Pascal Antoine

Bruno Dauvier

Eva Andreotti

Anne Congard

Individual differences in the effects of a positive psychology intervention: Applied psychology

Keywords: Positive psychology Self-help Mindfulness, Differential approach, Positive psychology intervention Cognitive emotion regulation

Objectives: A 6-week multicomponent positive psychology intervention (PPI) was assessed with the primary aim of determining its effects on affective variables including anxiety, depression and psychological distress, as well as processual ones, such as mindfulness and emotion regulation. Exploratory investigations were conducted to consider changes in individual differences according to baseline characteristics.

Method: Participants were from a community sample of the French population. They were assigned to the control (n = 43) or intervention group (n = 59). Self-assessment measures included the Mindful Attention Awareness Scale, Cognitive Emotion Regulation Questionnaire, Spielberger State-Trait Anxiety Inventory, Beck Depression Inventory and the General Health Questionnaire.

Results: Trait anxiety, depressive symptoms and psychological distress significantly decreased over the course of the PPI in comparison to the control group. Regarding processual variables, mindfulness increased with a large effect size, acceptance and positive reappraisal increased, and scores for otherblame strategy significantly de-creased. Exploratory analyses showed that mindfulness and positive reappraisal tended to increase even more when participants' initial levels were low.

Conclusion: Future clinical interventions should account for baseline characteristics to ensure that participants are referred to the most effective, suitable programs for their own needs.

Introduction

In recent years, conducting promising controlled interventions in-tended to reduce unpleasant feelings and enhance positive attributes has been a priority of the positive psychology field as part of efforts to promote mental health and well-being (Donaldson, Dollwet, & Rao, 2015;Rashid, 2015;Schueller & Parks, 2014). Obtaining a better un-derstanding of how to promote the experience of positive emotions is a fundamental aspect of positive psychology (Kobau et al., 2011). In-dividuals' responses to life events involve self-regulatory and conscious cognitive coping strategies. Affective experiences are greatly influenced by the emotion regulation strategies employed, and emotions can also influence the subsequent emotion regulation strategies used (Garnefski, Kraaij, & Spinhoven, 2001;Pavani, Le Vigouroux, Kop, Congard, & Dauvier, 2016). According to Fredrickson's (2001) Broaden-and-Build model, negative emotions narrow the thought-action re-pertoire and promote reactions that rely on known patterns. Rumina-tion might therefore be a consequence of a narrowed thought-action repertoire that creates the experience of negative affect (Pavani et al., 2016). On the other hand, positive emotions broaden individuals' at-tentional field and thought-action repertoire. New ideas and actions build resources that can be implemented in various situations (Fredrickson, Cohn, Coffey, Pek, & Finkel, 2008). Thus, positive emo-tions might counter negative ones through an "undoing effect" (Fredrickson, Mancuso, Branigan, & Tugade, 2000). The positive re-appraisal coping strategy, which involves reframing negative events by recalling their positive components, has been shown to prevent the incidence of affective disorders and to trigger positive affect (Garnefski et al., 2002;Levine, Schmidt, Kang, & Tinti, 2012;Pavani et al., 2016). Therefore, conducting and examining interventions that aim to enhance cognitive emotion regulation strategies (Garnefski et al., 2001) appears worthwhile.

Meta-analyses of positive psychology interventions (PPIs) have shown moderate effects on depression and well-being (Bolier et al., 2013;Mitchell, Vella-Brodrick, & Klein, 2010;Sin & Lyubomirsky, 2009). Specific findings have indicated a lower level of depression (Fava, Rafanelli, Cazzaro, Conti, & Grandi, 1998;Proyer, Gander, Wellenzohn, & Ruch, 2016b;Roepke et al., 2015;Schueller & Parks, 2012;Seligman, Rashid, & Parks, 2006;Seligman, Steen, Park, & Peterson, 2005) and negative affectivity (Moskowitz et al., 2012) and increases in well-being (Fava et al., 1998;Proyer et al., 2016b;Seligman et al., 2005), positive affectivity (Emmons & McCullough, 2003;Moskowitz et al., 2012) and life satisfaction (Lyubomirsky, Sousa, & Dickerhoof, 2006), as well as better physical and mental health (Lyubomirsky et al., 2006). The effective-ness of PPI in terms of affective variables has received substantial support; however, clarifying the underlying processes remains of in-terest.

The positive psychotherapy theory synthesizes the underlying me-chanisms of several PPIs: attention and memory re-education, changes in behavioral aspects and strength promotion (Walsh, Cassidy, & Priebe, 2016). For example, present-focused attention would allow for the identification of individuals' potential strengths (Shapiro, Schwartz, & Santerre, 2002) and therefore contribute to reducing psychological disorders, including anxiety and depression (Khoury et al., 2013) As positive psychology calls for the implementation of activities that favor well-being, we deliberately used a multidimensional and multi-component approach, as variety in programs has been associated with positive benefits (Parks, 2015;Parks, Della Porta, Pierce, Zilca, & Lyubomirsky, 2012;Thompson, Peura, & Gayton, 2015). Six main axes were defined according to the literature. These axes aimed to implement timely intentional activities and are more specifically de-fined below. According to the positive psychotherapy theory (Walsh et al., 2016), PPIs require three phases: engagement (similar to the committed flow experience when strengths are mobilized to solve a challenge; Nakamura & Csikszentmihalyi, 2014), pleasure (with positive emotions that individuals can mindfully experience, savor and amplify) and meaning and purpose in life (when actions occur in a broader field than one's existence), as outlined in Seligman's (2002) happiness com-ponent model. To address these constructs, the PPI we designed focused on both the "subjective" and "individual" levels of positive psychology (Meyers, van Woerkom, & Bakker, 2013) and purposely adopted no-tions from eudaemonist and hedonist doctrines (Ryan & Deci, 2001). The activities were designed based on the concept of psychological well-being (Ryff & Keyes, 1995) and therefore encompassed notions of selfacceptance, personal growth, purpose in life, positive relationships, environmental mastery and autonomy. Furthermore, close attention was paid to activities that were in line with life satisfaction and affec-tive life according to the subjective well-being model (Diener, 1994). Therefore, participants were presented with pleasant, engaging and meaningful activities that were consistent with their own aspirations and were included in the positive psychotherapy theory and Seligman (2002). Accordingly, several constructs were considered: the self-con-cordance motivation model (Sheldon & Elliot, 1999;Sheldon & Lyubomirsky, 2006) and the person-activity fit model, in-cluding characteristics of and congruence between activities and in-dividuals as well as psychological processes, involving positive psy-chology exercises effectiveness (Lyubomirsky & Layous, 2013;Schueller & Parks, 2014).

Moreover, as duration and format have been shown to influence outcomes, with longer interventions producing better outcomes than shorter ones (Sin & Lyubomirsky, 2009), we decided to implement this PPI over 6 weeks.

Self-help interventions might offer an accessible way of overcoming individual's reticence to attend one-on-one therapy and could integrate sessions as complementary resources (Norcross, 2006). As these inter-ventions often rely on self-administered activities, positive psychology approaches seem adequately suited to offer self-help interventions (Mitchell, Stanimirovic, Klein, & Vella-Brodrick, 2009;Parks, 2015).

The PPI we designed was meant to be easily self-administered and to not require clinician intervention.

Our approach aimed to address the need to disseminate alternative, innovative, cost-effective and evidence-based self-help psychological tools among the numerous re-sources available for individuals seeking personal and positive devel-opment (Bolier et al., 2014;Kazdin & Blase, 2011;Schueller & Parks, 2014).

