the experimental and calculated X ray powder diffraction patterns (Pawley refinement) obtained for a) C 13 H 25 OOH and b) C 23 H 45 OOH.

  C 13 H 25 OOH to C 23 H 45 OOH, irrespective of the high temper ature solid phase that is adopted (C'' for C 13 H 25 OOH and C 15 H 29 OOH; C' for the longer acids). Crystal structures of the high-temperature phases: The crys tal structures determined for the six fatty acids correspond to the best compromise between Rietveld refinement and energy minimisation (see the Experimental Section for more details). Projections in the (a,c) plane of the crystal structures of the C'' form of C 15 H 29 OOH and of the C' form of C 21 H 41 OOH are pre sented in Figure 6. The mole cules are stacked in bilayers in both forms, with dimers being formed by hydrogen bonding between the carboxyl groups.

Figure 4 .

 4 Figure 4. Superimposition in the 25 328 2q domain of the Pawley fits ob tained using the P2 1 /a and A2/a lattices for a) C 17 H 33 OOH and b) C 19 H 37 OOH.

Figure 6 .

 6 Figure 6. Representations in the (a,c) plane of the crystal structures of the high temperature solid forms of C 15 H 29 OOH (C'' form) and C 21 H 41 OOH (C' form).

Figure 7 .

 7 Figure 7. Packing arrangement of the alkyl chains of C 13 H 25 OOH perpen dicular to the chain axis.

  ) are related to each other by a translation of the lattice along the b vector. They are situated either side of (0) along the b axis. (3) is situated almost immediately below (0) along the a axis. The shortest H•••H distances between (0) and (

Finally, it

  may be noted that the crystal structures of the C'' forms of C 13 H 25 OOH and C 15 H 29 OOH presented herein are in good agreement with those already solved from single crystal data. Hence, it may be assumed that the crys tal structures of the longer fatty acids determined by appli cation of the same technique should be equally reliable. Comparison of the C' and C'' structures: The C' and C'' forms exhibit a similar packing arrangement of the mole cules within the bilayers. In the C' structures, the alkyl chains are stacked in the orthorhombic packing arrangement O ? , as in the case of the C'' structures. Moreover, they are tilted in the same way towards the (a,b) plane, at an angle close to 908 with respect to the b axis and at an angle of around 1258 with respect to the a axis. As regards the pack ing arrangement of the carboxyl groups, no significant varia tion in the C C C O torsion angle, the O H•••O angle, or the O•••O distance can be seen on going from C 13 H 25 OOH to C 23 H 45 OOH. In particular, the O•••O distance ranges from 2.60 to 2.72 for the C' structures, but taking into account the evaluated uncertainties, these values are all consistent with the 2.63 determined from the single crystal C'' struc tures. One interesting point worthy of mention concerns the C C C O torsion angle. For the six structures investigated, this parameter is close to 08 (it varies from 3 to 138), which corresponds to a trans conformation of the carboxyl groups.

Figure 8 .

 8 Figure 8. Packing arrangement of the methyl groups in the (a,b) plane at the methyl group interface for a) C 15 H 29 OOH and b) C 19 H 37 OOH. The methyl groups in black are just above the plane, the others are just below. The two arrangements are derived from one another by a translation of 1 = 2 a+ 1 = 2 b of one methyl group layer with respect to the other.

Figure 9 .

 9 Figure 9. Evolution of the total energy of the high temperature structures of the odd numbered fatty acids with chain length from C 7 H 13 OOH to C 23 H 45 OOH. *: the structures determined by us; *: the structures solved by Bond.[6]

Figure 10 .

 10 Figure 10. Evolution along the hydrocarbon chains of the equivalent tem perature factors (U eq ) determined by Bond for the non hydrogen atoms of the odd numbered fatty acids from C 7 H 13 OOH to C 15 H 29 OOH. 1 and 2 correspond to the two oxygen atoms; 3 to n+2 (where n is the total number of carbon atoms) denote the carbon atoms from the carboxyl group to the methyl group. The temperature factors have been linked for each molecule.

Figure 11 .

 11 Figure 11. Evolution of the mean temperature factors determined for the high temperature phases of the odd numbered fatty acids with chain length from C 7 H 13 OOH to C 23 H 45 OOH. The values have been calculated from the data of Bond for the fatty acids from C 7 H 13 OOH to C 11 H 21 OOH, and come from our own results for the longer acids.

4, and 351.7 K for C 13 H 25 OOH, C 15 H 29 OOH, C 17 H 33 OOH, C 19 H 37 OOH, C 21 H 41 OOH, and C 23 H 45 OOH, respectively. All of the reflections of the powder patterns of C 13 H 25 OOH and C 15 H 29 OOH have been indexed to the C'' form, which is monoclinic with space

  group A2/a and has eight molecules in the unit cell. For the fatty acids from C 17 H 33 OOH to C 23 H 45 OOH, the reflections have been indexed to the C' form, which is also monoclinic, but has space group P2 1 /a and Z = 4. The measured and cal Figure 1. Extract of the DSC signals obtained with a heating rate of 2 K min 1 .

