Alide A Tieleman

Hans Knoop

PhD Anne-Els Van De Logt

Md ; Gijs Bleijenberg

PhD ; Baziel

G M Van Engelen

PhD Sebastiaan Overeem
email: s.overeem@neuro.umcn.nl

PhD Md

Poor sleep quality and fatigue, but no excessive daytime sleepiness in myotonic dystrophy type 2

Keywords: myotonic dystrophy type 2, sleep quality, fatigue, excessive daytime sleepiness, myotonic dystrophy type 1

Background: In myotonic dystrophy type 1 (DM1), sleep disorders are common, with excessive daytime sleepiness (EDS) as a predominant feature. In myotonic dystrophy type 2 (DM2), the presence of sleep disturbances is unknown.

Objective: To investigate the frequency of EDS, poor sleep quality and fatigue in DM2.

Methods:

We surveyed 29 genetically proven DM2 patients with the Epworth Sleepiness Scale (ESS), Pittsburgh Sleep Quality Index (PSQI) and Checklist Individual Strength (CIS). The results were compared with 29 adult-onset DM1 patients and 65 population controls, both matched for age and sex.

Results: Only 6.9% of DM2 patients had EDS compared to 44.8% of DM1 patients and 6.2% of population controls (DM2-DM1: p=0.001, DM2-controls: p=0.51). Sleep quality was poor (PSQI >5) in both the DM2 and DM1 group, and differed significantly from population controls (DM2: 6.5 ± 3.0; DM1: 6.2 ± 3.7; controls 4.3 ± 3.0) (DM2-controls: p=0.002). Poor sleep quality was not explained by depression or other co-morbidity, but mainly due to sleep disturbances as a result of nocturnal pain.

Comparable to the DM1 group, DM2 patients experienced severe fatigue (DM2: 38.7 ± 13.1; DM1: 42.9 ± 8.5; controls: 21.1 ± 11.1; DM2-controls: p<0.001). Results were not confounded by abnormal thyroid function or medication use.

Conclusion:

These results provide new insight into the phenotype of DM2, and have consequences for clinical treatment. In addition, the absence of EDS in DM2 is a new discriminative feature with adult-onset DM1.

INTRODUCTION

The myotonic dystrophies (DM) are dominantly inherited multisystem diseases, with muscle weakness and myotonia as the main neuromuscular symptoms. Other organs are prominently involved, with frequent early-onset cataracts, cardiac conduction abnormalities, gastro-intestinal symptoms, endocrine changes and central nervous system symptoms. [START_REF] Harper | Myotonic Dystrophy: present management, future therapy[END_REF][START_REF] Tieleman | Gastrointestinal involvement is frequent in Myotonic Dystrophy type 2[END_REF][START_REF] Meola | Cerebral involvement in myotonic dystrophies[END_REF] Myotonic dystrophy type 1 (DM1) is the most common form of muscular dystrophy in adults, with a prevalence of 5-12 per 100,000. [START_REF] Harper | Myotonic Dystrophy: present management, future therapy[END_REF][START_REF] Norwood | Prevalence of genetic muscle disease in Northern England: in-depth analysis of a muscle clinic population[END_REF] The phenotype and genetics of myotonic dystrophy type 2 (DM2) have been described only recently, and its prevalence has not yet been established. [START_REF] Ricker | Proximal myotonic myopathy: a new dominant disorder with myotonia, muscle weakness, and cataracts[END_REF][START_REF] Liquori | Myotonic dystrophy type 2 caused by a CCTG expansion in intron 1 of ZNF9[END_REF] The molecular basis of both DM1 and DM2 is a repeat instability in a noncoding part of a gene: a CTG-trinucleotide repeat in the DMPK gene on chromosome 19 (DM1) and a CCTG-tetranucleotide repeat in the ZNF9 gene on chromosome 3 (DM2). [START_REF] Liquori | Myotonic dystrophy type 2 caused by a CCTG expansion in intron 1 of ZNF9[END_REF][START_REF] Brook | Molecular basis of myotonic dystrophy: expansion of a trinucleotide (CTG) repeat at the 3' end of a transcript encoding a protein kinase family member[END_REF] The resulting disruption of mRNA metabolism alters nuclear functions, including the splicing machinery. This leads to abnormal transcripts in many other genes, explaining the multisystemic nature of the diseases. [START_REF] Brook | Molecular basis of myotonic dystrophy: expansion of a trinucleotide (CTG) repeat at the 3' end of a transcript encoding a protein kinase family member[END_REF] Interestingly, repeat instability in two unrelated genes causes comparable clinical phenotypes. In fact, DM2 was not recognized as a separate disorder until 1994. [START_REF] Ricker | Proximal myotonic myopathy: a new dominant disorder with myotonia, muscle weakness, and cataracts[END_REF][START_REF] Thornton | Myotonic dystrophy with no trinucleotide repeat expansion[END_REF] However, some recent studies suggest important differences in the clinical symptomatology of DM1 and DM2. For example, the severe congenital form encountered in DM1 is absent in DM2, and there is no confirmed evidence of anticipation in DM2.

Sleep disorders are very common in DM1, and are in fact considered a core feature. Of these, excessive daytime sleepiness (EDS) is a predominant symptom. [START_REF] Harper | Myotonic Dystrophy: present management, future therapy[END_REF][START_REF] Hilton-Jones | Myotonic dystrophy--forgotten aspects of an often neglected condition[END_REF][START_REF] Laberge | Fatigue and daytime sleepiness in patients with myotonic dystrophy type 1: to lump or split?[END_REF][START_REF] Park | Hypersomnolence in myotonic dystrophy: demonstration of sleep onset REM sleep[END_REF] EDS in DM1 can be severe, and has been described to resemble the sleepiness of primary hypersomnias such as narcolepsy. Besides daytime sleepiness, severe fatigue is present in up to 74% of adult-onset DM1 patients.

12 In contrast to DM1, virtually nothing is known about sleep and fatigue in DM2. Some authors have suggested a comparable presence of daytime sleepiness in DM2, [START_REF] Moxley | III. 54th ENMC International Workshop: PROMM (proximal myotonic myopathies) and other proximal myotonic syndromes. 10-12th October 1997[END_REF][START_REF] Meola | Executive dysfunction and avoidant personality trait in myotonic dystrophy type 1 (DM-1) and in proximal myotonic myopathy (PROMM/DM-2)[END_REF] but systematic studies are lacking. We therefore performed a nationwide study into EDS, sleep quality, and fatigue in a cohort of DM2 patients, and compared these symptoms with both a matched group of adult-onset DM1 patients and with population controls.

METHODS

Subjects

All known Dutch DM2 patients (N=32) were approached to participate. DM2 patients, and sex-and age-matched DM1 patients were retrieved from CRAMP, the Dutch neuromuscular database.

Questionnaires

Sleep quality

Nocturnal sleep quality was assessed using the Pittsburgh Sleep Quality Index (PSQI). [START_REF] Buysse | The Pittsburgh Sleep Quality Index: a new instrument for psychiatric practice and research[END_REF] The PSQI is a self-rated questionnaire that measures seven components of sleep over a 1-month time interval: In all cases, a score of '0' indicates no difficulty, while a score of '3' indicates severe difficulty. The sum of the seven component scores is expressed as a global score, with a range of 0-21 points. The normal threshold is 5; higher scores indicate poorer sleep quality. [START_REF] Buysse | The Pittsburgh Sleep Quality Index: a new instrument for psychiatric practice and research[END_REF] Excessive Daytime Sleepiness Daytime sleepiness was measured with the Epworth Sleepiness Scale (ESS). [START_REF] Johns | A new method for measuring daytime sleepiness: the Epworth sleepiness scale[END_REF] The ESS measures the tendency to fall asleep during eight different situations that are commonly encountered in daily life, yielding a score range of 0-24. The upper limit of normal is 10, and ESS scores above 10 are generally taken to reflect abnormal daytime sleepiness.

Fatigue severity

The presence of fatigue was assessed using the subscale 'fatigue severity' of the Checklist Individual Strength (CIS). [START_REF] Prins | Cognitive behaviour therapy for chronic fatigue syndrome: a multicentre randomised controlled trial[END_REF] The CIS measures the experience of fatigue-associated problems during the previous two weeks. The CIS-fatigue severity subscale contains eight items scored on a 7-point Likert scale. Scores can range between 8 and 56; higher scores indicate higher levels of fatigue and scores of 35 or more are considered to indicate severe fatigue. [START_REF] Prins | Cognitive behaviour therapy for chronic fatigue syndrome: a multicentre randomised controlled trial[END_REF]

Co-morbidity and medication use

All participants filled out a standardized questionnaire regarding medication use. When available, thyroid function data was retrieved from the patients' medical files. Symptoms of depression were scored using the Beck Depression Inventory for primary care (BDI-pc). This shortened version of the BDI has seven items and includes cognitive and affective symptoms. [START_REF] Kalkman | Different types of fatigue in patients with facioscapulohumeral dystrophy, myotonic dystrophy and HMSN-I. Experienced fatigue and physiological fatigue[END_REF] Somatic symptoms of depression have been removed, to avoid overlap when used for patients with e.g. neuromuscular disorders. A score of 4 or more is indicative of clinical depression.

Statistical analysis

Numerical variables are shown as mean ± standard deviation (range). Categorical data is shown as a number (percentage of total). One-way ANOVAs were used to compare the three study populations.

Differences between DM2 and DM1 patients and between DM2 patients and population controls were then tested using t-test or chi-square test. Correlations were calculated with the Pearson coefficient.

P-values below 0.05 were considered to be significant.

RESULTS

Demography

Of the 32 DM2 patients that were approached, 29 (91%) responded and completed the questionnaires a home. DM2 patients originated from 12 unrelated families. A total of 34 matched DM1 patients were selected from the CRAMP database, 5 of which were excluded because of the use of modafinil (n=4)

or nocturnal continuous positive airway pressure (n=1). The demographic characteristics of both patients groups and the population controls are listed in Table 1.

The groups were well matched for age, sex and body mass index (BMI). Age-at-onset was identical for the DM groups. There were no differences between the three groups regarding the use of betablockers or sleeping medication. A quarter of DM2 patients used pain medication, as did 14% of DM1

Sleep quality

Both DM2 and DM1 patients had significantly higher PSQI global scores than population controls, indicating a decrease in sleep quality (Table 2, Figure 1). Sixty-six percent of the DM2 group showed a poor sleep quality (PSQI >5) compared to 45% in the DM1 group and 26% in controls. (DM2 vs. controls: p < 0.001, DM2 vs. DM1: p = 0.11).

DM2 patients showed worst on the PSQI component subjective sleep quality, which differed significantly from population controls (See Table 3 for PSQI component scores). In addition, DM2 patients differed significantly from both DM1 patients and population controls regarding the PSQI component score sleep disturbances (Table 3). Pain was the most commonly reported cause for sleep disturbances in the DM2 group. Sixty-nine percent of DM2 patients reported pain as the cause of having had trouble sleeping during the past month, versus 34% of DM1 patients and 17% of controls (DM2 vs. DM1: p=0.009 and DM2 vs. controls: p<0.001). The PSQI component score daytime dysfunction was significantly higher in both DM2 and DM1 patients compared with population controls.

The component scores on sleep duration, sleep efficiency and the use of sleeping medication did not differ significantly between the three groups (Table 3).

The sleep latency in the DM2 group (28.

Excessive daytime sleepiness

Patients with DM2 did not have elevated ESS scores compared to population controls, and the percentage of DM2 patients with EDS was also in the control range (Table 2). One DM2 patient had an ESS just above the cut-off (11), one DM2 patient reported severe EDS, with an ESS of 20. This latter patient also had poor nocturnal sleep quality (PSQI 11), experienced severe fatigue (CIS-fatigue 56) and symptoms of depression (BDI-pc 5). As expected, DM1 patients showed a significantly higher ESS score than population controls. Forty-five percent of DM1 patients showed significant EDS (ESS >10), compared to 6% of the population controls (Table 2, Figure 1). Significant associations were found between depression scores and EDS in DM2 and controls (DM2: r=0.42, p=0.03; DM1: r=0.33, p=0.08; controls: r=0.42, p=0.001). ESS scores were not correlated with age, age at onset or disease duration.