In most cases, the effects of PPIs have been studied using between-group analyses; however, such outcomes do not consider variance within groups (Woodworth, O'Brien-Malone, Diamond, & Schüz, 2016). Reducing data to averages might result in a loss of information; for example, participant samples might be heterogeneous and contain several subgroups (Schueller & Parks, 2012;e.g., in terms of psycholo-gical distress;Parks et al., 2012), and adverse effects might not be taken into consideration (Parks, 2014;Rozental et al., 2014). Exploratory analyses might highlight the differential effects of this PPI by in-vestigating the affective and processual variables involved and the participants' initial levels of these variables. Indeed, according to their dispositional characteristics, individuals' competencies in emotion regulation and mindfulness might experience different influences throughout the course of the PPI. Accordingly, our intervention design expanded to observe this potential phenomenon.

In summary, this study evaluated a 6-week self-help PPI that was based on six focal areas of activities that were supported by the lit-erature. The primary aim of this study was to assess the effects of this PPI on affective and processual emotion regulation variables. We hy-pothesized that, compared to a control group, participants in the self-administered PPI group would show significant improvement from pre-test to post-test in variables such as anxiety, depression and psycholo-gical distress. Furthermore, we hypothesized that significant processual changes in mindfulness and in cognitive strategies regarding emotion regulation would occur over the course of the PPI, based on comparisons with a control group. The exploratory aim of the study was to consider the differences in individuals' progress according to their specific characteristics at baseline. We aimed to understand the differ-ential effects of the PPI according to the individual's baseline char-acteristics.

Method

Participants

The participants' characteristics are displayed in Table 1. In total, 167 people from the French population were contacted from September 2013 to December 2013 by Lille University psychology students. The recruitment pool covered their social networks (i.e., relatives, online or leisure networks). Overall, 108 individuals voluntarily agreed to par-ticipate and were assigned to the intervention group. The control data corresponded to a control group previously assessed in a study sharing the same methodological design (n = 43). The exclusion criteria in-cluded people who had Axis 1 disorders, were receiving therapy and were deaf. To be included in the study, participants had to be over 18 years old. The criteria were based on participant reports. No re-muneration was provided.

Procedure

This study was approved by the French Ethical Research Comity Nord Ouest III. Information about the study was provided through letters, emails, phone calls, and face-to-face meetings. All the participants included in the study provided written informed consent. Detailed information regarding the experimental procedure is displayed in the flow chart (Fig. 1). Baseline questionnaires were completed by the intervention group participants, and they began the 6-week PPI three days later. The PPI was mailed to each participant with detailed instructions and the investigators' contact information. Immediate posttest questionnaires were completed three days after the end of the program. The control group had already completed the pre-test and post-test questionnaires during a former study based on the same design.

Positive psychology program overview

This program was based on a review of the PPIs in the literature and was adapted for the French population. The intervention included a diary that the participants kept as well as daily activities that required no more than 20 min per day to complete. This PPI was organized around six main axes:

-"A pleasant life": participants looked for and savored positive emotions in their daily experience. Additionally, they learned how to recognize pleasant moments and to cultivate feelings of gratitude (Bryant, Smart, & King, 2005;Emmons & McCullough, 2003;Seligman et al., 2005;Sheldon & Lyubomirsky, 2006).

-"Self-discovery": participants were invited to discover their key strengths and qualities as well as ways to apply them concretely in their daily life. Development of kindness was especially emphasized (Moskowitz et al., 2012;Otake, Shimai, Tanaka-matsumi, Otsui, & Fredrickson, 2006).

-"Positive relationships with others": participants' practices were shifted towards building and maintaining quality relationships by acknowledging others' qualities, experiencing gratitude, savoring fulfilling relationships, reflecting about a difficult communication exchange, and practicing listening to others effectively (Gable, Reis, Impett, & Asher, 2004).

-"Negative events/positive reappraisal": this aspect of the program aimed to reduce the emotional impact of a negative event (Gross, 2001). To do so, participants were suggested to observe and to approach negative life events by taking a step back, while considering emotions that rose; this method allowed them to reframe the facts and to look for potential benefits in the particular situation (Seligman et al., 2006).

-"Mindfulness": participants were taught to contemplate rising emotions, thoughts, and sensations as they experienced them. The suggested exercises included two formal meditation practices, i.e., a body scan and a mindful breathing exercise, and informal practices, such as walking mindfully and discovering their environment as if for the first time.

-"Personal development, meaning and purpose in life": this axis encompassed aspects of control over the environment and autonomy.

Participants were encouraged to find themselves in situations in which the decisions they made were congruent and true to their life purpose, allowing them to evolve in a chosen direction. Questions about values transmitted and shared with others were raised (Ben-Shahar, 2010). Participants were invited to plan ahead to identify ways of continuing to practice certain positive psychology activities.

Measures

Observance

The number of positive psychology activities completed was reported daily by the participants on a separate form.

Socio-demographic variables

A questionnaire was administered to collect information about participants' age, sex, family, education status and previous experience with mindfulness.

Mindfulness

Competence in mindful attention and awareness towards present experiences were measured using the French version of the Mindful Attention Awareness Scale (Brown & Ryan, 2003;Jermann et al., 2009).

This questionnaire evaluates the perceived frequency of trait mindful awareness as a single construct.

The 15 items ask participants to reply on a 6-point Likert scale ranging from 0 (almost always) to 6 (almost never). The internal consistency of the French version was 0.84 (Jermann et al., 2009).

Cognitive emotion regulation measure

The Cognitive Emotion Regulation Questionnaire (CERQ) was used to identify specific and conscious cognitive emotion regulation strategies exhibited by the individual after experiencing aversive life events (Garnefski et al., 2001). This 36-item questionnaire encompasses nine subscales representing nine coping strategies: Self-Blame, Acceptance, Rumination, Positive Refocusing, Planning, Positive Reappraisal, Putting into Perspective, Catastrophizing and Other-Blame. Answers are rated on a 5point scale ranging from 1 (almost never) to 5 (almost always).

The internal consistencies of the French version of the CERQ subscales were found to range from 0.68 to 0.87 (Jermann, Van der Linden, d'Acremont, & Zermatten, 2006).

Affective variables

Anxiety was assessed with the French version of the Spielberger State-Trait Anxiety Inventory (STAI, Spielberger, Gorsuch, & Lushene, 1970;Gauthier & Bouchard, 1993). The trait anxiety scale is composed of 20 items that measure trait anxiety as the frequency of perceiving external events as threatening on a 4-point scale ranging from 1 (no) to 4 (yes).

This scale showed a 0.91 internal consistency in this population.

Depressive symptomatology was assessed with the 13-item Beck Depression Inventory -Short Form (Beck & Beamesderfer, 1974).

Participants selected the responses to three suggestions that reflected their state of mind on a 4-point scale from 0 (none) to 3 (severe depressive symptom). The internal consistency of the French version was α= 0.90 (Bourque & Beaudette, 1982).

To evaluate psychological morbidity and distress and to uncover any arising psychiatric disorders, the General Health Questionnaire -12 (GHQ-12, Goldberg et al., 1997) was used. This self-assessment measure is rated on a 4-point scale (0-3) outlining the frequency with which respondents had experienced the symptoms described in the 12 items in the past weeks (from "more so than usual" to "more less able" for positive questions and from "not at all" to "much more than usual" for negative questions). The French translation has been validated and found to have an internal consistency of 0.78 (Salama-Younes, Montazeri, Ismaïl, & Roncin, 2009).