Table 1 .

 1 Temperatures (T in K), enthalpies (DH in kJ mol 1 ), and entropies (DS in J mol 1 K 1 ) of the various phase transitions.

			Solid solid transition (S III !S II )		Solid solid transition (S II !S I )		Melting (S I !liquid)
		S III	T	DH	DS	S II	T	DH	DS	S I	T	DH	DS
	C 13 H 25 OOH	A' l	287.7(6)	0.06(1)	0.21(4)	A' h	309.1(4)	8.5(3)	27(1)	C''	314.6(5)	33(1)	105(3)
	C 15 H 29 OOH	A' l	295.5(5)	0.27(7)	0.9(2)	A' h	320.8(3)			C''	325.5(4)	40.4(6)	124(2)
	C 15 H 29 OOH					B'	321.9(4)	8.2(6)	25(2)	C''	325.5(4)	40.4(6)	124(2)
	C 17 H 33 OOH					B'	331.2(5)	7.5(9)	23(3)	C'	333.5(5)	46.5(9)	139(3)
	C 19 H 37 OOH					B'	339.0(4)	7.4(6)	22(1)	C'	340.4(3)	57(1)	167(3)
	C 21 H 41 OOH					B'	344.6(4)	5(1)	13(3)	C'	346.7(5)	63(3)	183(9)
	C 23 H 45 OOH					B'	349.9(4)	2.5(6)	7(2)	C'	352.0(5)	75(3)	212(9)

  Evolution of the a parameter with increasing chain length from C 11 H 21 OOH to C 23 H 45 OOH.

						Figure 5.
	11 H 21 OOH [11]	296		P2 1 /a	4	9.62(3) 4.92(1) 34.2(1) 131.3(3)
	[6]	300	0.984	P2 1 /a	4 10.029(1) 4.912(1) 35.10(1) 133.36(1)
	C 13 H 25 OOH this work 313	0.031 0.981(1)	A2/a	8	9.854(1) 4.940(1) 73.66(1) 125.95(1)
	[6]	310	0.983	A2/a	8	9.812(1) 4.943(1) 73.74(1) 125.88(1)
	C 15 H 29 OOH this work 324	0.033 0.975(1)	A2/a	8	9.724(2) 4.952(1) 84.02(3) 125.30(1)
	[6]	320	0.975	A2/a	8	9.720(1) 4.956(1) 84.02(1) 125.29(1)
	C 17 H 33 OOH this work 333	0.034 0.974(1)	P2 1 /a	4	9.634(2) 4.953(1) 50.03(1) 129.44(1)
	C 19 H 37 OOH this work 340	0.035 0.974(1)	P2 1 /a	4	9.575(1) 4.953(1) 54.99(1) 128.72(1)
	C 21 H 41 OOH this work 346.4 0.035 0.970(1)	P2 1 /a	4	9.526(1) 4.957(1) 60.18(1) 128.10(1)
	C 23 H 45 OOH this work 351.7 0.029 0.969(1)	P2 1 /a	4	9.488(1) 4.957(1) 65.23(1) 127.63(1)

Table 3 .

 3 The chains are almost perpendicular to the b axis, but are tilted towards the a axis with angles of 125.88 and 125.28 for C 13 H 25 OOH and C 15 H 29 OOH, respec tively. These values are consistent with those of the q 1 angles (125.98 for C 13 H 25 OOH and 125.38 for C 15 H 29 OOH), similar hydrogen bonding framework is obtained for both the powder and single crystal C'' structures of C 13 H 25 OOH and C 15 H 29 OOH. The O H•••O angle formed between the ac ceptor and the donor in the hy drogen bond is close to 1808 in both cases (Table 3), indicative of strong hydrogen bonds. The C C C O torsion angle (O being the oxygen atom bearing the hydrogen atom) is close to 08 (this work) or 1808 (Bonds work), which shows that the carboxyl group is always almost coplanar with the alkyl chain. However, there are dis crepancies between the values obtained for the O•••O distan ces, that is, around 2.63 in the single crystal study (stan dard values for crystal struc tures of solid forms of fatty acids

defined by Bond as the angle between the plane parallel to the chain axis and the methyl group interface, in the present case the (a,b) plane. A

Table 5 .

 5 Mean temperature (T) factors determined for the high tempera ture phases of the odd numbered fatty acids from C 7 H 13 OOH to C 23 H 45 OOH.