Fatigue severity

DM2 patients experienced high levels of fatigue, with 66% reporting severe fatigue (Table 2, Figure 1).

This was also the case for DM1 patients with over 85% reporting severe fatigue (DM2 vs. DM1: p = 0.066). Both DM groups had significantly higher CIS-fatigue scores than population controls (Table 2, Figure 1). As with daytime sleepiness, fatigue correlated with depression scores on the BDI-pc in DM2

and controls (DM2: r=0.47, p=0.01; DM1: r=0.21, p=0.27; controls: r=0.52, p<0.001). Other demographic variables were not associated with fatigue, except a worsening of fatigue with age in DM1 (r=0.57, p=0.001).

DISCUSSION

We estimated the prevalence of poor sleep quality, daytime sleepiness and fatigue in patients with DM2, and compared these to adult-onset DM1 patients and population controls. DM2 patients showed significantly worse sleep quality than population controls. High levels of fatigue were equally present in both types of DM. In striking contrast to DM1 -in which EDS is a predominant feature-we found that daytime sleepiness is not part of the clinical picture of DM2.

DM2 and DM1 patients reported longer nocturnal sleep latencies than population controls. For DM1, this has been reported before. Laberge et al. found that only 47% of DM1 patients fell asleep within 30 minutes versus 76% of healthy controls, [START_REF] Laberge | Sleep complaints in patients with myotonic dystrophy[END_REF] although recent polysomnographic (PSG) data by this research group revealed a mean sleep latency of about 15 minutes in 43 DM1 patients. [START_REF] Laberge | A polysomnographic study of daytime sleepiness in myotonic dystrophy type 1[END_REF] The reason for the sleep onset insomnia in DM2 is unknown, and no PSG data of DM2 patients exists at the moment. It is likely that nocturnal myalgic pain is one of the influencing factors. Nocturnal sleep disturbances occurred significantly more often in DM2 than in DM1 or controls, and nocturnal pain was reported to be the most common cause. The prevalence of nocturnal awakenings because of pain was twice as high in DM2 compared with DM1. This high prevalence occurred despite the fact that almost a quarter of DM2 patients received pain medication at the time of study, and 10% used hypnotics.

Previous studies reported musculoskeletal pain to be a frequent symptom of DM2, and in one-third of patients, pain was even the most disabling symptom. [START_REF] George | Musculoskeletal pain in patients with myotonic dystrophy type 2[END_REF] The major pain type associated with DM2 is exercise-induced, with relief at rest. However, besides episodic pain, pain does persist for more than 6 months in many patients, indicating chronic pain. [START_REF] George | Musculoskeletal pain in patients with myotonic dystrophy type 2[END_REF] This is compatible with our finding of significant and sleep-disturbing nocturnal pain.

The mean ESS scores in patients with DM2 were identical to the population controls and comparable to previously reported normal values. [START_REF] Johns | A new method for measuring daytime sleepiness: the Epworth sleepiness scale[END_REF] Furthermore, the prevalence of excessive daytime sleepiness (ESS>10) in DM2 patients was equal to population controls. We confirmed the high prevalence of excessive daytime sleepiness in patients with DM1. [START_REF] Laberge | A polysomnographic study of daytime sleepiness in myotonic dystrophy type 1[END_REF][START_REF] Phillips | Daytime somnolence in myotonic dystrophy[END_REF][START_REF] Van Der | The relation between daytime sleepiness, fatigue, and reduced motivation in patients with adult onset myotonic dystrophy[END_REF] We excluded DM1 patients who were using psychostimulants for sleepiness, perhaps selecting patients with a relatively mild sleepiness.

Therefore, the difference in the prevalence of sleepiness in DM2 and DM1 may even be underestimated in our study. The reason for this difference remains unclear. It may be an indication for relatively minor involvement of the central nervous system in DM2, as has been suggested before.

3

Further study into the differential molecular pathophysiology of both disorders may also yield new insights in the pathogenesis of hypersomnia. It is unclear why the DM1 patients with EDS were not taking psychostimulants. As there was no obvious contraindication to the use of psychostimulants in the DM1 patient group, this may have reflected differences in clinical practice by the treating physician or patient decision.

The low prevalence of EDS, despite high levels of fatigue, underscores the fact that these are clearly different symptoms. [START_REF] Van Der | The relation between daytime sleepiness, fatigue, and reduced motivation in patients with adult onset myotonic dystrophy[END_REF] DM2 patients demonstrated high levels of fatigue, comparable with DM1. The proportion of DM2 patients with severe fatigue (66%) is also similar to figures reported for other neuromuscular disorders such as facioscapulohumeral dystrophy (61%) or hereditary motor and sensory neuropathy type 1 (64%). [START_REF] Kalkman | Experienced fatigue in facioscapulohumeral dystrophy, myotonic dystrophy, and HMSN-I[END_REF] Fatigue was not explained by medication use such as betablockers, or abnormal thyroid function.

Depression scores in both DM2 and DM1 were higher than in population controls. This has been repeatedly reported by others in DM1. [START_REF] Phillips | Daytime somnolence in myotonic dystrophy[END_REF][START_REF] Bird | Cognitive and personality function in myotonic muscular dystrophy[END_REF][START_REF] Duveneck | Depression in myotonic muscular dystrophy[END_REF] However, most of these studies were before the advent of DNA-based diagnosis and probably included a number of DM2 patients. Meola et al. investigated both DM1 and DM2 patients and did not find a higher frequency of clinical depression in either. [START_REF] Meola | Executive dysfunction and avoidant personality trait in myotonic dystrophy type 1 (DM-1) and in proximal myotonic myopathy (PROMM/DM-2)[END_REF] This difference may in part be explained by the smaller number of patients in their study and differences in study methodology (self-report versus structured interview). In the DM2 group as well as the controls, there were correlations between depression, sleepiness and fatigue scores. This is likely to reflect the fact that small increases in the ESS may not be specific for hypersomnia. The much higher ESS scores in DM1 patients point to more severe hypersomnia related to central nervous system dysfunction, which may occur independently of depression or fatigue. Depression was associated with sleepiness and fatigue scores in the DM2 group, and should be included in the differential diagnosis when DM2 patients experience hypersomnia.

We approached all known Dutch DM2 patients, from 12 families. The nationwide study combined with the high response rate of 91% makes the presence of a selection bias in the DM2 group unlikely.

Other strengths of this study are the DNA-based diagnosis of DM2 and DM1, the use of validated questionnaires and the consideration of comorbid depression and thyroid dysfunction. However, we are not informed about the range of CCTG-and CTG expansion on chromosome 3 and 21. Laberge et al found that DM1 patients with fatigue or EDS and fatigue had significantly longer CTG repeats than those with neither these symptoms. [START_REF] Laberge | Fatigue and daytime sleepiness in patients with myotonic dystrophy type 1: to lump or split?[END_REF] In DM2 however, phenotypical influence of the size of the CCTG-expansion -which is in part due to the somatic instability of the repeat-has not yet established. [START_REF] Day | Myotonic dystrophy type 2: molecular, diagnostic and clinical spectrum[END_REF] In conclusion, the absence of EDS in DM2 is another clinical feature that differentiates DM2 from DM1, in addition to absence of a severe congenital form and genetic anticipation. We have shown a decrease in the quality of sleep in patients with DM2. This poor sleep quality was not explained by depression or other co-morbidity, but mainly due to increased sleep latency and sleep disturbances.

Nocturnal awakenings due to pain were the most common symptom mentioned. Fatigue is another commonly experienced symptom in DM2, and is not correlated with the use of beta-blockers, thyroid dysfunction or a poor sleep quality.

  subjective sleep quality, sleep latency, sleep duration, habitual sleep efficiency, sleep disturbances, use of sleeping medication and daytime dysfunction. Each component score has a range of 0-3 points.

Future studies should assess

  the nature of the nocturnal sleep disruption in DM2 by polysomnographic assessment, for example to delineate the possible role of sleep related breathing disorders. Multiple sleep latency testing in DM2 patients would be less likely to demonstrate abnormalities in the absence of subjective daytime sleepiness on the ESS but may still be of value to perform as a more objective assessment. Future studies aiming to improve nocturnal sleep quality in DM2, may also assess the consequences on potential daytime sequalae such as depression, fatigue or health-related quality of life.Our findings may have important clinical consequences. In view of the negative impact of sleep disruption on the quality of life of DM2 patients, we would support a low threshold for screening for sleep disturbances -especially related to nocturnal myalgia-, and for performing sleep studies. In view of the findings in the current study, pain management throughout the day and night may improve sleep and quality of life in DM2 patients.

Figure 1 .

 1 Figure 1. Individual scores on the PSQI, ESS and CIS-fatigue. The cut-off for abnormal levels is indicated by a dotted line.

15

  Furthermore, 65 sex-and age-matched population controls were surveyed. All DM patients were above the age of 18, were ambulatory, and had a genetically confirmed diagnosis. Exclusion criteria concerned the use of central nervous system stimulant medication or assisted ventilation such as nocturnal continuous positive airway pressure. The presence of a neuromuscular disorder was the only exclusion criterion for the population controls. All subjects gave written informed consent to participate, and the study was approved by the local ethical committee.

  fall asleep within 30 minutes, compared to 59% in the DM1 group and 83% in the population control group. Total sleep duration was not different in the three groups.

	PSQI scores were not correlated with age, age at onset or disease duration. Furthermore, there was
	no association between depression or fatigue scores and PSQI total score in DM2 patients (DM2:
	r=0.29, p=0.13; r=0.35, p=0.06 respectively). In DM1 patients and controls, small but significant
	associations were found between the BDI-pc and PSQI (DM1: r=0.53, p=0.003; controls: r=0.29,
	p=0.02).

5 ± 26.1 minutes, range 2-120) was comparable with the sleep latency in the DM1 group (25.1 ± 26.4 minutes, range 2-120, p=0.63), both significantly longer than population controls (15.2 ± 12.6, range 3-60, p=0.001). Fifty-two percent of DM2 patients reported to

Table 2 .

 2 PSQI, ESS and CIS-fatigue score in DM2, DM1 and controls Data is shown as mean ± SD or N (%). PSQI = Pittsburgh Sleep Quality Index, ESS = Epworth Sleepiness Scale, CIS-fatigue = Checklist Individual Strength-fatigue score.

		DM2	DM1	Controls	P-value	P-value	P-value
					(ANOVA)	(DM2-DM1)	(DM2-Controls)
	N	29	29	65
	PSQI	6.5 ± 3.0	6.2 ± 3.7	4.3 ± 3.0	0.003	0.785	0.002
	PSQI > 5	19 (65.5%)	13 (44.8%)	17 (26.2%)	0.001	0.113	<0.001
	ESS	4.3 ± 4.5	9.6 ± 4.1	5.4 ± 3.9	<0.001	<0.001	0.214
	ESS > 10	2 (6.9%)	13 (44.8%)	4 (6.2%)	<0.001	0.001	0.508
	CIS-fatigue	38.7 ± 13.1	42.9 ± 8.5	21.1 ± 11.1	<0.001	0.149	<0.001
	CIS-fatigue ≥ 35	19 (65.5%)	25 (86.2%)	7 (10.8%)	<0.001	0.066	<0.001

Table 3 .

 3 Pittsburgh Sleep Quality Index (PSQI) component subscores in DM2, DM1 and controls

	PSQI component	DM2	DM1	Controls	P-value	P-value	P-value
					(ANOVA)	(DM2-DM1)	(DM2-Controls)
	Subjective sleep quality	1.1± 0.9	0.9± 0.7	0.7± 0.6	0.024		0.008
	Sleep latency	1.5± 1.1	1.0± 1.1	0.8± 0.7	0.010	0.147	0.001
	Sleep duration	0.3± 0.7	0.5± 0.7	0.4± 0.7	0.831	0.578	0.597
	Sleep efficiency	0.8± 1.2	1.0± 1.2	0.4± 0.8	0.016	0.449	0.075
	Sleep disturbances	1.4± 0.8	1.0± 0.7	1.1± 0.5	0.017	0.039	0.008
	Use of sleeping	0.1± 0.4	0.6± 1.1	0.3± 0.8	0.104	0.050	0.383
	medication
	Daytime dysfunction	1.2± 0.8	1.2± 0.9	0.7± 0.7	0.001	0.877	0.002
	Data is shown as mean ± SD or N (%).
	PSQI = Pittsburgh Sleep Quality Index

ACKNOWLEDGMENTS

We wish to thank the patients and controls for participating in this study and Dr. G. Borm for statistical assistance.