Statistical analyses

Statistical analyses were conducted with R software version 3.1.2 for Windows. Groups were compared regarding socio-demographic information and baseline variables with chi-square analyses, betweengroup differences were assessed with two-tailed t-tests (see Table 2), and subgroups were analyzed with the Mann-Whitney U test. A repeated-measures analysis of variance (ANOVA) was conducted to study the interaction effects between group and time. Effect sizes were calculated to rate the significance of the intervention's impact on several variables. Inter-individual differences in variables were analyzed with a generalized linear model (GLM), which required the "lme4" library.

Results

Differential attrition

In total, 102 datasets were examined: 59 in the intervention group and 43 in the control group (see Fig. 1). Two sets of questionnaires from the control group and one from the intervention group were excluded because of missing data. Table 1 presents the participants' general characteristics. The inclusion criterion for the analyses of the intervention effects and processes was set at completion of 75% of the activities. This strict adherence level was based on a desire to increase the reliability of the assessment of this PPI's quality and efficacy. Twelve participants dropped out over the course of the program. Eight persons did not complete more than one-fourth of the program, and six completed between 25% and 49% of the suggested activities. Twenty participants completed between 50% and 75% of the program.

The baseline characteristics of the participants who dropped out (n = 12) were compared with those of the intervention group using the Mann-Whitney U test and Χ2 test. Marital status was the only nonequivalent variable at baseline, with 61% of the participants in the intervention group being single compared to 16% in the drop-out group [Χ2 (4, n =71) =12.6, p = 0.013]. Participants who completed <75% of the program (n= 34, M =41.6, SD = 13.73) tended to be older than those who completed> 75% (n =59, M= 37.0, SD = 12.29), t(91) = 1.669, p =0.09.

PPI effects

The groups were found to be equivalent at pre-test for all variables except education level and professional status based on Χ2 and t-tests.

Intervention participants had on average 9.4 years of schooling after primary school (SD =3.02), whereas control group participants had received 8.3 years (SD = 3.19), t(100) = 1.90, p = 0.05. In the intervention group, 89.8% of the participants were professionals and 6.8% were students, whereas in the control group, 65.1% were professionals and 30.2% were students [Χ2 (2, n= 102) = 10.22, p = 0.006].

To study the effects of the group x time interaction on the variables of interest, repeated-measures ANOVA was conducted (see Table 2).

Affective variables such as trait anxiety, psychological distress and depressive symptoms significantly decreased in the intervention group, with a moderate effect size, whereas the control group displayed no such improvements. Processual variables such as daily mindful attention increased with a large effect size in the intervention group but not in the control group. Some cognitive emotion regulation strategies significantly changed over the course of the program in the intervention group compared to the control group: acceptance and positive reappraisal scores increased with small effect sizes, while use of the otherblame strategy decreased. Other-blame and positive refocusing increased in the control group but not in the intervention group. Although putting into perspective and positive refocusing strategies increased significantly in the intervention group, no between groups interactions were found. No significant effects were observed for catastrophizing, planning, rumination or selfblame.

3.3. Individual differences in PPI effects according to baseline characteristics

General procedure

Inter-individual differences for all variables showing significant comparison outcomes were assessed using a GLM. The aim of these exploratory analyses was to identify the profiles that would benefit from the PPI by comparing differences in effects according to differences in baseline characteristics between the two groups from pre-test to post-test.

3.3.2. Individual differences in PPI effects according to MAAS and CERQ positive reappraisal scores

In Fig. 2, the graph on the left shows the evolution of individual MAAS scores from pre-test on the xaxis to post-test on the y-axis; each single dot represents a participant. Gray dots indicate control group participants, and black dots represent PPI participants. In this type of graph, if there was no intervention impact, the dots would be around the diagonal dotted line (light gray), demonstrating an identical score before and after the PPI. Thus, dots located under the diagonal dotted line represent individuals whose scores decreased from pre-test to posttest.

In most cases, the black dots are above the diagonal dotted line, indicating that participants who completed the PPI showed improved MAAS scores during the intervention. The GLM analyses indicated what occurred in the control group (gray line) and the intervention group (black line). The experimental group black line is above the diagonal line on the left side of the graph and thus shows that MAAS scores increased significantly for individuals starting with a lower level. A significant interaction effect was observed between the MAAS baseline and post-test levels by group, with r reflecting the interaction coefficient

[t= -3.319, r = -0.47, p < 0.001]. Participants' levels of daily mindful attention increased even more when they had low baseline scores, whereas participants who started with higher MAAS scores did not progress from pre-test to post-test.

Subsequently, analyses of the CERQ subscales were conducted and showed significant mean changes from baseline to post-test. In these analyses, we aimed to account for specific variables that might exhibit potential for improvement. Positive reappraisal was the only subscale that showed such a tendency, as shown in the graph on the right.

Indeed, an interaction effect between the evolution of positive reappraisal from pre-test to post-test and group was observed, although it was not significant [t= -1.825, r= -0.27, p= 0.07]. Thus, participating in the PPI led to an increased frequency of positive reappraisal use among participants, especially when their baseline levels were low.

Discussion

This study investigated how a multicomponent PPI could promote changes in affect by exploring the underlying potential mechanisms and the different patterns of change over the course of the intervention.

First, this self-administered intervention experienced less attrition than the rates reported in the literature. Indeed, up to 87% of the initial sample returned post-test data, and 54% of the intervention group completed > 75% of the activities. As hypothesized, and consistent with the literature, we witnessed moderate changes between pre-test and post-test in affective variables such as trait anxiety, depression symptoms and psychological distress (Sin & Lyubomirsky, 2009). Mindful attention in daily life significantly improved over the course of the intervention with a strong effect, while slight patterns in change occurred for acceptance, positive reappraisal and other-blame among the cognitive emotion regulation strategies assessed with the CERQ (Garnefski et al., 2001).

This multicomponent intervention represented an opportunity to target different underlying regulatory processes through six main axes (Quoidbach, Mikolajczak, & Gross, 2015). The variety of activities might explain the slightly better attrition rate compared to those of other studies, as this diversity could have acted as a protective factor against hedonic adaptation to positive outcomes (Parks et al., 2012;Parks-Sheiner, 2009;Roepke et al., 2015;Schueller & Parks, 2012). Indeed, the participants might have found adequate and relevant activities that they could implement in their daily life, as proposed in the person-activity fit model (Schueller & Parks, 2012). Considering discrepancy between engagement in appreciated activities and the benefits received, offering a large variety of activities by axis might have enhanced strategies that otherwise were neglected (Parks et al., 2012). Additionally, given the mostly fixed program, participants could experiment with activities they were not familiar with, potentially building additional competencies (Quoidbach et al., 2015;Schueller & Parks, 2012).

Measuring mindfulness in a PPI was an innovative step that resulted in major improvements.

Mindfulness has a shared history with positive psychology (Hamilton, Kitzman, & Guyotte, 2006;Niemiec, 2012;Shapiro et al., 2002) and emotion regulation strategies (Brockman, Ciarrochi, Parker, & Kashdan, 2017;Chambers, Gullone, & Allen, 2009).

