Julie Davot
email: juliedavot6@gmail.com

Marie Thomas-Pohl

Coralie Villa

Xavier Bonnet

Eric Lapeyre

Jospeh Bascou

He ´le `ne Pillet

Experimental characterization of the moment-angle curve during level and slope locomotion of transtibial amputee: Which parameters can be extracted to quantify the adaptations of microprocessor prosthetic ankle?

Keywords: Walking, microprocessor-controlled feet, energy, amputation, adaptability, ramp

In case of transtibial amputation, the deficit resulting from the loss of the lower limb can be partly compensated with a prosthetic foot and adapted rehabilitation. New prosthetic feet have been developed for transtibial amputees to mimic ankle adaptability to varying terrain. Among them, Microprocessor Prosthetic Ankles (MPA) have a microprocessor to control an electric or a hydraulic actuator to adapt ankle kinematics in stairs and slopes. The objective is to investigate parameters extracted from the moment-angle curve (MAC) and use them to compare 3 MPA during level and slope locomotion against energy storing and return (ESR) foot. Five persons with lower limb transtibial amputation successively fitted with 3 MPA (Propriofootä, Elanä, Meridiumä) compared to their ESR foot. The participants had 2 weeks of adaptation before data acquisition and then a 3 week wash-out period. Range of motion, equilibrium point, hysteresis, late stance energy released, and quasi-stiffness were computed on level ground and 12% slope (upward and downward) thanks to the MAC at the ankle. The study shows the relevance of MAC parameters to evaluate the behavior of MPA. In particular, compared to ESR, all MPA tested in the present study demonstrated a better angle adaptation between walking conditions but a decrease of available energy for the propulsion. Among MPA, main results were: (i) for the Propriofootä: an adaptation of the ankle angle without modification of the pattern of the MAC (ii) for the Elanä: a limited adaptation of the range of motion but a modification of the energy released (iii) for the Meridiumä, the highest adaptation of the range of motion but the lowest available energy of propulsion. One of the main findings of the research is to show and quantify the relationship between range of motion and energy available when using different prosthetic feet in different walking conditions.

Introduction

Even if recent studies have shown that the gait of people with transtibial amputation can be as energetically efficient as the one of able bodied when considering young and active people, 1,2 some limitations are still reported by amputee people particularly when walking in slopes. Indeed, for unimpaired people, the adaptation to slope locomotion is mainly performed by the ankle. [START_REF] Hansen | The human ankle during walking: implications for design of biomimetic ankle prostheses[END_REF] Due to limited adaptability of the prosthetic ankle in stance, people with a trans-tibial amputation may adapt to slope with the residual and contralateral joints. In particular, the analysis of joint powers highlighted the role of the ipsilateral hip in slope ascent and of the residual knee in slope descent. [START_REF] Vickers | Elderly unilateral transtibial amputee gait on an inclined walkway: a biomechanical analysis[END_REF][START_REF] Vrieling | Uphill and downhill walking in unilateral lower limb amputees[END_REF][START_REF] Langlois | Influence of physical capacities of males with transtibial amputation on gait adjustments on sloped surfaces[END_REF][START_REF] Fradet | Biomechanical analysis of ramp ambulation of transtibial amputees with an adaptive ankle foot system[END_REF] Nowadays, new prosthetic feet have been developed for transtibial amputees in the aim to mimic ankle adaptability to varying terrain. Among them, Microprocessor Prosthetic Ankles (MPA) have a microprocessor to control an electric or a hydraulic actuator to adapt ankle kinematics in stairs and slopes. Different studies have already analyzed the improvement induced by these prosthetic feet compared to energy storing and return (ESR) feet by quantifying some parameters individually. The energetic cost decreased with the Propriofootä 8 compared to ESR during walking on level ground. Kinematic data have also been used to quantify the differences between prosthetic feet. The dorsiflexion in slope ascent and the plantarflexion in slope descent were closer to the ones observed during unimpaired people gait with the Propriofootä [START_REF] Fradet | Biomechanical analysis of ramp ambulation of transtibial amputees with an adaptive ankle foot system[END_REF] and the Elanä. [START_REF] Struchkov | Biomechanics of ramp descent in unilateral trans-tibial amputees: comparison of a microprocessor controlled foot with conventional ankle-foot mechanisms[END_REF] However, few studies compared more than 1 MPA prosthetic foot tested by the same participant, due to the heaviness of such protocol. In static conditions, Ernst et al. investigated a cohort of people with an amputation using five different feet while standing on flat and inclined surfaces (Meridiumä, Propriofootä, Elanä, Triton,ä and Raizeä) and showed that the increased range of motion and the dorsiflexion stop allow an adaptation closer to the one of asymptomatic subjects. [START_REF] Ernst | Standing on slopes-how current microprocessor-controlled prosthetic feet support transtibial and transfemoral amputees in an everyday task[END_REF] In dynamic conditions, Ko et al. [START_REF] Ko | Comparison of ankle angle adaptations of prosthetic feet with and without adaptive ankle angle during level ground, ramp, and stair ambulations of a transtibial amputee: a pilot study[END_REF] compared two different MPAs (Elanä and Propriofootä) with an ESR foot on one transtibial patient. They observed an increase of the stance phase duration during ambulation combined with a greater dorsiflexion while using the MPAs on slope. Schmalz et al. studied the effect of abrupt change of ramp inclination in patients while walking with the Meridiumä and observed that the ankle dorsiflexion and the hip flexion patterns were similar to the ones observed in asymptomatic participants. [START_REF] Schmalz | Ramp walking with abruptly changing inclines: motion pattern of TT amputees fitted with a microprocessor-controlled and a conventional prosthetic foot[END_REF] If the above mentioned studies allowed to highlight the benefit of MPA on separated gait parameters, none have adressed the functional outcome resulting from the effect of MPA from simultaneous evaluation of these parameters.