Data is shown as mean ± SD (range) or N (%). BMI = Body Mass Index.


L Malinowski

S Bielski

Transient temperature field in a parallel-flow three-fluid heat exchanger with the thermal capacitance of the walls and the longitudinal walls conduction

Keywords: Three fluid heat exchanger, Transient heat transfer, Implicit MacCormack method, Transient temperature field

Transient temperature response of a parallel-flow three-fluid heat exchanger with the thermal capacitance of the walls and the longitudinal heat conduction through the walls is investigated numerically, by the implicit MacCormack method, for a step change in flow rate of one fluid. The impact of thermal properties of the walls on temperature field is examined. The results of calculations show that as the thermal diffusivity of the walls decreases, the effect of the walls increases.

ACCEPTED MANUSCRIPT

With these assumptions, the model equations for heat transfer can be stated as

t x ∂ ∂ + + = ∂ ∂ T T V b 0 (1) 2 2 2 2
x y t x y

∂ ∂ ∂ + + + = ∂ ∂ ∂ w w w T T T A A u 0 (2)
where Anisotropic walls are assumed for calculations in order to allow for the impact of heat conduction across or/and along the walls being accounted for or not.

( ) ( ) ( ) 1 2 3 , , ,
T x t T x t T x t = T (3) ( ) ( ) ( ) 1 2 3 , , , , , , w w w

T x y t T x y t T x y t

= w T (4) 1 2 3 0 0 0 0 0 0 v v v = V (5)
y w y i i w w i i a c λ ρ = (9) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 3 1 3 2 1 2 1 2 2 2 2 3 2 3 2 3 3 3 3 , , , , , , , , , , , , , , , , , ,

x t T x y t b T x t T x y t b T x t T x y t b T x t T x y t b T x t T x y t b T x t T x y t

- + - = - + - - + - b (10) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 2 1 1 2 2 2 2 2 3 2 2 3 1 3 3 1 3 3 3 3 , , , , , , , , , , , , , , , , , ,

x y t T x t u T x y t T x t u T x y t T x t u T x y t T x t u T x y t T x t u T x y t T x t

- + - = - + - - + - u (11)
In this study a transient response of the heat exchanger is determined for a step change in flow rate of fluid no 1. For the case under consideration, the initial conditions are given by ( ) ( )

,0 x x = T ϕ ϕ ϕ ϕ (14) ( ) ( ) , ,0 , x y x y = w w T ϕ ϕ ϕ ϕ (15)
where

( ) ( ) ( ) ( ) 1 2 3 x x x x ϕ ϕ ϕ = ϕ ϕ ϕ ϕ (16) ( ) ( ) ( ) ( ) 1
The ( ) [START_REF] Das | Dynamic behaviour of plate heat exchangersexperiments and modeling[END_REF] Conditions [START_REF] Das | Dynamic analysis of plate heat exchangers with dispersion in both fluids[END_REF] and [START_REF] Das | Dynamic behaviour of plate heat exchangersexperiments and modeling[END_REF] mean that the edges of the walls are thermally insulated.

Numerical solution

The set of partial differential equations given by Egs. ( 1) -( 13) is solved numerically by means of the MacCormack implicit predictor-corrector method [22 -24]. This two-step finite difference method of second order accuracy is very effective for solving classical transient heat transfer problems in heat exchangers, both for a step change in flow rate and for a step change in inlet temperature [START_REF] Bielski | A semi-analytical method for determining unsteady temperature field in a parallel-flow three-fluid heat exchanger[END_REF][START_REF] Bielski | An analytical method for determining transient temperature field in a parallel-flow three-fluid heat exchanger[END_REF][START_REF] Malinowski | Equations for transient behaviour of parallel-flow multichannel heat exchangers[END_REF].

While meshing the walls we used only two node points in the y direction, situated on the surfaces of the walls, because L w << δ

. These nodes are designated as "a" and "b" (see Fig. 2). To simplify the solution of the problem given by Eqs. ( 1) and

(2), we replaced the two-dimensional equation of heat conduction (2) with a onedimensional equation in which the heat conducted in the y direction is considered as the heat generated by an equivalent heat source.

0 b T V T * = + ∂ ∂ + ∂ ∂ x t (21) 0 u T A T * w x w = + ∂ ∂ + ∂ ∂ 2 2 x t ( 22
)
Vector w T and matrix x A have now the following form, respectively The source term, u * , in Eq. ( 22) takes into account the heat exchanged in the y direction both by conduction and by convection. A numerical scheme for solving Eqs. ( 21) and ( 22) is developed on the basis of expressions formulated by MacCormack [START_REF] Maccormack | A numerical method for solving the equations of compressible viscous flow[END_REF]. The finite-difference representations of Eqs. ( 21) and ( 22 (  )

1 1 1 1 * 1 1 1 1 1 1 1 1 1 1 1 1 1 1 * 2 1 1 1 1 1 0.5
∆ ∆ - ≥ 0 , 5 . 0 max t x v i i φ 3 , 2 , 1 = i (29) ∆ ∆ - ∆ ≥ 0 , 2 5 . 0 max t x x a i wi φ 3 , 2 , 1 = i ( 30
)
Interconnections vectors * b and * u have the form

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 3 3 1 * 2 1 1 2 2 2 2 2 3 2 2 3 3 3 3 3 , , , , , , , , , , , ,
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 2 1 2 1 1 1 1 2 2 2 2 2 2 2 * 3 2 3 2 2 2 2 1 3 1 3 3 , , , , , , , , , , , , , , , , ,

x t T x t w T x t T x t u T x t T x t w T x t T x t u T x t T x t w T x t T x t u T x t T x t w T x t T x t u T x t T x t w T

- + - - + - - + - = - + - - + u ( ) ( ) ( ) ( ) ( ) ( ) 3
The value of coefficient i w results from the equality of heat conducted to a cell and the heat generated in the cell by an equivalent volumetric heat source with capacity vi q .

( ) x ∂ ∂ , is approximated with a central difference both in the case of predictor and corrector equations. In the implicit MacCormack method the calculation for each time step is divided into two stages. In the first stage, the explicit MacCormack method is used to calculate the changes in temperatures. In the second stage these changes are used in the implicit difference formula to determine the final temperatures for a given time step. Such two stages take place both at the predictor and corrector steps. During all calculations performed in this paper, we use the spatial step equal to 0.001

a
x m ∆ =
to achieve good accuracy of the results.

Validation of the model and method

The correctness of the mathematical model adopted and the method of solution used is verified by comparing the results obtained from the numerical method with those from a semi-analytical solution for the case of a co-current three-fluid heat exchanger with two thermal couplings [START_REF] Bielski | A semi-analytical method for determining unsteady temperature field in a parallel-flow three-fluid heat exchanger[END_REF]. The present model with three thermal couplings, accounting for the thermal capacity of the walls and heat conduction along the walls, is reduced to the model analysed in the work [START_REF] Bielski | A semi-analytical method for determining unsteady temperature field in a parallel-flow three-fluid heat exchanger[END_REF] by the adoption of the following data for calculations: Verifying calculations are carried out assuming that the system, initially at steady-state, undergoes an exponential rise of the inlet temperature of the fluid flowing through channel no. 1. The temperature profiles calculated using the semi-analytical method and the implicit MacCormack method are compared pictorially in Fig. 3. Very good consistency of the results is observed for the two methods applied.

Sample calculations

Sample calculations for the heat exchanger presented schematically in Fig. 1 are carried out using the implicit MacCormack method. The calculations account for the thermal capacity of the walls, longitudinal heat conduction through the walls, as well as the walls thermal resistance in the direction perpendicular to the heat exchanger axis.

We consider a case where heat is transferred from a hot fluid to two cold fluids. Such a case is encountered in various technological processes where one heating agent is used to warm two different fluids (or the same fluids to different temperatures). Our calculations do not concern one specific practical process. The date was selected to be

K m W = α , ) /( 2271 2 2 K m W = α , /( 3150 2 3 K m W = α
. The thermophysical parameters of the fluids correspond with the values for water. The thermophysical parameters of the walls have values corresponding to typical materials used for construction of heat exchangers: copper alloy C24000, stainless steel AISI 410 and titanium alloy Ti6Al4V. The thermal properties of these constructional materials are presented in Table 1.

In Figures 4567the transient response of the sample heat exchanger is presented for the case of a step-like twofold increase of fluid inlet velocity in channel no. 1. In our calculations we took into account the increase of heat transfer coefficient in channel no.1 resulting from the increase in the fluid velocity. Figure 4 shows the dimensionless exit temperatures of fluids, ( , characteristic for good heat conductors, such as copper alloy C24000 and stainless steel AISI 410, the impact of walls on the temperature field in the heat exchanger is negligibly small. The lower the value of thermal diffusivity (e.g. for titanium alloy Ti6Al4V), the higher the impact of walls on the temperature field in the heat exchanger.

min max min / , T T T t L T i i - - = Θ , ) [ ] ( )

Conclusions

Transient and steady state temperature fields have been determined, by the MacCormack implicit method, in a parallel-flow three-fluid heat exchanger with regard to the transverse resistance and thermal capacitance of the walls, as well as the longitudinal walls conduction. Impact of the walls material on the transient temperature profiles has been examined. This impact is not very large. The walls influence the fluids temperatures in three ways: (1) they resist heat conduction in the transverse direction,

(2) they accumulate heat during transient process, (3) they conduct heat longitudinally.

Good thermal conductivity of the walls increases the influence of longitudinal heat conduction and at the same time it decreases the effect of resistance in transverse direction. An increase in specific heat always enlarges the effect of the walls on the transient temperature field in the exchanger. Low thermal conductivity and high specific heat result in low thermal diffusivity. It has been observed that the impact of walls on the temperature of fluids flowing in the channels of the exchanger is the higher, the lower is the value of thermal diffusivity of walls. Obviously, this impact increases with the increase of the wall thickness. ( ) [ ( )

min max min / , T T T t L T i i - - = Θ , max / t t = τ , L x X / = .