One axis was dedicated to mindfulness and was incorporated throughout the PPI. Mindfulness might play a significant role in the initiation of emotion regulation strategies, which in turn could reduce perceived distress, anxiety and depressive symptoms (Chiesa, Anselmi, & Serretti, 2014;Garland, Farb, R. Goldin, & Fredrickson, 2015). Furthermore, trait mindfulness mediates the use of maladaptive coping (Keng & Tong, 2016), such as rumination and experiential avoidance strategies (Chiesa et al., 2014). Recently, mindfulness was considered an emotion regulation strategy that represented an overarching contextual adaptive profile (Brockman et al., 2017;Chambers et al., 2009).

One of the main contributions of this study was that it provided evidence that a PPI could enhance positive reappraisal and acceptance and reduce other-blame. Other cognitive emotion regulation strategies did not evolve over the course of the program; it is possible that our PPI did not implement activities targeting all strategies. Other-blame represents a sense of powerlessness and absence of mastery, which would not allow for transformations in experience (Tedeschi, 1999); this strategy has been found among people experiencing relational stress (Schroevers, Kraaij, & Garnefski, 2007). Two of the activities in the "Positive relationships with others" axis encouraged individuals to take a step back in relational situations, and these activities might have influenced the use of this strategy. Acceptance and positive reappraisal were found to reduce psychological distress and avoidance strategies when facing adverse events (Wolgast, Lundh, & Viborg, 2011). Acceptance appears to be strictly opposed to experiential avoidance and would enable increased tolerance to aversive emotional stimuli (Wolgast et al., 2011). Acceptance seems to be covered by both emotion regulation and mindfulness concepts, given the overlap between attention towards the moment, acceptance of experience, identification of one's inner experience and ability to address unpleasant experiences (Bishop et al., 2004;Coffey, Hartman, & Fredrickson, 2010;Shapiro et al., 2002). Therefore, this strategy might have been enhanced by the axes selected to orient the program.

One program axis was specifically dedicated to regulating negative emotions with positive reappraisal; participants could thus learn to transform the content of their cognitive and affective events (Chambers et al., 2009). Developing this type of strategy might enhance positive attitudes towards life challenges and contribute to individuals' wellbeing (Levine et al., 2012). Positive reappraisal is hypothesized to be supported by mindfulness through a metacognitive process involving decentering, alternatively approaching life events with acceptance and changing usual cognitive patterns (Garland, Gaylord, & Park, 2009;Garland, Kiken, Faurot, Palsson, & Gaylord, 2016). This process, which represents an upward spiral, would broaden the attention field and enhance savoring, and thus all experiences would be considered factors in individuals' growth and transformation (Garland et al., 2015;Garland et al., 2016). Experiencing rewards from beneficial daily events and savoring were specifically addressed in the "Pleasant life" axis and would also foster this upward spiral (Garland et al., 2015(Garland et al., , 2016)). The relationship between positive reappraisal and mindfulness was found to be reciprocal, according to the process model of mindful positive emotion regulation (Garland et al., 2016). Nevertheless, this finding introduces a paradox: mindfulness favors a non-evaluative perspective, and antithetically, positive reappraisal reframes meanings of adverse experiences to assign a positive valence (Chambers et al., 2009;Garland et al., 2015). Accordingly, individuals would not only interpret fixed and negative events without changing the reality but would also broaden their understanding spectrum from negative aspects to positive aspects. Awareness of this cognitive phenomenon would occur simultaneously, allowing individuals to "let go".

Another contribution of this study was the investigation of different patterns of change according to individuals' baseline characteristics. The exploratory analyses highlighted that mindfulness and positive reappraisal tended to increase to a greater extent when participants' initial levels were low. A similar pattern was previously observed for mindfulness in a mindfulness-based intervention, but no relation could be found between positive reappraisal at baseline and its progression (Garland et al., 2016). This growth might have been enhanced as part of the upward spiral proposed in the process model of mindful positive emotion regulation (Garland et al., 2015). Our design addressed several of the limitations of PPIs that were primarily based on aggregated interindividual data analyses; however, more effort should be devoted to account for differential and intra-individual perspectives (Molenaar & Campbell, 2009;Woodworth et al., 2016).

The limitations of this study should be discussed as well as the resulting implications. The sample was self-selected, which might contribute to enhancing the program impact, as PPIs have been found to be more effective when congruent with individuals' interests, motivations, needs and values (Lyubomirsky, Dickerhoof, Boehm, & Sheldon, 2011;Sin & Lyubomirsky, 2009). Identifying methods to evaluate factors influencing participants' outcomes might be an interesting perspective.

Considering the composite nature of the program design, the findings cannot be attributed to any particular activity, as they stem from a combination of approaches; accordingly, whether combining positive psychology and mindfulness masked the specific effects remains unclear. Future research is still needed to establish the differential effects of activities at the individual level (Woodworth et al., 2016), as well as to personalize activities according to participants' characteristics (Quoidbach et al., 2015). Moreover, as the relationship between the number of activities delivered and the outcomes seems to be curvilinear (Schueller & Parks, 2012), more studies are needed to address this topic and to study the optimal number of daily exercises needed to produce lasting positive results. Adding wellbeing and affectivity measures appears necessary for outcomes to be considered within the scope of the literature. In addition, follow-up assessments to consider the evolution of the sample should be added to future study designs.

Overall, this study provided evidence that a 42-day PPI enhanced mindfulness and emotion regulation strategies as well as reduced anxiety, depression and psychological distress. The exploration of differences in outcomes identified a greater progression in mindfulness and a tendency towards positive reappraisal throughout the PPI among participants who had lower baseline levels. As emotional dysregulation appeared to be associated with affective disorders (Chambers et al., 2009), further empirical research in the emotion regulation field is warranted to better understand the influence of PPIs.


Mathilde Tiennot
email: mathilde.tiennot@gmail.com

Odile Majérus

Daniel Caurant

Gilles Bastian

Myriam Eveno

Elisabeth Ravaud

Colourless Powdered Glass as a Drier for Red Lakes: On the Influence of Composition and Particle Size

Keywords: Powdered glass, Oil paint, FTIR, Red lakes, Historic sources, Drier

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Introduction

For over a century, scholars have begun to take note of references relating to use of powdered glass as an additive to paint [START_REF] Merrifield | Original Treatises, dating from the XVIIth to XVIIIth Centuries on the Arts of Painting[END_REF]. Sporadic observations of transparent particles in oil paintings from 15 th -17 th -century have been reported since the 1970s (Figure 1). Evidence of this painting studio practice was presented and discussed in 2003 and 2004 during the international studies of a large corpus of paintings by Perugino and Raphael [START_REF] Martin | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF][START_REF] Spring | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF][START_REF] Spring | Raphael's painting technique: working practices before Rome[END_REF]. In subsequent years, additional studies have focused on glass additives found in German, Flemish, French, Spanish and Portuguese school paintings from 15 th -17 th -century [START_REF] Martin | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF][START_REF] Spring | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF][START_REF] Seccaroni | Proc LabS Tech Work Quad di Kermes[END_REF][START_REF] Berrie | Scientific Examination of Art: Modern Techniques in Conservation and Analysis[END_REF][START_REF] Lutzenberger | [END_REF]8,9,10]. Several hypotheses have since been presented in an attempt to explain the addition of glass to oil paint mentioned in historical recipes and contemporary sources: a) to increase the transparency of the paint b) to modify the texture and application of the paint and c) to act as a drier. Our study focuses on the latter and aims to study the siccative effect of powdered glass on painting layers. In this introduction, we first review the historical sources mentioning explicitly the use of glass powders as driers, before presenting our experimental strategy.