		T meas [K]	T melting [K]	Ref.	Mean T factor [ 2 ]
	C 7 H 13 OOH	230.0	265.83(1)	[12]	0.099(1)
	C 9 H 17 OOH	270.0	285.53(1)	[12]	0.151(2)
	C 11 H 21 OOH	300.0	301.63(1)	[12]	0.171(3)
	C 13 H 25 OOH	313.0	314.6(5)	this work	0.217(6)
	C 15 H 29 OOH	324.0	325.5(4)	this work	0.191(5)
	C 17 H 33 OOH	333.0	333.5(5)	this work	0.174(6)
	C 19 H 37 OOH	340.0	340.4(3)	this work	0.099(5)
	C 21 H 41 OOH	346.4	346.7(5)	this work	0.063(4)
	C 23 H 45 OOH	351.7	352.0(5)	this work	0.073(4)

  •••O distances. Highly pure samples of C 13 H 25 OOH, C 15 H 29 OOH, C 17 H 33 OOH, C 19 H 37 OOH, C 21 H 41 OOH, and C 23 H 45 OOH were supplied by Fluka. The purities of all these compounds are estimated by the sup plier to exceed 99 %.

	Experimental Section
	Materials:


Improvements to the WRF-Chem model for quasi-hemispheric simulations of aerosols and ozone in the Arctic

Louis Marelle 1,2,a , Jean-Christophe Raut 1 , Kathy S. Law 1 , Larry K. Berg 3 , Jerome D. Fast 3 , Richard C. Easter 3 , Manish Shrivastava 3 and Jennie L.

DMS

Dimethylsulfide (DMS) oceanic emissions (NighFngale et al., 2000) and simple gas--phase chemistry [START_REF] Chin | A global three-dimensional model of tropospheric sulfate[END_REF].

SNOWDEP

Force reduced « winterFme » dry deposiFon of trace gases over seasonal snow.

SNOWPHOT

UV--albedo dependence on snow and ice cover for photolysis calculaFons.

NOAH_SEAICE

Correct skin temperatures over melFng ice in the Noah Land Surface Model.

KFCUP_CHEM

Include the recent KF--CuP cumulus parameterizaFon (Berg et al., 2015) including the effect of cumulus clouds on aerosols and trace gases (removal, transport, cloud chemistry)

• Updates are evaluated by turning off indivual updates one by one.

• We also perform NO_UPDATES and ALL_UPDATES simulations.

Effect of the updates on zonal mean PM 10 in the Arc/c (60°N -90°N, April--July average)

--KFUP_CHEM decreases are mostly due to increased wet removal by cumuli --NOAH_SEAICE reduces sea ice skin temperatures, increasing stability over sea ice, reducing verFcal mixing.

Evalua/on against mean rBC profiles from the ARCTAS campaigns (2008)

--BC RMSE reduced by 28 % (spring) and 50 % (summer), due to KFCUP_CHEM. Evalua/on against surface measurements in the Arc/c

Effect of the updates on surface O 3 (April--July average)

•

  Improve WRF--Chem's performance compared to recent intercomparisons (AMAP, 2015) in order to study aerosols and ozone in the the ArcFc (long--range transport, local sources). • We idenFfy missing processes in WRF--Chem 3.5.1, update the model, and evaluate the corrected model in the ArcFc. WRF--Chem 3.5.1 simulaFons, 1 March 2008 to 1 August 2008 • MOSAIC aerosols (cloud chemistry and SOA), SAPRC--99 gas--phase chemistry • Morrison 2--moment microphysics • KF--CuP cumulus parameterizaFon • Noah Land Surface Model • MOZART boundary and iniFal condiFons • Nudging to NCEP FNL Domain (100 x 100 km resoluFon) and locaFon of the measurements Update name Descrip/on SEDIMENTATION Aerosol sedimentaFon above the first model level.

  Thomas 1 1 LATMOS/IPSL, UPMC Univ. Paris 06 Sorbonne Universités, UVSQ, CNRS, Paris, France 2 Total S.A., Direction scientifique, Paris La Défense, France 3 Pacific Northwest National Laboratory, Richland, WA, USA a Now at: Center for International Climate and Environmental Research, Oslo, Norway

and photolysis over snow

  (SNOWDEP & SNOWPHOT) have a large effect on ozone.• Halogen chemistry and detailed DMS gas-phase chemistry, as wells as higher resolutions are needed to improve results further.

	• Model updates reduce RMSE significantly (-10 % to -50 %)
	for all datasets. Large improvements for BC, especially
	during summer.
	-NOAH_SEAICE (improving skin temperatures over ice
	and stability) and KFCUP_CHEM (Including cumulus
	cloud interactions with aerosols and gases) have the
	largest effect on aerosols.
	-Improved deposition

EBC Sulfate

Spring Summer