To overcome this limitation and compare different prosthetic feet, some authors have also proposed to analyze the moment-angle curve (MAC) at the ankle in the sagittal plane during walking. [START_REF] Hansen | Net external energy of the biologic and prosthetic ankle during gait initiation[END_REF][START_REF] Pillet | APSIC: training and fitting amputees during situations of daily living[END_REF] Different parameters can be extracted from this curve that have been shown to be characteristics of the mechanical behavior of the prosthetic foot. First, Hansen et al. [START_REF] Hansen | The human ankle during walking: implications for design of biomimetic ankle prostheses[END_REF] computed the hysteresis which is the net external energy lost in the ankle. Second, the stiffness can also be assessed. [START_REF] Pillet | APSIC: training and fitting amputees during situations of daily living[END_REF][START_REF] Frossard | Automated characterization of ankle stiffness of prosthetic feet fitted to bone-anchored transtibial prosthesis[END_REF] The slope of the best linear fit of the MAC characterizes the ankle behavior in the propulsion period of the stance. [START_REF] Shamaei | Estimation of quasi-stiffness and propulsive work of the human ankle in the stance phase of walking[END_REF] However, to the author knowledge, these parameters have never been used yet to characterize MPA behavior.

Whereas all the MPAs claims a better slope adaptation, the results in the literature are not consistent and the design parameters difficult to extract from these biomechanical studies.

Hansen and Starker 17 proposed a list of five mechanical parameters of the foot determinant of the outcome of walking of persons with amputations on level ground three out of five of these parameters can be quantified from the moment-angle curve, that is therefore a way to quantify the intrinsic foot adaptation on slope and can be used to compare prosthetic feet.

The hypothesis of the present study is that parameters extracted from moment-angle curve are relevant to compare MPA adaptations while walking in slope and can be used for the design of such feet.

To test this hypothesis, the study aims at -computing different parameters extracted from the moment-angle curve and investigating their meaning relative to the foot adaptation. -quantifying these parameters during level and slope locomotion of 5 persons with lower limb transtibial amputation successively fitted with three microprocessor prosthetic feet compared to their usual ESR foot.

Material and methods

This study was approved by the local ethics committee (2014-A01938-39 CPP Ile de France VI Groupe Hospitalier Pitie´-Salpeˆtrie`re).