Several historical sources, reviewed below, document the use of powdered and/or crumbled glass added to oil paint, particularly when the paint contains lake pigments. The siccative property of powdered glass is mentioned in various historical treatises that include additional technical information relating to paint preparation. These sources need a careful attention, as the word 'glass' could be mistranslated or misunderstood. Spring [8] and Van de Graaf [11], for instance, have already pointed out that terminology associated with "glass" could also refer to 'resin'. The sources mentioned discuss the uses of glass in paint [START_REF] Lutzenberger | [END_REF]12,[START_REF] Ancel | L'utilisation du verre broyé dans les couleurs des peintures de chevalet à travers les sources historiques du xve au xviie siècle[END_REF]. The first mention of glass as a paint additive can be found in 15th century manuscripts, referring specifically to powdered glass being added to aid in the grinding of pigments such as orpiment [START_REF] Cennini | Il Libro dell'arte[END_REF][START_REF] Merrifield | Original Treatises, dating from the XVIIth to XVIIIth Centuries on the Arts of Painting[END_REF]. To our knowledge, the oldest treatise indicating that pulverised glass can be used as a drier for paint is the Paduan manuscript (Ricette per far ogni sorte di colori ), dated around 1580 and discussed in [START_REF] Merrifield | Original Treatises, dating from the XVIIth to XVIIIth Centuries on the Arts of Painting[END_REF]. Another major historical source from the late 16th century is the anonymous French manuscript BnF Ms.Fr.640 [START_REF] Ms | Recueil de recettes et secrets concernant l'art du mouleur[END_REF]. According to our researches on this primary source document, it should be dated from 1585 [START_REF] Ravaud | Back to basics : Proceedings of the sixth symposium of the ICOM-CC Working Group for Art Technological Source Research[END_REF]. This manuscript details the use of powdered/crushed glass as a drier when added to paint with a specific reference to lakes. In Folio 58v (58v in modern numbering, 56 of the historic numbering) for instance, the author indicated that "le cristallin estant broye [...] se broie avec la laque et avec l'aspalte qui ne seichoient de fort long temps sans cela", translated as "The cristallin glass being ground [...] is ground with lake and asphaltum which would not dry for a long time without it". This manuscript also mentioned in Folio 57r (57r in modern numbering, 55 historical one) that "la laque est longue a seicher a huile Et pour ceste occasion il faut parmy broyer du verre Mays il fault choisir du cristallin pour ce quil est plus net", translated as "Lake is long to dry in oil And for this occasion one has to grind it with glass But one has to choose cristallin glass because it is cleaner". The term "cleaner" in this context probably means with less impurities.

Then, in most of the 17 th -century sources documenting, glass used as an additive to paint is described as a drier. From the early 17 th -century, the de Mayerne manuscript describes in Folio 85v the glass as one of the driers a painter can use [START_REF] Turquet De Mayerne | Pictorja Sculptorja et quae subalternarum artium, british library[END_REF]: "les grands a" b" c" siccatifs pour estre meslés parmy les couleurs sont l'alun bruslé, la coupperose, l'umbre, la mine, le vert de gris", translated as " The strong siccatives to be bound with colours are burnt alum, vitriol, umber, red lead, verdigris". There is also a note in the margin that states the following: " Verre de Venise ou simplement broyé ou estient en eau plusieurs fois, seiché et broyé", which means "Venitian glass either ground or quenched into water several times, dried and ground". In Folio 18r, we can read that "Les couleurs qui ne seichent point le feront en y adjoustant le verdegris ou la couperose, ou du verre christallin pulverisé impalpablement [...] La laque ne sèche jamais de soy meme", meaning that "The colours that do not dry will do with added verdigris or vitriol, or cristallin glass ground to an impalpable powder [...] Lake never dries alone". 'Impalpablement' is a precise term and means that the glass should be extremely finely ground until no granularity is detected. Throughout the 17 th -century, several sources mention the use of finely ground glass powder to be used as a drier for colours that dry slowly when bound in oil, and especially for lakes. Such reference include the Turquet de Mayerne, Brussels, Baldinucci, and Pacheco manuscripts [START_REF] Turquet De Mayerne | Pictorja Sculptorja et quae subalternarum artium, british library[END_REF] (fol. 12r, 18r), [START_REF] Pacheco | Arte de la pintura, su antiguedad, y grandezas. Descriuense los hombres eminentes que ha auido en ella, assi antiguos como modernos, del dibujo, y colorido; del pintar al temple, al olio[END_REF] (p.388), [START_REF] Merrifield | Original Treatises, dating from the XVIIth to XVIIIth Centuries on the Arts of Painting[END_REF], (p.200-202).

Several technical examinations confirmed the presence of colourless glass particles in various layers of paintings [START_REF] Spring | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF][START_REF] Spring | Raphael's painting technique: working practices before Rome[END_REF][START_REF] Lutzenberger | [END_REF]8,10]. Observations of 15 th -16 th -century Italian and French school paintings at the Centre de Recherche et de Restauration des Musées de France (C2RMF) allowed the identification of these colourless glass particles in numerous easel paintings [START_REF] Martin | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF]. Based on SEM-EDS observations and 2D-image analysis of samples, the amount of glass particles as well as their morphology, length, size distribution within the painting stratigraphies and composition were evaluated, and reported for instance in [START_REF] Lutzenberger | [END_REF]8,12]. Investigations have produced results similar to conclusions deduced from previous studies [START_REF] Martin | Postprints of the workshop on the painting technique of Pietro Vannucci, called il Perugino, organised[END_REF][START_REF] Cooper | [END_REF]. Particles ranging from 5 µm to 50 µm can be observed, most of them are either in the range of 5-10 µm, and 20-30 µm. The surface of the glass particles detected varies from 2 to 20 % of the total layer area and they present an homogeneous distribution within the considered layer. The morphology and distribution of these particles in historic painting layers could be studied following the non-invasive imaging approach proposed in [20]. The influence of grinding processes on the morphology, size and size distribution and on physical behaviour of glass mixed in paint was evaluated by means of OCT and nanoindentation on dried red lake layers.

The chemical composition of the glass particles observed in paint layers was investi-gated [START_REF] Cooper | Projet vip : Influence de l'addition de verre broyé sur les propriétés physicochimiques des couleurs employées en peinture à l'huile (artistique)[END_REF]. Previous studies detected manganese in the glass particles found in paintings [8]. As mentioned in sources since 1290, manganese oxides were commonly used to discolourise the glass and counter the naturel greenish tint induced by iron impurities [START_REF] Verità | Modern methods for analysing archaeological and historical glass[END_REF].

The manganese content has been suspected to be the source of the siccative effect [START_REF] Merrifield | Original Treatises, dating from the XVIIth to XVIIIth Centuries on the Arts of Painting[END_REF][START_REF] Lutzenberger | [END_REF]. This hypothesis is studied in the present paper. On another hand, the BnF Ms.Fr.640 manuscript, mentioned above, described carefully the siccative effect of glass added to paint [START_REF] Ms | Recueil de recettes et secrets concernant l'art du mouleur[END_REF]. This source pointed out that the glass to be used in this purpose should be cristallin glass (Folio 57r). The Folio 68r, related to casting of metal objects, provides a precise definition of cristallin glass, by comparison with commun glass (usual glass) : "Le cristallin est plus excellent car le commun ne tient que du sel de salicor, mays le cristallin tient du sel de tartre et de salicor tout ensemble, qui tout deux servent à la fusion", translated as "The cristallin is better because the commun consists only in salt of salicornia, but the cristallin consists in salt of tartar and salicornia all together, both of them helping the fusion". With this description, the tartar and salicornia are respectively identified as the potash and sodium sources in glass composition. In light of the late sixteenth century definition from the BnF Ms.Fr.640 manuscript, mixed sodium and potassium or cristallin glass was identified as the accurate drier when added to paint and lakes. Thus, the impact of the chemical content of the glass on the drying rates has to be studied with respect to both sodium and potassium, and manganese contents.