2 a 1 x

 21 sectional area of channel no. i, m dependent on the shape of the wall, m L -length of channels, of fluid velocity, m s i v -fluid velocity in channel no. i, m s u -interconnection vector, s / 1 w -coefficient resulting from replacing the heat conducted in the y direction by an equivalent heat source, s / -spatial co-ordinate, m X -dimensionless spatial co-ordinate y -spatial co-ordinate, m α -heat transfer coefficient, -labels of the nodes situated on the opposite surfaces of the wall o -initial steady state distribution of temperature x -in the x direction y -in the y direction 1. Introduction In the general design process of multi-fluid heat exchangers, the stationary operating conditions are of decisive importance, however, in reality heat exchangers frequently undergo transients resulting from external load variations and regulations. Knowledge of dynamic behaviour of heat exchangers is necessary for designing control and regulation systems of different industrial processes and operations, such as in nuclear reactors, cryogenic and petrochemical process plants and HVAC systems. A lot of attention has been given to mathematical modelling of three-and multifluid heat exchangers in the literature. However, in most cases, the solutions presented refer to the determination of steady-state temperature fields [1 -7]. According to the best knowledge of the authors, the available literature gives little information regarding mathematical modelling of transient behaviour of such exchangers [8-21]. Sekulic and Herman [8] solved numerically the set of partial differential equations describing temperature field in a counter-flow three-fluid heat exchanger. They used the Wendroff implicit finite difference approximation and steady state initial conditions. In Reference [9] Sekulic et al. studied experimentally and numerically transient temperature fields in a three-fluid heat exchanger with two thermal connections. The experiments confirmed the accuracy of the method used in Reference [8]. A semi-analytical solution for a three-fluid parallel-flow heat exchanger with two thermal communications and the steady state initial conditions was formulated by Bielski and Malinowski [10]. The authors applied the Laplace transform technique with numerical inversion. The same authors [11] derived fully analytical expressions for temperatures in a parallel-flow three-fluid heat exchanger with two heat connections between the fluids, constant temperature in one channel, the uniform temperature initial conditions, and a step increase in the inlet temperature of one fluid. Luo et al. [12] investigated semianalytically and numerically dynamic responses to temperature and flow transients in multi-stream parallel-and counter-flow heat exchangers taking into account the heat capacities of walls. They used the uniform temperature initial conditions or steady-state conditions. For linear and linearized cases, the governing equations were solved by the semi-analytical Laplace transform method with numerical inversion. Non-linear cases were solved numerically. Malinowski [13] formulated equations for transient behaviour of multi-fluid heat exchangers and solved numerically, by the MacCormack explicit predictor-corrector method, a four-fluid case. He analysed the response of the exchanger to a step change in temperature or flow rate of one fluid using the uniform temperature initial condition or steady state initial condition. It is worth mentioning that an n-fluid heat exchanger characterizes itself by n separate channels in which can flow up to n different fluids. A two-fluid n-channel heat exchanger, e.g. multipass heat exchanger, can be considered mathematically as an nfluid heat exchanger, i.e. the temperature field is described by n differential equations. Dynamic behaviour of n-channel two-fluid heat exchangers is studied in References [14-21]. Among References [1-21], only the authors of Reference [19] have accounted for the thermal capacity of the walls and the conduction of heat along the walls in their mathematical model of transient temperature field in a plate-type heat exchanger (they have, however, omitted the impact of heat resistance on the heat transfer across the walls). In the present paper we solve numerically, by the implicit MacCormack predictor-corrector method, the system of partial differential equations describing the transient temperature field in a parallel-flow three-fluid heat exchanger with three heat connections between the fluids. The model accounts for the thermal capacitance of the walls, the longitudinal heat conduction through the walls, and the conductive resistance across the walls. Exemplary calculations are carried out to determine the unsteady response of the heat exchanger, initially at steady-state, to a step change in flow rate of one fluid.

2 .

 2 Mathematical model A parallel-flow three-fluid heat exchanger with three heat connections between the fluids is illustrated schematically in Fig. 1. For deriving the governing partial differential equations describing the transient temperature field in such an exchanger, the following assumptions are made: physical properties of the fluids and walls materials are constant, the heat transfer coefficients are independent on temperature, but they depend on the flow rate, mass flow and fluid temperature in each channel are taken to be uniform over the cross-section perpendicular to the flow direction, no heat is lost to the ambient.

  spatial co-ordinates outlining the steady-state temperature field in the analysed heat exchanger at a start time 0 t s = . The boundary conditions to be applied to set (1) -(2) are

  25) and (26), n is a time step, j is a grid point, δ and ∆ are implicit and explicit temporal difference operators, respectively. The entries of matrixes and w are determined from the conditions for the method's stability formulated by MacCormack

  a T are the temperatures of nodes a and b, respectively. The general expression characteristic dimension dependent on the shape of the wall. In the predictor equation we use a backward difference for x ∂ ∂ , while in the corrector equation a forward difference is used. A second derivative,2 2

  of walls no. 1 and no. 2 in the direction perpendicular to the axis of the heat exchanger equals zero) and 3 0 y w λ → (wall no. 3 also does not conduct heat in the y direction).

.

  representative and to enable us to best illustrate the influence of walls on temperatures of fluids.The steady-state distributions of fluids temperatures, to be known. The following values of fluids temperatures at the exchanger inlet are chosen: The remaining data taken for the calculations are: 1

  time. Time transients of the dimensionless average walls temperatures at the exchanger outlet, seen in Figs. 4 and 5 that as the time elapses, the fluids temperatures at the outlet and the walls temperatures at the outlet cross-section approach the steady-state values. It appears from Figs. 4 and 5 that the durations of transients depend on the wall material. The exchanger reaches the steady state in about 8 -10 s.

Figure 6

 6 Figure 6 presents unsteady fluids temperature profiles, ( ) t x T i , , for 3 , 2 , 1 = i , for time s t 75 . 0 = . Figure 7 presents unsteady average walls temperature profiles,

Fig. 1 Schematic

 1 Fig.1

Fig. 2 Cross

 2 Fig.2

Fig. 3 ComparisonDimensionless

 3 Fig.3

Fig. 5 DimensionlessFig. 6 Transient

 56 Fig.5

Table 1

 1 Selected thermophysical properties of typical materials used for construction of heat

	exchangers
		ρ		w c	w λ	a ⋅	10	6
	Material	kg m	3	( ) J kgK	( ) W mK	2 m s
	Copper alloy C24000	8530	380	111	34.20
	Stainless steel AISI 410	7770	460	25	7.00
	Titanium alloy Ti6Al4V	4420	610	5.80	2.15


Geert Silversmit
email: geert.silvermit@ugent.

Hilde Poelman

Veerle Balcaen

Philippe M Heynderickx

Maria Olea

Sergey Nikitenko

Wim Bras

Philippe F Smet

Dirk Poelman

Roger De Gryse

Marie-Françoise Reniers

Guy B Marin

Philippe M Heynd- Erickx

In situ XAS study on the

Keywords: A. oxides, C. XAFS (EXAFS and XANES), D. electronic structure, D. microstructure

Introduction

Transition metal based catalysts are frequently applied as substitute for the more expensive noble metal catalysts. Supported copper oxide has received considerable attention in this respect, as it is one of the most active and selective catalysts for various reactions: steam reforming of methanol [START_REF] Oguchi | Steam reforming of methanol over Cu/CeO 2 /ZrO 2 catalysts[END_REF], water gas shift reaction [START_REF] Yahiro | Study on the supported Cu-based catalysts for the low-temperature water-gas shift reaction[END_REF], reduction of NO x and SO 2 [START_REF] Xie | and Simultaneous removal of SO 2 and NO x from flue gas using a CuO/Al 2 O 3 catalyst sorbent II. Promotion of SCR activity by SO 2 at high temperatures[END_REF]. Furthermore, supported CuO has been successfully applied in CO and CH [START_REF] Park | The influence of surface structure on the catalytic activity of alumina supported copper oxide catalysts -Oxidation of carbon monoxide and methane[END_REF] oxidation reactions, making it a candidate for VOC (volatile organic compound) emission control [START_REF] Park | The influence of surface structure on the catalytic activity of alumina supported copper oxide catalysts -Oxidation of carbon monoxide and methane[END_REF]. The properties of supported CuO catalysts can be enhanced by addition of yet another oxide to the support. For this purpose, the properties of CeO 2 are to be noted because of its enhancement of CuO activity and stabilising effect against sintering [START_REF] Larsson | Oxides of copper, ceria promoted copper, manganese and copper manganese on Al 2 O 3 for the combustion of CO, ethyl acetate and ethanol[END_REF][START_REF] Larsson | Complete oxidation of CO, ethanol, and ethyl acetate over copper oxide supported on titania and ceria modified titania[END_REF][START_REF] Dow | TPR and XRD studies of yttria-doped ceria/gamma-alumina-supported copper oxide catalyst[END_REF].

In view of application as total oxidation catalyst for elimination of light alkanes, the structural changes of a CuO-CeO 2 /Al 2 O 3 commercial catalyst under propane reduction and reoxidation have been studied in the temperature range 600-763 K. Reduction of CuO can either follow a one-step Cu 2+ ĺ Cu 0 mechanism or rather proceed through an intermediate Cu 1+ state. The presence of an intermediate Cu 1+ state depends on the conditions of reduction such as gas flow rate and temperature ramping speed [START_REF] Kim | Reaction of CuO with hydrogen studied by using synchrotron-based x-ray diffraction[END_REF][START_REF] Wang | Interaction of H 2 O and NO 2 with BaY faujasite: Complex contraction/expansion behavior of the zeolite unit cell[END_REF]. In studies on supported copper oxide, Cu 2 O has equally been observed as an intermediate phase, e.g. with ex situ XRD [START_REF] Oguchi | Cu 2 O as active species in the steam reforming of methanol by CuO/ZrO 2 catalysts[END_REF] or through analysis of XAFS data identifying Cu 1+ during reduction [START_REF] Wang | Interaction of H 2 O and NO 2 with BaY faujasite: Complex contraction/expansion behavior of the zeolite unit cell[END_REF][START_REF] Oguchi | Cu 2 O as active species in the steam reforming of methanol by CuO/ZrO 2 catalysts[END_REF][START_REF] Als-Nielsen | QEXAFS in seconds at an undulator source[END_REF][START_REF] Caballero | An in situ XAS study of Cu/ZrO2 catalysts under de-NOx reaction conditions[END_REF][START_REF] Yamaguchi | In situ time-resolved energy-dispersive XAFS study on the reduction processes of Cu-ZSM-5 catalysts[END_REF]. In literature, the addition of CeO 2 to the catalyst is held responsible for an enhanced reducibility of CuO [START_REF] Larsson | Complete oxidation of CO, ethanol, and ethyl acetate over copper oxide supported on titania and ceria modified titania[END_REF][START_REF] Dow | TPR and XRD studies of yttria-doped ceria/gamma-alumina-supported copper oxide catalyst[END_REF][START_REF] Radwan | Effects of CeO2-doping on surface and catalytic properties of CuO/Al 2 O 3 solids[END_REF]. Hence, for a complete picture of the catalyst's redox properties, a study of structural changes under redox conditions must include both CuO and CeO 2 compounds. In this way, the specific contribution of each compound to the reaction can be separated and evaluated. In situ XAS presents the ideal tool for this purpose, as it is element specific and applicable under reaction conditions.

In this work, the redox properties of the CuO-CeO 2 /Al 2 O 3 catalyst were investigated using quick X-ray absorption spectroscopy (Q-XANES and Q-EXAFS). With appropriate choice of redox conditions, this technique allows following the catalyst under reaction, yielding the structural and electronic properties of Cu and Ce during insitu propane reduction and re-oxidation. After a preliminary analysis of the Cu environment in the CuO-CeO 2 /Al 2 O 3 catalyst [START_REF] Silversmit | An in-situ XAS study of the structural changes in a CuOCeO2/Al2O3 Catalyst during total oxidation of propane[END_REF], a detailed XAS analysis of the changes at both the Cu K and Ce L 3 edge is now presented. In this way, intermediate

A c c e p t e d m a n u s c r i p t

Cu K and Ce L3 on CuO-CeO2/Al2O3 3/24

Geert Silversmit states and contribution of each specific compound to the structural changes of the catalyst are identified.

Experimental

Catalyst characterisation

The CuO-CeO 2 /Al 2 O 3 FDWDO\VW ZDV V\QWKHVL]HG YLD LPSUHJQDWLRQ RI Ȗ-Al 2 O 3 with Cu(NO 3 ) 2 and Ce(NO 3 ) 4 precursors, pressed into extrudates, dried and calcined above 723 K. The latter material was crushed to fine powder (< 20 μm) for XAS experiments and characterisation.

X-ray diffraction (XRD) measurements were performed with a Siemens Diffractometer Kristalloflex D5000, using Cu .Į UDGLDWLRQ. The catalyst material as received presented broad lines from ceria and alumina, and narrow diffraction peaks for CuO (Figure 1,A). The XRD pattern of a sample used in a XAS propane reduction showed very sharp Cu diffraction lines instead of the original CuO lines (Figure 1,B).

Estimates of the crystallite size of the different particles for both samples were obtained from the width of the diffraction peaks using Scherrer's equation [START_REF] Cullity | Elements of X-ray Diffraction[END_REF]. In the fresh sample, CuO is mainly present as large crystallites, whereas both the alumina and ceria are smaller sized crystallites, a few nm large (Table 1). Within experimental error, no significant difference could be found between different peaks from one compound.