Participants and protocol

Five persons with transtibial amputation were included (individual characteristics are given in Table 1) (For the participant TT01, only 2 MPA feet have been tested (Propriofoot & Meridium). The inclusion criteria were the following: being over 18 years old, amputated for more than 6 months, daily user of their habitual foot (HF), correctly fitted, without walking aid, for example, cane or crutches.

Three microprocessor prosthetic feet (described in the Table 2) and the habitual foot (ESR) of each individual were tested in a randomized order.

For each foot and after socket and alignment validation by one expert prosthetist (always the same), the subjects had 2 weeks to get used to the new prosthetic foot. Instrumental and functional evaluations were then performed. Between the sessions, a 3 weeks wash-out period with the habitual foot was observed before testing the next MPA foot.

Motion analysis

For quantitative analysis of gait, the subject was equipped with 54 reflective markers used to define 13 rigid segments. [START_REF] Pillet | APSIC: training and fitting amputees during situations of daily living[END_REF] As concerns joint centers definition, the ankle joint was assessed as the middle of the malleoli for the sound limb. For the prosthetic ankle, this center was assessed as the middle of the mechanical foot rotation axis which could be identified for the 3 MPA. For the HF, the center was taken as the symmetric of the sound side. For each patient and session, the same experimenter systematically placed the markers. Pictures of markers positions were taken in order to enhance the repeatability of positioning.

Three dimensional positions of these markers were recorded using an optoelectronic system with eight cameras (Vicon 8i, 100 Hz, Oxford Metrics, Oxford, UK) combined with two force plates (AMTI, Watertown, MA, USA). A 12% ramp was specifically designed to allow force plates recording during walking. [START_REF] Pillet | APSIC: training and fitting amputees during situations of daily living[END_REF] During a first acquisition, the subject was asked to stand still during 2 s with his feet parallel. He had to stay as much as possible without any flexion or extension of the lower limb, keep his eyes opened and look straight ahead. Then, three walking conditions at comfortable speed were recorded: on level ground, on a 12% (7°) ramp ascent and on a 12% (7°) ramp descent of 6.2 m long. At least, three clean trials (meaning with the whole foot on the force plate) were processed for every participant with each foot.

Data analysis

The preliminary static acquisition was used to define the local anatomical coordinate systems associated to each body segment. [START_REF] Pillet | APSIC: training and fitting amputees during situations of daily living[END_REF] The angular position of the joints were then computed as the variation, from the static reference, of the angular position of the proximal segment relatively to the distal one. The joint moments were computed at the joint centers, by an inverse dynamic procedure.

To obtain the ankle moment/angle curve, the evolution of the moment is then drawn as a function of the angle. The Figure 1 shows a typical pattern of this curve. On the graph, the heel strike corresponds to the number 1. From point 1 to point 2, lies the foot flattening. The number 5 indicates the end of the stance phase.

The following parameters have also been extracted (Figure 1):

-Range of motion (arrow on the Figure 1) computed as the difference between the maximal dorsiflexion (number 4 on Figure 1) and maximal plantarflexion (number 2 on Figure 1), -Equilibrium point (number 3 on Figure 1) as defined by William et al. corresponding to the angle reached when the moment equals zero during the period between the foot flat and the maximum dorsiflexion. [START_REF] Williams | Prosthetic anklefoot mechanism capable of automatic adaptation to the walking surface[END_REF] -Hysteresis (gray area on the Figure 1) defined as the net energy loss of the system, computed on the entire gait cycle as: Ð Md u ð Þ (with M the moment and u the ankle angle), [START_REF] Hansen | The human ankle during walking: implications for design of biomimetic ankle prostheses[END_REF] -Late stance energy released (black triangle on Figure 1) corresponding to the energy released from the maximal dorsiflexion of the ankle to the end of the stance phase (toe off -number 5 on Figure 1). -Quasi-stiffness (black line on the Figure 1) computed as the slope of the line that best fits the MAC of the ankle during the unipodal stance phase. -Global range of motion computed as the range between maximal dorsiflexion reached during slope ascent and the maximal plantarflexion reached during slope descent.