In this study, we propose an experimental investigation to evaluate the possible siccative effect of powdered glass added to oil paint, focusing on red lakes. We investigated the first steps of the drying processes of fresh red lakes prepared with cochineal lake pigment in boiled linseed oil. The detailed oxidative polymerisation mechanisms of drying oils, consisting in an autoxidation based on the reaction of hydroperoxides with the double bonds, and followed by polymerisation by decomposition of the peroxide groups, have been described in various research publications [START_REF] Lazzari | [END_REF]24]. These chemical reactions occurring along the curing of the oil upon exposure to oxygen can be studied by Fourier Transform Infra-Red (FTIR) analyses of paint samples [25]. Such methodology can estimate the drying rates and leads to discriminate oxidation and isomerization steps by monitoring samples over time. We studied the differences induced by the addition of glass particles in the natural drying. To further discuss the effect of the nature of the glass added as a drier for cochineal lake, we considered three varieties of glass: i) a common soda-lime industrial glass, ii) a sodium-potassium glass enriched in manganese, iii) the same sodium-potassium glass without manganese. To evaluate the influence of the shape of the glass, we considered two ranges of particles sizes and studied their siccative effect. As mentioned earlier, this study is part of a larger experimental research on the various effects of the addition of crushed glass in paint layers [START_REF] Cooper | Projet vip : Influence de l'addition de verre broyé sur les propriétés physicochimiques des couleurs employées en peinture à l'huile (artistique)[END_REF]20].

Experimental

Materials

Fresh red lake paint samples were prepared using cochineal pigment bound in linseed oil. The cochineal pigment was purchased at Sennelier (reference 133677 by Couleurs du Quai Voltaire), and the presence of carminic acid was confirmed by chromatography. The linseed oil was purchased at D. Plantes and was boiled for two hours at 120 • C [START_REF] Yvel | Le métier retrouvé des maîtres[END_REF].

Three varieties of glass with different chemical compositions were selected to evaluate the possible impact of the nature of the alkalis and total alkali content on the drying mechanisms associated with cochineal lake. The first glass particles result from the grinding of a commercial soda glass container, henceforth named modern glass. The second and third glasses were elaborated for this research [START_REF] Cooper | Projet vip : Influence de l'addition de verre broyé sur les propriétés physicochimiques des couleurs employées en peinture à l'huile (artistique)[END_REF]. The composition of the second and third glasses can be described as follows: A) the second glass is enriched in potassium and sodium according to the description of the cristallin glass in Folio 68r of the BnF Ms.Fr.640 manuscript, and slightly enriched in manganese and iron for our investigation. This glass is henceforth designed as Mn-enriched cristallin glass. B) The third glass has a similar composition as the second but does not contain manganese or iron. The manganese content was lowered on purpose to evaluate the impact of this element on the drying process. This third glass is henceforth designed as Mn-free cristallin glass. The chemical compositions of the raw glass materials, measured by Proton Induced X-Ray Emission (PIXE) analyses, are reported in Table 2.1 [START_REF] Cooper | Projet vip : Influence de l'addition de verre broyé sur les propriétés physicochimiques des couleurs employées en peinture à l'huile (artistique)[END_REF].

Caption of the Table 2.1: Composition of the modern, Mn-free cristallin and Mnenriched cristallin glasses used for the research, measured by PIXE analyses and presented in [START_REF] Cooper | Projet vip : Influence de l'addition de verre broyé sur les propriétés physicochimiques des couleurs employées en peinture à l'huile (artistique)[END_REF]. 1 mol% Eu 2 O 3 was added to the batch composition of the prepared glass to allow to follow possible glass alteration in paint by luminescence spectroscopy (Eu 3+ ion is an optically active local probe that can be used to probe glass structure and alteration [START_REF] Ollier | Conference on Dynamical Processes in Excited States of Solids[END_REF][START_REF] Molières | Angeli[END_REF]). These studies are not presented in the present paper.

We used two sets of glass particles, the first one with particles ranging from 25 µm to 32 µm, and the second one with particles around 10 µm in diameter [START_REF] Cooper | Projet vip : Influence de l'addition de verre broyé sur les propriétés physicochimiques des couleurs employées en peinture à l'huile (artistique)[END_REF]. The preparation of the particles at specific ranges was performed following a protocol presented in [START_REF] Alloteau | Contribution à la compréhension des mécanismes de l'altération atmosphérique et étude d'un traitement de protection à base de sels de zinc. application à la conservation des objets en verre du patrimoine culturel[END_REF]. Manual grinding was first used employing a mortar and pestle in order to produce millimeter-sized glass particles. Smaller particles from 125 µm to 80 µm were separated using sieves. After a ultrasound separation of the < 80 µm particles in ethanol, the fraction between 25 to 32 µm was obtained using the finest sieves easily available. Finally, sedimentation (employing Stokes law and using ethanol as the suspension liquid) was performed in order to separate particles that were less then 10 µm in length. This powder fraction was washed to eliminate the very fine particles, so that the particle size fraction finally obtained is estimated at 5-10 µm. Irregular angular shape similar to the one observed in historical paint layers (Figure 1) results from this preparation.

Red lake samples

Five red lake samples were prepared and stored under controlled laboratory conditions (T = 21 • C, RH = 50 %). First, the required proportions of oil to cochineal pigment was determined to provide an easy-to-apply red lake, with a deep colour and glaze effect, as well as an adequate consistency for brush application. The reference red lake consists of 0.3 g of cochineal pigment in 0.42 ml of linseed oil, mixed together with a mortar and a glass board (Figure 2). Then, we studied the effect of the addition of 20 % in mass (with respect to the pigment's mass), ie 0.06 g of powdered glass, and mixed the oil-pigment and glass together under the same protocol.

Analytical protocol -FTIR spectroscopy analyses

FT-IR analyses were carried out to evaluate the drying and curing processes of the samples, by following the evolution of the degree of oxidation and isomerisation. Spectral changes, like variation in intensity, disappearance/appearance or broadening of the IR absorption peaks were used as markers of the oil curing steps. The natural drying under laboratory conditions (T = 21 • C, RH = 50 %) was followed directly on the paint film applied on ZnSe discs, using a Frontier spectrometer, in transmission mode. The spectra are 20-scans summation over a range from 4000 cm -1 to 500 cm -1 at a 4 cm -1 resolution. The rotation of the supporting disc does not modify the acquired spectrum. We studied the impact of glass as a siccative additive for fresh lakes, and performed the analyses during the first four months of drying. The reactions were followed along the drying at and after the application, at 3 hours, 24 hours, 1 and 2 weeks, 2, 3, and 4 months.