Hence, it is concluded that the crystallites are essentially isotropic. The sharp CuO and Cu diffraction lines point towards crystallites of some 100 nm in size, i.e. an order of magnitude larger than the alumina and ceria. As the width of these CuO and Cu peaks lies close to the instrumental width, small differences in FWHM can lead to large variation in resulting size and hence, accurate crystallite size determination is impossible. Therefore, an order of magnitude is indicated in Focussing on a ceria cluster, rings from the alumina matrix are accompanied by ring fragments arising from ceria nanoparticles (Figure 3,B). The distances agree with crystalline CeO 2 . As the rings from ceria are not complete, it seems that there is a partial preferential orientation, aligning the particles within about 20°around the <110> evaluate the presence of reduced copper. The value found here is lower than the literature values of ~0.5 for bulk CuO [START_REF] Park | The influence of surface structure on the catalytic activity of alumina supported copper oxide catalysts -Oxidation of carbon monoxide and methane[END_REF][START_REF] Larsson | Complete oxidation of CO, ethanol, and ethyl acetate over copper oxide supported on titania and ceria modified titania[END_REF][START_REF] Caballero | An in situ XAS study of Cu/ZrO2 catalysts under de-NOx reaction conditions[END_REF]. Hence, this could point towards the presence of some reduced copper, possibly caused by photoreduction of CuO in the process of the XPS measurement.

X-ray absorption measurements

The copper K-edge and cerium L 3 -edge X-ray absorption spectra were recorded in transmission mode at the DUBBLE beamline (Dutch-Belgian beamline, BM26A) [START_REF] Nikitenko | Implementation of a combined SAXS/WAXS/QEXAFS set-up for time-resolved in situ experiments[END_REF] of the 6 GeV ESRF synchrotron (Grenoble, France) during a uniform filling mode, giving a typical storage ring current of 200 down to 160 mA within one synchrotron run. The synchrotron radiation emitted by the bending magnet (magnetic field strength: 0.4 Tesla) was monochromatized with a double crystal Si(111) monochromator. The higher harmonics of the primary energy that are also being transmitted by the monochromator were suppressed with the mirror after the monochromator. Ionisation chambers filled with Ar/He mixtures at atmospheric pressure were used to measure the intensity of the incoming, I 0 , and transmitted, I t , X-ray beam. A reference sample placed between the second and the third ionisation chamber is used for energy scale correction, especially during the QEXAFS mode.

The samples were pressed into self-supporting pellets in the rectangular shaped hole of a stainless steel sample holder. The pellet thickness was chosen to give an absorption jump of about 1.0 over the Cu K or Ce L 3 absorption edges. In a typical sample preparation, 43 mg of catalyst powder was mixed and pressed with about 12 mg of BN, an inert and weakly absorbing binder, for the Cu K-edge spectra while 50 mg of pure catalyst powder was used for the Ce L 3 -edge spectra.

The in-situ X-ray absorption spectroscopy (XAS) measurements were performed in a PID temperature control. A gas flow through the reactor was established using mass flow controllers. The design resembles that of a pellet cell with gas flow streaming on both sides of the pellet [START_REF] Grunwaldt | X-ray absorption spectroscopy under reaction conditions: suitability of different reaction cells for combined catalyst characterization and time-resolved studies[END_REF].

Reduction treatments were performed with propane gas flows diluted in He (2.2 or 10% propane in He), and re-oxidation treatments with O 2 flows in He (50%) at atmospheric pressure. Specific temperatures and gas flow rates are given below. The catalyst reduction was followed in-situ by recording full EXAFS scans in 1 minute in a quick scanning EXAFS mode (Q-EXAFS). The fast scans resulted in high quality Cu K EXAFS spectra. Although good Ce L 3 XANES spectra were obtained in the quick scanning mode, the data quality did not allow to extract acceptable Ce L 3 EXAFS signals.

The XAS spectra of Cu foil, Cu 2 O, CuO, Ce, CeF 3 and CeO 2 powders were recorded in transmission mode at ambient temperature and pressure as references. The energy scale for the Cu K-edge absorption spectra was calibrated to the first maximum of the first derivative spectrum of a metallic Cu foil measured simultaneously with the samples by using the second and third ionisation chamber at ambient conditions. For the Ce L 3 spectra there was insufficient flux left to measure a reference spectrum in between the second and third ionisation chamber. Therefore a glitch in the I 0 signal around 5987.46 eV was used to correct the energy scale during the Q-EXAFS scanning mode.

EXAFS data analysis and fit parameter errors

The EXAFS data reduction and analysis were performed with the XDAP software [START_REF] Vaarkamp | A new method for parametrization of phase-shift and backscattering amplitude[END_REF]. The pre-edge background was subtracted using a modified Victoreen curve [START_REF] Vaarkamp | Comparison of theoretical methods for the calculation of extended X-ray absorption fine structure[END_REF] and the atomic background, μ 0 , was subtracted with a cubic spline routine [START_REF] Cook | Criteria for automatic X-ray absorption finestructure background removal[END_REF]. The preedge background subtracted spectra were normalised to the edge jump, which was taken to the value of the atomic background at 50 eV above the edge position. The fit parameters were determined by multiple shell fitting in R-space, by applying the difference file technique using Fourier Transformations [START_REF] Koningsberger | XAFS spectroscopy; fundamental principles and data analysis[END_REF]. The agreement between model and fit in R or k-space is expressed by a variance, which gives the relative deviation between model and experiment in percentages [START_REF] Vaarkamp | Comparison of theoretical methods for the calculation of extended X-ray absorption fine structure[END_REF]. Phase shift and As a second step, new fits using up to 3 shells for the Cu foil and 2 shells for the Cu 2 O structures (both spectra recorded at 12 K and ambient conditions) were performed in order to treat these reference spectra as 'unknown' samples. The Debye-Waller factors over Cu shells in the Cu foil fit were constrained to one optimised value. The maximum absolute differences between the crystal structure and the fit values over different kweightings (k 1 , k 2 and k 3 ) and over the four spectra are taken as systematic error values and are summarized in Table 3. For the systematic error on the Debye-Waller factor (V 2 ) we take 10%, a typical value found for the amplitude factors from theoretical references [START_REF] Li | X-ray absorption fine-structure standards -a comparison of experiment and theory[END_REF]. The errors calculated from the statistical error in the data were smaller than 10% of the systematic errors and can therefore be neglected. An EXAFS fit can be considered to be proper if it yields a good result in different kweightings (k 1 , k 2 and k 3 ). Therefore, EXAFS fits were performed with a k 1 , k 2 and k 3

weighting and the reported fit parameters are the average values. The standard deviation over the values is added to the systematic errors to obtain the total error: Err tot = Err systematic + V kweightings . The k 1 weighted fits on Cu 2 O and Cu metal taken at ambient conditions resulted in co-ordination numbers for the first Cu shell in the Cu 2 O and the higher shells in Cu metal that were considerably larger than the crystal structure values (up to 40 %), while the corresponding co-ordination numbers obtained from the k 2 and k 3 weighted fits only deviated by maximum 10%. Reported co-ordination numbers for these Cu contributions are therefore the average over the k 2 and k 3 weighted fits only.

Results and discussion

Local Cu structure

Local Cu structure at ambient conditions

The Cu K XANES spectrum for the as prepared catalyst recorded in He at ambient temperature is compared in Figure 4 with the spectra of Cu metal, Cu 2 O and CuO references taken at ambient conditions. The good resemblance with the CuO XANES indicates that at ambient temperature the local structure in the catalyst is as in CuO.

However, the catalyst has a more intense white line (first peak after the absorption edge), indicating a higher 4p ı density of states compared to the bulk CuO crystal [START_REF] Luo | In situ XRD, Raman, and TPR studies of CuO/Al2O3 catalysts for CO oxidation[END_REF].

For lower calcination temperatures and low loadings of Cu, < 8-10 wt%, well-dispersed isolated Cu 2+ has been observed, as well as a copper surface spinel [START_REF] Park | The influence of surface structure on the catalytic activity of alumina supported copper oxide catalysts -Oxidation of carbon monoxide and methane[END_REF]26]. The latter is a defective CuAl 2 O 4 -like species, with Cu 2+ occupying a distorted octahedral geometry in the alumina surface [START_REF] Strohmeier | surface spectroscopic Characterization of Cu/Al 2 O 3 catalysts[END_REF]. With increasing copper loading, > 8-10 wt%, bulk CuO starts to appear, giving rise to XRD diffraction peaks [START_REF] Park | The influence of surface structure on the catalytic activity of alumina supported copper oxide catalysts -Oxidation of carbon monoxide and methane[END_REF]26,[START_REF] Hu | Activities of supported copper oxide catalysts in the NO plus CO reaction at low temperatures[END_REF]. If ceria is added to the alumina, the threshold between well-dispersed and bulk CuO still holds for low ceria loadings [START_REF] Larsson | Oxides of copper, ceria promoted copper, manganese and copper manganese on Al 2 O 3 for the combustion of CO, ethyl acetate and ethanol[END_REF][START_REF] Hu | Activities of supported copper oxide catalysts in the NO plus CO reaction at low temperatures[END_REF]. At very high ceria loadings, ~ 25 wt%, CuO is no longer found in crystalline form but rather appears surface dispersed on both alumina and ceria, even for high Cu loadings [START_REF] Hu | Activities of supported copper oxide catalysts in the NO plus CO reaction at low temperatures[END_REF].

For the present system, XRD gives no indication of bulk copper aluminate being formed, the calcination temperature being too low. The diffraction peaks for CuO as well as the TEM images clearly show that the Cu loading in this CuO-CeO 2 /Al 2 O 3 catalyst gives rise to bulk CuO crystallites (see Table 1, Figure 2, A and Figure 3,C).

The good EXAFS fit obtained starting from the CuO structure is in accordance with the CuO species identification for this catalyst. Further, the Cu-Cu contributions around 3 Å

show that the copper oxide has indeed neighbouring CuO in the catalyst. Moreover, the satisfactory fit leaves no indication of a significant amount of Cu 2 O present in the catalyst sample in ambient conditions. Hence, the lower Cu sat /Cu main ratio of 0.28 as found with XPS ( § 2.1) can be ascribed to photoreduction during the XPS measurements rather than to the intrinsic presence of reduced copper oxide.

Local Cu structure after drying, pre-oxidation and C 3 H 8 adsorption

The local structure of a catalyst may be altered by pre-treatments given to it like drying, pre-oxidation, adsorption of reactants below reaction temperature, … . No Hence, the above mentioned pre-treatments do not influence the local Cu structure.

Further drying under He flow of the as prepared catalyst up to 873 K does not alter the XAS spectra either (spectra not shown).

Local Cu structure after reduction with C 3 H 8

The XANES, k 2 *F(k) and FT[k 2 *F(k)] spectra for the catalyst after reduction with propane at a reaction temperature of 723 K in a propane flow of 7.4u10 -6 mol/s in 6.7u10 -5 mol/s He at ambient pressure are given in Figure 7. A clear metallic Cu spectrum is present, indicating that complete reduction took place. The Cu K EXAFS fit result is given in Figure 8 and Table 5, the nearest Cu-Cu bond distance is somewhat smaller than the bond distance for the crystal structure of metallic fcc Cu.

Reversibility of the reduction/oxidation process

After an initial drying period of 2 hours in a He flow of 1u10 -3 mol/s at 423 K, four The corresponding Cu K-edge QXANES spectra are given in Figure 9. Effect of the reduction on the XANES spectra can already be seen from the very beginning of the heating, before the reaction temperature was reached, as appears from the decreasing intensity in the 4p ı transition just after the edge. Although the post-edge structure can be seen as a linear combination of the first (Cu 2+ O) and last (Cu 0 ) spectrum, the edge structure cannot. During the reduction process, a shoulder appears on the lower half of the absorption edge which moves to lower energy values. A small pre-edge peak starts to develop from this shoulder, but then this pre-edge peak evolution stops and disappears again, see the inset in Figure 9. This implies that the XANES spectra cannot solely be regarded as a linear combination of the first (Cu 2+ O) and last (Cu 0 ) spectrum.

As the Cu 2 O structure has a large pre-edge peak, see Figure 4, the observed pre-edge development can be ascribed to the presence of some Cu 2 O during the propane reduction process.