Spectral Changes Corresponding to Oil Polymerization

After the paint samples were prepared, the autooxidation and polymerization of the linseed oil was followed as the paint was exposed to atmospheric oxygen over a period of time. The various steps involved with the drying processes, reflected by the structural changes of the oil polymer, have been followed by IR analyses in previous studies [START_REF] Lazzari | [END_REF][START_REF] Van Den | Analytical chemical studies on traditional linseed oil paints[END_REF][START_REF] Mallégol | [END_REF]24,25]. Based on these studies, the following spectral changes can be expected: -The amount of the cis-double bonds present will decrease and ultimately disappear, which is highlighted by the corresponding decrease of the bands at 3010 cm -1 and 722 cm -1 -A decrease in peak intensities at 2927 cm -1 and 2855 cm -1 , markers that indicate advanced stages of oxidation -The C=O peak at 1744 cm -1 may progressively shift to 1740 cm -1 and can show a broadening in association to oxidation products -A decrease in peak intensity at 1652 cm -1 (assigned to -CH=CH vibrations) as well as the formation of the shoulder peak at 1633 cm -1 (assigned to the conjugated C = C carboxyles); both are the markers of the isomerisation process -the triglycerides region and the triad at 1238 -1164 -1101 cm -1 may show a broadening and increase during oxidation processes.

We focus on the differences on these specific spectral regions and bands to evaluate the effect of glass particles as a drier for the cochineal lake and to underline the differences induced in the drying processes. The significant evolution on the spectra and their initiation time are indicated on the figures.

Results

Monitoring the Natural Drying Processes Associated with

Red Lake Paint

The spectra acquired for the sample of pure cochineal lake bound in oil during the first few weeks monitoring are presented in Figure 3. Some features can be related to the carminic acid of the cochineal used as a pigment for the red lakes, like the 660 cm -1 and 1562 cm -1 bands assigned to aromatic functions, the 771 cm -1 and the 880 cm -1 band (OH group) [32,33]. The signal of the specific bands assigned to the carminic acid do not evolve during the early stages of the drying. On another hand, some modifications of the signal are observed in the 1600-1652 cm -1 region (Figure 3). The appearance of a shoulder associated with the 1633 cm -1 peak, attributed to the conjugated C=C, was initiated after 1 week of drying, as well as the decrease of the 1652 cm -1 band. Both of these observations are related to the isomerisation process of the linseed oil. A slight decrease of the cis C=C 3010 cm -1 band is initiated after 3 months of drying.

Siccative effect of powdered glass

Modern glass

The IR absorption spectra of the samples prepared with the modern glass particles with sizes ranging from 25 to 32 µm show an evolution of the 1600-1652 cm -1 region along the first weeks of drying, with the progressive decrease of the 1652 cm -1 peak and the 1633 cm -1 shoulder appearance (Figure 4). The size of the modern glass particles does not influence the drying: the spectra obtained with the addition of the 10 µm particles present the same modifications with time than the ones observed for the lakes with the 25 to 32 µm particles (Figure 4). Moreover, the addition of modern powdered glass does not induce significant difference in the chemical Transmittance (a.u.)

Wavenumbers

Figure 3: Evolution of the FTIR spectrum of reference cochineal lake bound in linseed oil, in the range of 4000 cm -1 -500 cm -1 from the application of the paint to 4 months of natural drying evolution of the red glaze layer. The results are similar for the red lake used as reference and when modern glass is added to the layer.

Manganese-enriched cristallin glass

The influence of the sodium potassium glass enriched in manganese added to red lakes on their drying rates is then illustrated in Figure 5. For both 10 µm and 25-32 µm grain sizes, the 1633 and 1652 cm -1 bands/shoulders also evolve after 1 week of natural drying (Figures 5).

Significant differences appeared in the evolution of the cis double-bonds at 3010 cm -1 . While there was no significant evolution of the absorption band for the previous samples (Reference and with modern glass in Figures 3 and4), the decrease of the cis C=C bonds at 3010 cm -1 for the red lakes with 25-32 µm Mn-enriched cristallin particles starts after 2 months of drying (Figure 5). Compared with the drying rates identified for the reference cochineal lake (Figure 3), the decrease of the 3010 cm -1 band after 2 months of drying is a marker of the accelerated isomerisation processes induced by the powdered Mn-enriched cristallin glass.

Furthermore, when 10 µm particles of Mn-enriched cristallin glass are added to the paint, this 3010 cm -1 band disappears, starting from 2 weeks of drying, alongside the progressive decrease of the 722 cm -1 band (Figure 5). The combined evolution of these bands indicates a cis-trans isomerisation of the double-bonds, initiated during the 2 first weeks of natural drying. Moreover, with the addition of particles of 10 µm Mn-enriched cristallin glass, the intense 1744 cm -1 band shows a broadening and begins to shift at 1740 cm -1 , also after 2 weeks of drying (Figure 5). These broadening and shifting continue along the natural drying of this sample. Thus, the addition of particles of 10 µm of Mn-enriched cristallin glass clearly speeds up the isomerisation process of the oil.

Manganese-free cristallin glass

To evaluate the influence of the alkali content on the drying processes of the red lakes, the cristallin glass without manganese was added to paint. FTIR results obtained with from the application of the paint to 4 months of natural drying the 25-32 µm particles and the 10 µm particles are presented in Figure 6. These two particles sets induce the same decrease of the 1652 cm -1 peak and the 1633 cm -1 shoulder appearance observed after the first two weeks of drying. However, major differences are identified in the drying evolution with the 3010 cm -1 evolution. The decrease of the cis C=C bonds at 3010 cm -1 starts after 1 month, and disappears after 2 months with the 25-32 µm particles of Mn-free cristallin glass, alongside the broadening of the 1744 cm -1 , as described for the Mn-enriched cristallin glass. On another hand, the paint mixed with the 10 µm in size particles of the sodium potassium glass without manganese does not present significant evidence of accelerated drying processes during the first months.

In conclusion, these results illustrate differences in the drying process, with respect to the composition and size of the glass particles. We observed that : i) after 2 months, 25-32 µm particles of both sodium-potassium enriched glass with a high amount of manganese, and without manganese, induce an accelerated natural drying; ii) the 10 µm particles significantly speed up the drying process of the red lakes within two weeks, only when the glass contains a higher manganese content.

Discussion

In this study we were able to apply FTIR as a means of monitoring the natural drying processes associated with cochineal lake bound in linseed oil as well as evaluating the potential effect of the glass powder added as a drier. Our results point out differences in the drying with respect to the nature of the glasses we investigated, modern, Mnfree cristallin, Mn-enriched cristallin" as well as the size of the particles. The modern glass does not seem to influence the drying of the red cochineal lakes we prepared. An accelerated drying is identified with the 25-32 µm Mn-free and Mn-enriched alkali glass. The 10 µm particles of Mn-enriched alkali glass significantly speed up the drying process. The modern glass composition contains higher Al 2 O 3 and CaO contents, indicating a strong chemical durability. Indeed, a slight increase in Al 2 O 3 content in the glass, by only a few 0,1 wt%, strongly improves the durability especially when subjected to a basic or neutral pH [34,[START_REF] Hamilton | Practical Implications of Glass Structure[END_REF]. Raising the alkaline earth oxides at the expense of alkali or SiO 2 also considerably increases the chemical durability in water, so that alkaline earth oxides are referred to as « stabilizers » [START_REF] Hench | [END_REF]37]. This stabilizing effect, attributed to the high ionic strength of alkaline earths with respect to alkalis and to structural aspects, culminates at about 10-12 wt% of CaO, beyond which value an opposite effect is observed. In historic glassware, the CaO/SiO 2 ratio is one important parameter which is used to evaluate the overall durability of the glass, having typically 5-10 wt% CaO, from poorly durable one having less than 5 wt% CaO (the terms « stable » and « unstable » are also used in this context) [38,[START_REF] Verità | Modern methods for analysing archaeological and historical glass[END_REF][START_REF] Melcher | Glass Degradation by Liquids and Atmospheric Agents[END_REF][START_REF] Iliffe | [END_REF][START_REF] Davison | Conservation and restauration of glass[END_REF]. Thus, the modern glass, with its high Al 2 O 3 and CaO contents, may be less likely to interact with its surrounding environment. Furthermore, based on our FTIR results, the sodium and potassium content in the glass composition is of major interest for the siccative action. The greater efficiency of the two glasses with a high sodium and potassium content in enhancing the chemical transformation of the linseed oil may be related to the poorer chemical durability, as compared to the commercial modern glass. Indeed, alkali silicate glasses are chemically reactive to water. Their high content in alkali induces reaction processes like hydration, selective leaching by ionic exchange and hydrolysis [START_REF] Conradt | [END_REF]43,[START_REF] Bunker | PAC RIM Meeting on Glass and Optical Materials[END_REF][START_REF] Hench | [END_REF]. Such processes result in the release of chemical species from the glass (metallic cations and silicate anions), with alkalis typically being released faster than other species. Chemical durability directly refers to the kinetics of this glass-water reactivity, which is highly dependent on the composition of the glass. An important parameter is the nature of the alkali, or N a 2 O/K 2 O ratio. Potassic glasses are generally less durable than sodic glasses [START_REF] Bunker | [END_REF]46,[START_REF] Wittstadt | Crizzling -exploring degradation and simulation on model glasses[END_REF]. Mixed alkali glasses having both alkali types tend to be more durable in liquid water, because of structural and electronic modifications decreasing the alkali mobility (mixed alkali effect). However, this trend may not be true when this type of glassware is subjected to high levels of humidity as potassium-containing glass seems to be less durable against weathering [48,49,50]. Then, the nature of the alkali is a compositional parameter that also controls the stable/unstable classification of glasses [38,[START_REF] Verità | Modern methods for analysing archaeological and historical glass[END_REF][START_REF] Melcher | Glass Degradation by Liquids and Atmospheric Agents[END_REF][START_REF] Iliffe | [END_REF][START_REF] Davison | Conservation and restauration of glass[END_REF]. From the composition of the materials we tested, a higher chemical reactivity with water -liquid and moisture content -of the two sodium-potassium bearing glasses is predictable, compared to the modern glass.

However, in the paint layers, the binding medium in which the drying processes reactions occur is oil, and the chemical reactivity as well as the degradation products of glass mixed in the oil-pigment systems is at stake. To the authors knowledge, the reactivity of glass in oil needs further investigation. Water is likely to be detected in the linseed oil during the natural drying. We can expect that the reactivity of the glass with liquid water and moisture content that may be present in the system, by releasing OH-ions and alkalis, may induce chemical reactions with the triesters like saponification and produce fatty acids and alcohols. These species may act as ligands towards metallic cations of the glass, accelerating their release from the glass surface. The enhancement of the glass dissolution by organic acids has been put in evidence in several studies [51,52,53,54] and attributed to protonation of the glass surface and chelation of the metallic surface sites by the anionic acid. Thus, the oil medium may be favourable to the extraction of cationic species from the glass, which may in turn be responsible for the siccative effect of glass particles. Further studies are necessary to investigate these hypotheses. Thus, these hypotheses may explain the effective siccative effect of the two sodium-potassium glasses. Moreover, the manganese content in glass also influences the natural drying rates of the red lakes, with respect to the size of the particles. The reactions and mechanisms involving manganese as related to drying rates and chemical processes seem to be active when the glass particles are the smallest. The finer the Mn-enriched cristallin glass particles, the stronger is their siccative effect on our cochineal lakes. This phenomenon may be in close correlation with the increase of the surface area, allowing the proposed reactions to occur. The accelerated drying rates may also be the consequences of the release of manganese ions in the drying paint system, activated during the grinding process used to produce finer particles. The influence of the grinding process of glass on the mechanical behaviour of lakes after natural drying was also investigated in [20], and the results indicate that the finer glass particles induce the higher effect on the properties. All these results illustrate the differences related to the extremely finely ground particles, described in the historic sources.

Practical recommendations about studio practices concerning the addition of glass, crushed and finely pulverized, as a solid drier for paint layers (especially red lakes), mentioned the higher efficiency of such glass particles. As early as the late sixteenth century, the nature of the glass, and the impact of the potash and soda sources, were identified as a key parameter to ensure a proper siccative effect of the glass particles in paints and lakes that need a long time to dry. Based on this research, the combination of a higher sodium-potassium content and a higher manganese content, as well as the size of the particles, seem to be both crucial parameters for the efficient siccative effect of glass added to paint.

Conclusion

FTIR analyses allowed the investigation of the effect on the addition of colourless powdered glass on the drying of red lakes. A siccative action of glass particles added to colours that require a long dry time is mentioned in several historic sources, as well as the importance of the size. We studied the influence of the composition and size of the glass particles on the drying of cochineal lake. Differences are identified in the natural drying, with various sodium-potassium and manganese contents. Our results illustrate that 25-32 µm particles of both soda-potassium enriched glass with a high amount of manganese, and without manganese, induce an accelerated natural drying of cochineal lakes and that only the 10 µm particles with a higher manganese content significantly speed up the drying process of the red lakes. Thus, the siccative effect of cristallin colourless glass, a soda-potassium glass enriched in manganese, and the influence of the particles size of the finely ground glass, added to cochineal lakes is observed and quantified by these FTIR analyses. Such modification of the drying rates may be related to the reactivity of the glass with the binding medium, that highly depends on the composition of glass. This research is a step further to uncover the rationale behind the addition of colourless glass to paint.

Figure 1 :

 1 Figure 1: Déploration sur le Christ mort, Bronzino, 1540-1545, (Inv D799.1.29, Musée des Beaux-Arts et d'archéologie de Besançon, France) -Optical microscope, under UV light and SEM observations of a cross-section from the red drapery of Marie-Madeleine, revealing angular crumbled glas particles with irregular shape (indicated with arrows) ( c M. Eveno)

CompositionFigure 2 :

 2 Figure 2: Preparation of the red lakes fresh paints, with cochineal bound in linseed oil using a mortar and a glass board ( c M. Tiennot)

Figure 4 :

 4 Figure 4: Evolution of the FTIR spectrum of cochineal lake bound in linseed oil with 25-32 µm and 10 µm particles of modern glass, in the range of 4000 cm -1 -500 cm -1 from the application of the paint to 4 months of natural drying

Figure 5 :Figure 6 :

 56 Figure 5: Evolution of the FTIR spectrum of cochineal lake bound in linseed oil with 25-32 µm and 10 µm particles of Mn-enriched cristallin glass, in the range of 4000 cm -1 -500 cm -1 from the application of the paint to 4 months of natural drying

Acknowledgements

This work was supported by the Paris Seine Graduate School Humanities, Creation, Heritage, Investissement d'Avenir ANR-17-EURE-0021 -Foundation for Cultural Heritage Science. The authors thank Isabelle Biron (C2RMF) for the fruitful discussions and help about the nature and composition of the glasses. The authors also thank Lucy Cooper and Berfin Karakalic for the preparation of the glasses considered in the present research.

Competing interests

The authors do not have any competing interest.