The corresponding QEXAFS spectra are also given in Figure 9. Following the evolution of the XANES spectra, a linear combination fit with three base components (one for each Cu oxidation state) was performed on this QEXAFS spectrum series. As The evolution of the XANES and EXAFS spectra (Figure 9) clearly shows the

Local Ce structure

Local Ce structure at ambient conditions

The Ce L 3 XANES spectra for Ce 3+ compounds have a strong absorption line at the absorption edge (white line: WL) due to a 2p 3/2 ĺ I 1 )5d * electronic transition (d *

A c c e p t e d m a n u s c r i p t

Cu K and Ce L3 on CuO-CeO2/Al2O3 13/24

Geert Silversmit denotes an excited electron in the d orbital). Ce 4+ compounds however present a double white line. These two peaks correspond to the 2p 3/2 ĺ I 1 L)5d * and 2p 3/2 ĺ I 0 )5d * transitions (L denotes that an electron from an O2p orbital is transferred to a Ce4f orbital) [START_REF] Hu | X-ray absorption study of PrO 2 at high-pressure[END_REF][START_REF] Bianconi | Specific intermediate-valence state of insulating 4f-compounds detected by L3 Xray absorption[END_REF][START_REF] Soldatov | Crystal-strucutre effects in the Ce L(3)-edge X-ray absorption spectrum of CeO2 -A c c e p t e d m a n u s c r i p t Cu K and Ce L3 on CuO-CeO2[END_REF][START_REF] Kaindl | Pressure-induced changes in LIII X-ray absorption near-edge structure of CeO 2 and CeF 4relevance to 4f-electronic structure[END_REF]. The Ce L 3 spectra for CeO 2 , CeF 3 and Ce powder are given in Figure 11 as references, while more spectra of Ce 3+ and Ce 4+ compounds can be found in for example [START_REF] Takahashi | Determination of the oxidation state of cerium in rocks by Ce L-III-edge X-ray absorption near-edge structure spectroscopy[END_REF].

The Ce L 3 XANES spectrum for the CuO-CeO 2 /Al 2 O 3 catalyst at ambient conditions is compared with the references in Figure 11 1), while TEM showed them to be clustered within the alumina matrix (Figure 2B). At ambient conditions the observed Ce oxidation state is 4+ (Figure 11). Hence, it is concluded that Ce is present as CeO 2 particles only and not as CeAlO 3 precursor state, which bears a Ce 3+ state.

Local Ce structure after C 3 H 8 reduction and re-oxidation

Two subsequent reductions (RED1 and RED2) were performed on the CuO- The fit procedure used is explained below.

Ce L 3 XANES spectra are commonly analysed by fitting procedures in which the white line transitions are approximated with Lorentzian curves and the absorption step by an arctangent function [START_REF] Hu | X-ray absorption study of PrO 2 at high-pressure[END_REF][START_REF] Kaindl | Pressure-induced changes in LIII X-ray absorption near-edge structure of CeO 2 and CeF 4relevance to 4f-electronic structure[END_REF][START_REF] Takahashi | Determination of the oxidation state of cerium in rocks by Ce L-III-edge X-ray absorption near-edge structure spectroscopy[END_REF][START_REF] Chen | NEXAFS investigations of transition metal oxides, nitrides, carbides, sulfides and other interstitial compounds[END_REF]. The resulting fits on the CeF 3 and CeO 2 references are given in Figure 13. For the CeF 3 reference compound spectrum for example, the fit function was

1 2 / * 2 1 * 2 / arctan * a e d E c b E S S
, with E the X-ray energy value. The first term represents an arctangent with a and b the height and position of its inflection point respectively, while the second term is a Lorentzian function with c, d and e its height, position and width at half maximum respectively. For the CeO 2 , three Lorentzians are needed, one for each WL and an extra component at the rising edge. This third component is in literature often ascribed to some Ce 3+ present in the CeO 2 [START_REF] Kaindl | Pressure-induced changes in LIII X-ray absorption near-edge structure of CeO 2 and CeF 4relevance to 4f-electronic structure[END_REF], but more recently attributed to many-body final states of the 2pĺG transition [START_REF] Soldatov | Crystal-strucutre effects in the Ce L(3)-edge X-ray absorption spectrum of CeO2 -A c c e p t e d m a n u s c r i p t Cu K and Ce L3 on CuO-CeO2[END_REF]. According to this last reference, we have considered this third component as an intrinsic feature of the CeO 2 XANES spectra.

Relative constraints on the height, position and width for the arctangents and

Lorentzians were determined from fits on the Ce L 3 XANES spectra for the CeO 2 and CeF 3 references and on the catalyst taken at ambient conditions. These constraints were then applied to all further fits on the spectra for the reduced catalyst. In this way, from the 16 parameters (4 Lorentzians and 2 arctangents) needed to fit an unknown spectrum only 7 remained as free parameters. The fits on the XANES spectra for the reductions RED1 and RED2 from Figure 12 are given in Figure 14, with indication of the resulting percentages Ce 3+ and Ce 4+ . A contribution of about 30% Ce 3+ is found after each reduction. The absolute error on this concentration determination is estimated to amount to 2-3 percent.

Ce 4+ /Ce 3+ evolution during temperature programmed C 3 H 8 reduction

The heating of the catalyst from 600 to 763 K in temperature intervals of 8 K (1°/min) in a propane flow of 7.4u10 -6 mol/s in 3.4u10 -4 mol/s He at ambient pressure was followed in-situ by taking Ce L 3 spectra with a measuring time of 1 min. For each temperature interval the Ce L 3 XANES spectrum was fitted to obtain the relative Ce 3+ A clear two-step propane reduction of ceria in the CuO-CeO 2 /Al 2 O 3 catalyst appears from Figure 15. This two-step process reminds of the bimodal H 2 -reduction curve that is characteristic of high surface area ceria [START_REF] Aneggi | Insights into the redox properties of ceria-based oxides and their implications in catalysis[END_REF]. Moreover, a XAS investigation of the H 2redox properties of ceria in the temperature range of 573 to 773 K has yielded similar observations: for high surface area ceria kept at 673 K, a fast initial H 2 -reduction up to about 20% Ce 3+ was found, followed by a slower reduction [START_REF] Fallah | Redox processes on pure ceria and on Rh/CeO 2 catalyst monitored by X-ray absorption (fast acquisition mode)[END_REF]. This sequential process for pure ceria was thought to consist of first a fast surface reduction (of outermost Ce 4+ layers or small particles), followed by slower bulk reduction. The twostep profile is then governed by a balance between reduction kinetics and morphological changes (sintering of ceria into larger particles) [START_REF] Aneggi | Insights into the redox properties of ceria-based oxides and their implications in catalysis[END_REF][START_REF] Fallah | Redox processes on pure ceria and on Rh/CeO 2 catalyst monitored by X-ray absorption (fast acquisition mode)[END_REF]. For low surface area ceria, only the bulk reduction step is observed [START_REF] Aneggi | Insights into the redox properties of ceria-based oxides and their implications in catalysis[END_REF]. When ceria is supported on alumina, quite different results are being reported regarding H 2 -reduction: no reduction below 773 K [START_REF] Larsson | Oxides of copper, ceria promoted copper, manganese and copper manganese on Al 2 O 3 for the combustion of CO, ethyl acetate and ethanol[END_REF], two reduction peaks at 873 and 1073 K [START_REF] Shyu | Surface characterization of alumina-supported ceria[END_REF] or a single H 2 -reduction temperature of 623K has been reported [START_REF] Ferrandon | Copper oxide-platinum/alumina catalysts for volatile organic compound and carbon monoxide oxidation: Synergetic effect of cerium and lanthanum[END_REF].

Even though C 3 H 8 and H 2 reduction can only be linked to a certain extent [START_REF] Chen | The relationship between the electronic and redox properties of dispersed metal oxides and their turnover rates in oxidative dehydrogenation reactions[END_REF],

similarities can help identifying the processes that occur. The first transition in the C 3 H 8 -reduction of Figure 15 occurs in the temperature range 610-640 K. This temperature region can be related to surface reduction of the ceria nanoparticles. The second transition sets off at 640 K and continues with a lower rate up to 763 K. The different slope of both transitions indicates the reduction is dominated by a different mechanism. Given the XRD detection of 7 nm particles, this transition could be related to ceria bulk reduction, which follows a first faster surface reduction. At 763 K the reduction has reached about 32%, but from the constant slope at the end of the temperature range in Figure 15, it can be expected that this reduction process is still incomplete.

The onset of C 3 H 8 reduction of ceria in the present catalyst, ~610 K, occurs at quite low temperature, which is similar to the starting reduction of CuO, <623 K (see § 3.1.5).

A c c e p t e d m a n u s c r i p t

Cu K and Ce L3 on CuO-CeO2/Al2O3 16/24

Geert Silversmit

For CuO-CeO 2 /Al 2 O 3 catalysts, the presence of CeO 2 is reported to enhance the reducibility of CuO, but most often, H 2 -TPR reduction peaks up to 773 K are identified as CuO related only [START_REF] Larsson | Oxides of copper, ceria promoted copper, manganese and copper manganese on Al 2 O 3 for the combustion of CO, ethyl acetate and ethanol[END_REF][START_REF] Dow | TPR and XRD studies of yttria-doped ceria/gamma-alumina-supported copper oxide catalyst[END_REF][START_REF] Ferrandon | Copper oxide-platinum/alumina catalysts for volatile organic compound and carbon monoxide oxidation: Synergetic effect of cerium and lanthanum[END_REF]. On the other hand, interaction between CuO and CeO 2 is sometimes believed to enhance the reducibility of both compounds [START_REF] Tang | CuO/CeO2 catalysts: Redox features and catalytic behaviours[END_REF]. Such mutual promotion between copper oxide and ceria is then responsible not only for lowering the CuO reduction temperature, but also for inducing a higher ceria reducibility than expected [START_REF] Tang | CuO/CeO2 catalysts: Redox features and catalytic behaviours[END_REF]. In the present CuO-CeO 2 /Al 2 O 3 catalyst system, temperature programmed C 3 H 8 reduction induces at first a fast reduction of some 25 % of the Ce 4+ to Ce 3+ followed by a slower proceeding reduction. The combined presence of CuO and CeO 2 lowers C 3 H 8 reduction temperatures for ceria, so that both compounds start reducing in the same temperature range ( K).

Conclusions

A c c e p t e d m a n u s c r i p t

Cu K and Ce L3 on CuO-CeO2/Al2O3 21/24

Geert Silversmit

A c c e p t e d m a n u s c r i p t

Cu K and Ce L3 on CuO-CeO2/Al2O3

Figure 2

 2 shows the STEM images and corresponding elemental mappings for Cu K, Ce L and Al K fluorescence radiation on the CuO-CeO 2 /Al 2 O 3 catalyst. The left image (Figure 2, A) presents a large CuO feature in an Al 2 O 3 matrix, and no Ce intensity. The CuO entity displays sharp edges and measures at least 100 nm the right image (Figure 2, B), a cluster of ceria particles about 100 nm wide is visible within the alumina matrix. No Cu intensity was registered in this image. Similar images were observed throughout the catalyst sample. Performing selective area diffraction (SAD) upon this sample, the crystallinity of the different compounds was determined (Figure3). The alumina matrix of the catalyst gives rise to rings of diffraction in the SAD pattern (Figure3, A), indicating randomly oriented nanoparticles. The distances between the rings correspond with gamma-alumina.

  stainless steel XAS chemical reactor cell (volume ~ 1.75 l) designed and built at the department of Solid State Sciences at the Ghent University. Kapton foils (25 μm thickness) were used as X-ray transparent windows. The cell has a double wall design, allowing a cooling water flow and preventing the heating of the Kapton windows. The sample holder with pressed pellet was mounted inside the reactor in an inconel block with thermocoax wiring for resistive heating allowing a maximum sample holder temperature of 973 K. The sample holder temperature was controlled with an Eurotherm

  backscattering amplitude functions used to calculate the Cu-Cu and Cu-O contribution spectrum were obtained with FEFF 8.0 calculations[START_REF] Ankudinov | Real-space multiplescattering calculation and interpretation of x-ray-absorption near-edge structure[END_REF] on fcc Cu metal and Cu 2 O spherical clusters with a radius of 8.0 Å and 8.2 Å respectively.In order to quantify the error upon the EXAFS analysis and fits, both systematic and statistical errors should be taken into account. As recommended in the report of the International Workshop on Standards and Criteria in X-ray Absorption Spectroscopy[START_REF] Lytle | Report of the international workshop on standards and criteria in X-ray absorption-spectroscopy -March 7-9[END_REF] by the International X-Ray Society, an estimate of the systematic errors in the EXAFS analysis and data reduction can be obtained by using the calculated Cu-Cu and Cu-O phase and amplitude functions to fit the experimental spectra of different references with known structure and treating them as 'unknown' samples. The differences between the fit results and the crystal structures serve as an estimate of the systematic errors. Four reference measurements were available for the systematic errors evaluation: Cu metal foil and Cu 2 O powder measured at 12 K and at ambient conditions. The following procedure was used to estimate these systematic errors. As a first step, the first shell in Cu foil (Cu-Cu) and Cu 2 O (Cu-O) are fitted with the calculated phase shift and backscattering amplitude functions. The S 0 2 factor for the Cu-Cu and Cu-O contribution was tuned to have agreement with the co-ordination number of the first Cu-Cu shell in Cu metal (R = 2.556 Å, N = 12) and the first Cu-O shell in Cu 2 O (R = 1.849 Å, N = 2) [25], both for the spectra taken at 12 K and under ambient conditions. The resulting S 0 2 values for the Cu metal and the Cu 2 O spectrum taken at 12 K were 0.89 and 0.73 respectively, comparable with the values reported in [25] for the same structures measured at 83 K. The resulting S 0 2 factors for the spectra taken at ambient conditions were 0.86 and 0.80 for the Cu-Cu and Cu-O contributions respectively.

A c c e p t e d m a n u s c r i p t

  Cu K and Ce L3 on CuO-CeO2/Al2O3 8/24 Geert Silversmit The nearest neighbours for Cu in CuO are two O shells at bond distances of 1.951 and 1.961 Å, both with a co-ordination number of 2. Using the optimized theoretical Cu-Cu and Cu-O amplitude and phase functions, a fit of the CuO EXAFS spectrum taken at ambient conditions with the crystallographic co-ordination numbers was possible, but large absolute 'E 0 values were needed for the Cu-O shells compared to the Cu 2 O fits. A fit with acceptable 'E 0 values was possible by combining the two nearest Cu-O shells into one single Cu-O shell with a co-ordination number of 4, using a S 0 2 of 0.63.

  structure. The local CuO structure in the catalyst is further supported by the good agreement between the k 2 -weighted EXAFS signals and corresponding Fourier Transforms for the catalyst and the CuO reference as shown in Figure 5. The intensity in the k 2 -weighted Fourier Transform for the Cu-O shell (0.0-2.0 Å) is more intense for A c c e p t e d m a n u s c r i p t Cu K and Ce L3 on CuO-CeO2/Al2O3 9/24 Geert Silversmit the catalyst than for the CuO reference, while the intensity for the Cu-Cu shells (2.0-3.0 Å) is lower. An EXAFS fit with the parameters from the CuO structure as starting values was possible, see Figure 6 and

A c c e p t e d m a n u s c r i p t

  Cu K and Ce L3 on CuO-CeO2/Al2O3 10/24Geert Silversmit changes could be observed in the Cu K XANES spectra for the catalyst after drying up to 423 K in a He flow of 7.4u10 -5 mol/s (at standard temperature and pressure), after a pre-oxidation at 423 K in a O 2 flow of 3.7u10 -5 mol/s in 3.7u10 -5 mol/s He and after pre-adsorption with C 3 H 8 at 473 K in a C 3 H 8 flow of 7.4u10 -6 mol/s in 6.7u10 -5 mol/s He. Moreover the EXAFS analysis for these pre-treatment spectra resulted in fit parameters similar to the values for the catalyst recorded at ambient temperature in He.

  propane reductions and three intermediate re-oxidations were performed consecutively on the CuO-CeO 2 /Al 2 O 3 catalyst. The reduction and re-oxidation treatments were carried out at 698 K in respectively a propane flow of 7.4u10 -6 mol/s in 6.7u10 -5 mol/s He and an O 2 flow of 3.7u10 -5 mol/s in 3.7u10 -5 mol/s He. A metallic Cu structure develops after each reduction and each re-oxidation restores the CuO structure as is present at ambient conditions, indicating a reversible local Cu structure in the catalyst (spectra not shown).

5 .

 5 Evolution of the local Cu structure during isothermal C 3 H 8 reductionThe evolution of the local Cu structure in the CuO-CeO 2 /Al 2 O 3 catalyst during reduction with propane was followed by recording full XAS spectra in a measuring time of 1 minute. The reduction was performed at a reaction temperature of 623 K in a propane flow of 7.4u10 -6 mol/s in 3.4u10 -4 mol/s He at ambient pressure. The catalyst was pre-treated by flushing with C 3 H 8 /He for 15 minutes at 424 K, followed by a fast heating to the reaction temperature of 623 K. The acquisition of the XAS spectra was already started during the heating and reaction temperature was reached after 3 minutes.

Cu

  2+ component in the linear combination fit, a fully oxidized spectrum (i.e. at the beginning of the reduction series) was used, a fully reduced spectrum (i.e. at the series' end) was taken as Cu 0 component and the Cu 2 O reference spectrum was chosen as Cu 1+ component. The resulting percentages of each component as a function of time in the reduction process are given in Figure10. The exact fit percentages are dependent on the amplitude of the base spectra. As the reference Cu 2 O spectrum was taken at ambient temperature from a Cu 2 O reference powder, presenting a different disorder than present in the catalyst, the scaling factor for the Cu 2 O contribution is not known. Hence, the reported concentrations are only qualitative and not quantitative. The Cu 2 O spectrum is minor intermediate component, which has a maximum after about 6 minutes reduction time.

CeO 2 /

 2 Al 2 O 3 catalyst, with a re-oxidation in between. The sample was heated from 600 to 763 K (723 K for RED2) in steps of 8 K in a propane flow of 7.4u10 -6 mol/s in 3.4u10 -4 mol/s He at ambient pressure. The final Ce L 3 spectra for each reduction and the intermediate re-oxidation (performed at 763 K, in an O 2 flow of 7.4u10 -6 mol/s in 3.4u10 -4 mol/s He at ambient pressure) are shown in Figure12. The two reductions yield a similar spectrum. The re-oxidation brings back the CeO 2 structure. Compared to the oxidized spectrum, the main edges in the spectra for the reduction treatments are shifted to lower X-ray energy values and there is a different ratio in the intensity of the two white lines. As two white lines can still be noticed after reduction, Ce 4+ cations are still present. In order to quantify the amount of Ce 3+ in the spectra upon the reduction fit of the Ce L 3 XANES was performed with the CeO 2 XANES spectrum as model for the Ce 4+ oxidation state and the CeF 3 spectrum for the Ce 3+ oxidation state.

A c c e p t e d m a n u s c r i p t

  Cu K and Ce L3 on CuO-CeO2/Al2O3 15/24 Geert Silversmit and Ce 4+ concentrations. The amount of Ce 3+ in the spectra as function of the treatment time and temperature is given in Figure 15. A transition from 0 to about 25% Ce 3+ in the fit occurs in the 610-640 K temperature interval. After this transition, a further increase in the Ce 3+ fit percentage as function of time of about 1.3 %/hour can be noticed. Hence, the CuO-CeO 2 /Al 2 O 3 catalyst presents a clear reduction of the CeO 2 particles during temperature programmed C 3 H 8 reduction. This means that not only CuO is reduced by C 3 H 8 in this temperature interval, but also CeO 2 to a certain extent.

Figure 1 :

 1 Figure CaptionsFigure 1: XRD pattern for the CuO-CeO 2 /Al 2 O 3 catalyst: A) as received, B) after reduction under propane/He.

Figure 2 :

 2 Figure 2: STEM images and element mappings of the CuO-CeO 2 /Al 2 O 3 catalyst, CuO entity in alumina matrix (A); cluster of CeO 2 particles in alumina matrix (B).

Figure 3 :

 3 Figure 3: Inverted Selective Area Diffractions (SAD) for the CuO-CeO 2 /Al 2 O 3 catalyst, centred on alumina matrix (A), cluster of CeO 2 particles (B) and CuO entity (C).

Figure 4 :

 4 Figure 4: Cu K XANES spectra for Cu metal, Cu 2 O, CuO and the CuO-CeO 2 /Al 2 O 3 catalyst taken at ambient temperature.

Figure 5 :

 5 Figure 5: k 2 -weighted EXAFS signals and Fourier Transforms for the CuO-CeO 2 /Al 2 O 3 catalyst at room temperature and the CuO reference (Catalyst: 'k = 3.47-14.09 Å -1 ; CuO: 'k = 3.55-9.96 Å -1 ).

Figure 6 :

 6 Figure 6: k 2 *F(k) and FT[k 2 *F(k)] spectra for the experimental Cu K EXAFS signal of the CuO-CeO 2 /Al 2 O 3 catalyst at room temperature and the fit ('k = 3.47-14.09 Å -1 , 'R = 0.6-3.3 Å, k 2 variances : 0.66 (Imaginary part) and 0.27 (Absolute part)).

Figure 7 :

 7 Figure 7: Cu K XANES (left), k 2 *F(k) and FT[k 2 *F(k)] (right) spectra for the CuO-CeO 2 /Al 2 O 3 catalyst taken at 723 K, after reduction with C 3 H 8 /He and for Cu foil at RT in air (Catalyst: 'k = 1.34-12.40 Å -1 ; Cu foil: 'k = 2.07-17.40 Å -1 ).

Figure 8 :

 8 Figure 8: Fit and experimental k 3 *F(k) (left) and FT[k 3 *F(k)] (right) spectra for the CuO-CeO 2 /Al 2 O 3 catalyst after full reduction ('k = 3.29-10.40 Å -1 , 'R = 1.00-5.0 Å, k 3 variances: 0.92 (Imaginary part) and 0.39 (Absolute part)).

Figure 9 :

 9 Figure 9: Cu K QXANES (left) and QEXAFS (right) spectra for the CuO-CeO 2 /Al 2 O 3 catalyst during propane reduction, 1 minute measuring time per XAS spectrum. The inset shows a detail of the edge structure.

Figure 10 :

 10 Figure 10: Percentages of Cu 2+ , Cu 1+ and Cu 0 contributions to the Cu K QEXAFS spectra of Figure 9 as function of propane reduction time. During the first 3 minutes, the temperature was increased from 423 to 623 K. The error bars represent the 99% confidence intervals from the fitting procedure.

Figure 11 :

 11 Figure 11: Ce L 3 XANES spectra for the CuO-CeO 2 /Al 2 O 3 catalyst at ambient conditions and the CeO 2 , CeF 3 and Ce powder reference compounds.

Figure 12 :

 12 Figure 12: Ce L 3 XANES spectra for the CuO-CeO 2 /Al 2 O 3 catalyst in a cycle of two subsequent propane reductions with a re-oxidation in between.

Figure 13 :

 13 Figure 13: Ce L 3 XANES spectra and fits for the CeF 3 (left) and CeO 2 (right) references.

Figure 14 :

 14 Figure 14: Ce L 3 XANES spectra and fits for the spectra RED1 (left) and RED2 (right) from Figure 12.

Figure 15 :

 15 Figure 15: Percentage of the CeF 3 spectrum (Ce 3+ contribution) in the CuO-CeO 2 /Al 2 O 3 Ce L 3 XANES fit as function of reduction time. The temperature increase per step was about 8 K (1 K/min), after an initial heating from 423 to 600 K.

A c c e p t e d m a n u s c r i p tFigure01A c c e p t e d m a n u s c r i p tFigure02A c c e p t e d m a n u s c r i p tFigure03A c c e p t e d m a n u s c r i p t 2

 2 Figure01

Figure04A

  Figure04

Figure07_leftA

  Figure07_left

Figure07_rightA

  Figure07_right

Figure09_leftA

  Figure09_left

Figure09_rightA

  Figure09_right

Figure11A

  Figure11

Figure12 A c c e p t e d m a n u s c r i p t 3

 3 Figure12

Figure13_leftA

  Figure13_left

Figure13_rightA

  Figure13_right

Figure15

  Figure15

table 1

 1

	for CuO and Cu

Table 2

 2

	CuO crystallites.
	Surface atomic concentrations were obtained by means of XPS using a Perkin Elmer
	PHI ESCA 5500 system equipped with a monochromatic 450 :DWW $O .Į VRXUFH The
	crushed CuO-CeO 2 /Al 2 O 3 catalyst gave rise to a Cu/Al XPS intensity ratio of 0.12 (see

contains general characteristics of the CuO-CeO 2 /Al 2 O 3 catalyst. The specific surface area of the catalyst was determined with a Micromeritics ASAP 2010 instrument with N 2 adsorption at 77 K. Full elemental composition of the catalyst was obtained using inductively coupled plasma (ICP-MS) analysis (IRIS Advantage system, Thermo Jarrell Ash) by fusion in NaO and NaOH. All samples were dried at 378 K before mineralization. The catalyst contains 9.3 wt% Cu and 5.2 wt% Ce, corresponding to 9.17 ȝPRO &XP 2 and 2.35 ȝPRO &HP 2 respectively. Larsson et al. have investigated a series of CuO catalysts supported on ceria modified alumina

[START_REF] Larsson | Oxides of copper, ceria promoted copper, manganese and copper manganese on Al 2 O 3 for the combustion of CO, ethyl acetate and ethanol[END_REF]

. They found CuO diffraction peaks for catalysts containing at least 6 ȝPRO &XP 2 . Hence, the given loading of 9.17 μmol Cu/m 2 is high enough to give rise to bulk CuO and thus also to

Table 2 )

 2

. The overall Ce 3d signal was very weak and allowed no further analysis (not shown). The Cu 2p photoline displayed a satellite feature at higher binding energy, characteristic for Cu 2+ , with a Cu sat /Cu main ratio of 0.28 (not shown; see Table

2

). As Cu 1+ is known not to exhibit such feature, the Cu sat /Cu main intensity ratio can be used to

  Table 4 for the optimised parameters. Compared to the CuO crystal structure, similar bond distances are obtained, but a higher total Cu-

	O co-ordination number is found, 5.8 (± 0.4) instead of 4, and a lower total Cu-Cu co-
	ordination number, 3.3 (±1.5) instead of 8.
	For CuO/Al 2 O 3 , different species are reported depending on copper loading and
	calcination temperature [4, 26]. If the calcination temperature is high enough (> 973 K),
	bulk CuAl 2 O 4 can form through solid-solid interaction between CuO and Al 2 O 3

  presence of an intermediate Cu 1+ phase upon propane reduction at 623 K over the CuO-CeO 2 /Al 2 O 3 catalyst. Caballero et al. investigated a CuO/ZrO 2 catalyst under C 3 H 8diluted in He at 773 K[START_REF] Caballero | An in situ XAS study of Cu/ZrO2 catalysts under de-NOx reaction conditions[END_REF]. Under these conditions, reduction of the catalyst was incomplete and factor analysis of the XANES spectra identified three components: CuO, Cu 2 O and Cu. In methanol steam reforming over CuO/ZrO 2 , Cu 2 O was obtained as post-reaction oxidation state for certain Cu loadings and water/methanol ratios[START_REF] Oguchi | Cu 2 O as active species in the steam reforming of methanol by CuO/ZrO 2 catalysts[END_REF].H 2 reduction of the same catalyst confirmed the presence of the Cu + , now as intermediate towards metallic Cu[START_REF] Oguchi | Cu 2 O as active species in the steam reforming of methanol by CuO/ZrO 2 catalysts[END_REF]. In H 2 reduction or oxidative methanol reforming over CuO/ZnO 2[START_REF]QWHU % %HPV 5 6FKOĘJO 7 5HVVOHU In situ studies on the structure of copper oxide/zinc oxide catalysts[END_REF][START_REF] Reitz | Timeresolved XANES investigation of CuO/ZnO in the oxidative methanol reforming reaction[END_REF] and in CO-CO 2 -H 2 /Ar reduction of a CuO/ZnO 2 /Al 2 O 3 catalyst,

Cu 2 O was equally identified as an intermediate copper phase preceding the formation of metallic Cu

[START_REF] Als-Nielsen | QEXAFS in seconds at an undulator source[END_REF]

. But the presence of Cu 2 O as intermediate during reduction of CuO is not general: CuO in ZSM5 was found to reduce in H 2 -TPR via Cu 2 O in small CuO particles only, while the larger ones exhibited a direct Cu 2+ AE Cu 0 transition

[START_REF] Yamaguchi | In situ time-resolved energy-dispersive XAFS study on the reduction processes of Cu-ZSM-5 catalysts[END_REF]

. For unsupported CuO, it was found that the presence of an intermediate Cu 2 O phase upon CO or H 2 reduction strongly depends on the reduction conditions and the reduction can follow either a direct or a two-step transition

[START_REF] Kim | Reaction of CuO with hydrogen studied by using synchrotron-based x-ray diffraction[END_REF][START_REF] Wang | Interaction of H 2 O and NO 2 with BaY faujasite: Complex contraction/expansion behavior of the zeolite unit cell[END_REF]

. The sequential pathway is observed when either a limited feed or fast temperature ramping conditions are applied, i.e. a more 'mild' reduction, where Cu 2 O can appear.

Hence, the presence of Cu 1+ in present CuO-CeO 2 /Al 2 O 3 catalyst during the propane reduction process is not surprising but related to the CuO particle structure and conditions of reduction. Under a flow of 7.4u10 -6 mol/s propane in 3.4u10

-4

mol/s He at ambient pressure and 623 K, the large CuO crystallites of the catalyst are reduced through a Cu 1+ intermediate state. These conditions are hence 'mild' enough to allow the Cu 2 O intermediate state to occur during reduction.

  . A local CeO 2 structure can be concluded for the CuO-CeO 2 /Al 2 O 3 catalyst at ambient conditions, with Ce 4+ oxidation state. When ceria is supported on alumina, up to 3 different Ce species have been identified in literature [37]: Ce species in Al 2 O 3 cation vacancies (named a CeAlO 3 precursor phase, with Ce 3+ oxidation state), well-dispersed small CeO 2 particles, too small to be detected in XRD, and bulk-like CeO 2 . In the present CuO-CeO 2 /Al 2 O 3

catalyst, the ceria loading of 2.35 μmol Ce/m 2 was in the XRD analysis identified as ceria particles of size around 6 nm (see Table

  X-ray absorption spectroscopy was used to follow the C 3 H 8 reduction and reoxidation behaviour of a CuO-CeO 2 /Al 2 O 3 catalyst, by measuring in-situ both Cu K and Ce L 3 transmission XAS spectra. A detailed analysis including error estimation of the XAS data was performed. The starting material displayed fully oxidized Ce 4+ and Cu 2+ and these states were preserved upon pre-treatment (heating to 873 K in He or preoxidation at 423 K). From the combined XAS, XRD, XPS and TEM characterisation, it follows that in this CuO-CeO 2 /Al 2 O 3 catalyst, CuO is present as large single crystallites, while CeO 2 and Al 2 O 3 occur as nanoparticles. Both processes occur at far lower temperature than expected for bulk ceria, which can only be accounted for by interaction between CuO and CeO 2 .

	Cu K and Ce L3 on CuO-CeO2/Al2O3	17/24
	particles.
	Upon reduction with C 3 H 8 in the temperature range 600-763 K, Cu 2+ reduced fully towards metallic Cu 0 . QEXAFS was applied to follow this reduction in detail. Analysis of the XANES edge region and a linear combination fit to the EXAFS spectra allowed to identify the presence of some Cu 1+ during the first stage of the reduction, indicating a A c c e p t e d m a n u s c r i p t
	two-step reduction process.
	In XANES temperature programmed C 3 H 8 reduction, Ce was found to partially
	reduce to Ce 3+ in two steps: a fast initial reduction up to 25% at low temperature,
	followed by a slower transition, which continued beyond the investigated temperature
	range (32% Ce 3+ at 763 K). The first transition was ascribed to surface reduction of the
	ceria nanoparticles. The onset temperature of 610 K is similar to the one for the Cu
	reduction. The second slower reduction is related to bulk reduction of the CeO 2
	Geert Silversmit

Table 1 :

 1 Crystallite sizes determined from XRD in the crushed CuO-CeO 2 /Al 2 O 3 catalyst as received and after reduction under C 3 H 8 /He flow at 770 K. An order of magnitude is given for CuO and Cu; averaged values over several diffraction peaks for CeO 2 and Al 2 O 3 .

	Tables
	crystallite size (nm)	CuO/Cu	CeO 2	Al 2 O 3
	as received	~ 100	6	4
	reduced	~ 100	8	5

Table 2 :

 2 Specific surface area, nominal ratio Cu/Al and Cu/Ce (from ICP), surface Cu/Al and Cu/Ce ratio and Cu satellite/main peak ratio (from XPS) for the crushed CuO-CeO 2 /Al 2 O 3 catalyst.

		S BET (m 2 /g)	Nominal Cu/Al	Nominal Cu/Ce	Surface Cu/Al	Surface Cu/Ce	Cu sat /Cu main
	CuO-CeO 2 /Al 2 O 3	156	0.10	3.9	0.12	27	0.28

Table 3 :

 3 Estimated systematic errors in the EXAFS analysis. Error on the

	Debye-Waller factor (V 2 ): 10%.
			systematic error
	Absorber -scatterer	|'R| (Å)	_'N/N| (%)	_'( | (eV)
	Cu-Cu (1 st shell) in Cu metal	<0.018	6	1
	Cu-Cu (1 st shell) in oxides
	N values from k 2 and k 3 weighted	<0.018	14	<3
	fits only
	Cu-Cu (higher shells)	<0.022	20-30	<3
	Cu-O (1 st shell)	<0.013	5	1
	s

Table 4 :

 4 Bond distances, R, co-ordination numbers, N, for the EXAFS fit on the experimental Cu K EXAFS spectrum for the CuO-CeO 2 /Al 2 O 3 catalyst at room temperature compared to the CuO reference structure values ('k = 3.47-14.09 Å -1 , 'R = 0.6-3.3 Å, k 2 variances: 0.53 (Imaginary part) and 0.23 (Absolute part)).

		Crystal structure		EXAFS fit values
	Absorber -scatter	R (Å)	N	R (Å)	N	V² (Å 2 )	'E 0 (eV)
	Cu-O	1.955	2+2	1.938 (±0.022)	6.1 (±1.3)	0.0064 (±0.001)	-0.4 (±1.5)
	Cu-O	2.784	2	2.822 (±0.030)	1.0 (±0.5)	0.0064 (±0.001)	-0.2 (±2.4)
	Cu-Cu	2.901	4	2.970 (±0.032)	1.6 (±0.3)	0.0029 (±0.001)	-2.7 (±3.6)
	Cu-Cu	3.083	4	3.094 (±0.020)	1.5 (±0.3)	0.0029 (±0.001)	-4.6 (±3.2)

Table 5 :

 5 Comparison between the bond distances R, co-ordination numbers N, for the Cu K EXAFS fit result on CuO-CeO 2 /Al 2 O 3 catalyst after full reduction and the fcc Cu crystal structure values ('k = 3.29-10.40 Å -1 , 'R = 1.00-5.0 Å, k 3 variances: 0.92 (Imaginary part) and 0.39 (Real part)).

		Cu fcc crystal structure	EXAFS fit values for CuO-CeO 2 /Al 2 O 3 catalyst		difference
	Absorber -scatterer	R Cu (Å)	N Cu	R (Å)	N	V² (Å 2 )	(eV) 'E 0	(Å) |'R|	N/N Cu
	Cu-Cu	2.556	12	2.483 (±0.019)	7.42 (±1.0)	0.019 (±0.003)	5.78 (±1.2)	0.073	0.62
	Cu-Cu	3.615	6	3.488 (±0.024)	3.58 (±1.03)	0.019 (±0.003)	10.0 (±3.)	0.127	0.60
	Cu-Cu	3.427	24	4.498 (±0.025)	8.02 (±1.7)	0.019 (±0.003)	3.58 (±3.0)	0.071	0.33

Acknowledgements

Geert Silversmit is a Postdoctoral Fellow of the Fund for Scientific Research -Flanders (FWO-Vlaanderen). The authors thank the FWO-Vlaanderen for the access to the DUBBLE beam line and financial support. Part of this work was performed in the framework of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-3) initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by its authors.

A c c e p t e d m a n u s c r i p t

Cu K and Ce L3 on CuO-CeO2/Al2O3 18/24

Geert Silversmit