Statistics

The differences of the parameters observed between level and the other conditions were compared using the analysis of variance (ANOVA) with ''ankle type'' (ESR, Elanä, Propriofootä, Meridiumä) as factors. Post hoc analyses were conducted using Tukey tests. The level of significance was set at p \ 0.05. In the results part, only significant differences will be reported.

Results

Table 3 summarizes the values of the different parameters per condition averaged over all the participants whatever the foot used.

The following results refer only to the prosthetic side, not to the sound side of the participants.

The effect of the foot worn by the participant has been studied in the three conditions: level ground, ascent, descent. The speed was not statistically different for each participant whatever the foot for the three situations.

Figure 2 shows the typical patterns of the momentangle curves. They were similar among the participants while they were wearing the same foot except for the Elanä for which two profiles could be observed (Figure 2(b) and(c)).

Range of motion (ROM)

The highest plantarflexion of the prosthetic ankle complex among all prosthetic feet was observed when participants walked down the ramp when using the Meridiumä foot and could reached 17°(Table 3).

The maximal dorsiflexion was also observed with the Meridiumä (10°) in descent. On the contrary, the Elanä presented the lowest value of maximal dorsiflexion in ascent (9°) and maximal plantarflexion in descent (12°). The difference of the maximal dorsiflexion was statistically significant for the Meridiumä compared to the Elanä (p = 0.008) and to the ESR (p = 0.0027).

In every situation, the highest ROM was observed with the Meridiumä (on average, 19.5°in descent, 20.5°on level ground, 22.6°in ascent) and the lowest ROM with the Elanä (on average, 18.9°in descent, 18.9°on level ground and 13.9°in ascent).

When considering all the conditions, the global range of motion (from the maximal plantarflexion to the maximal dorsiflexion across all conditions) was also quantified. The highest global range of motion was observed for the Meridiumä (27.8°in average) and the lowest for the Elanä (20.5°). The global range of motion was statistically different between the Meridiumä and the Elanä (p = 0.0358).

Equilibrium point

For the ESR, the equilibrium point was similar in the three conditions (no shift of the curve along the X axis) (Figure 2(a)). For the Elanä, the equilibrium point was not shifted for the first characteristic pattern (Figure 2(b)). This was not true for the second characteristic pattern (Figure 2(c)). For the Propriofootä, there was no shift of the equilibrium point between level ground and descent. On the contrary, a shift could be observed between level ground and ascent (Figure 2(d)). Finally, there is a shift of the equilibrium point with the Meridiumä, between level ground and descent as between level ground and ascent (Figure 1(e)).

Hysteresis

The hysteresis (Figure 2 and Table 3) was different for the 4 feet and the three conditions. The Propriofootä and the ESR presented the lowest hysteresis and their averaged values remain similar in all conditions. The Meridiumä hysteresis was statistically higher (2-3 times) than the one of the other 3 feet (p = 0.001).

Concerning the Elanä, 2 different behaviors were observed:

-For two subjects, during the ascent, the hysteresis was almost null: all the energy stored was returned (Figure 2(b)). On level ground and in descent, the hysteresis was not null but was similar in both conditions. -For two subjects, on the contrary, the MAC showed a real loading phase (Figure 2(c)) and the hysteresis changed depending on the condition (Area descent . Area flat . Area ascent ).

Late stance energy released

Concerning the late stance energy released corresponding to the propulsion energy, the same trends as for the hysteresis could be observed for all feet depending on the situation. The energy released was the lowest in descent and the highest in ascent. On level ground, it was higher than in descent and lower than in ascent. The foot with the lowest energy for the propulsion was the Meridiumä.

Quasi-stiffness

The values of stiffness quantified for the different feet and conditions did not reveal statistical differences.

Discussion

The first aim of the study was to investigate the ability of different parameters extracted from the momentangle curve in the quantification of prosthetic feet adaptation between level and slope locomotion. To this purpose, some parameters coming from the literature were quantified from gait analysis data of five people with transtibial amputation successively fitted with 3 MPAs compared to their usual ESR foot in three walking conditions (level ground, upslope, and downslope). The present study confirms the interest of the MAC for the design and the evaluation of biomimetic prosthetic feet as already suggested in the literature. [START_REF] Hansen | The human ankle during walking: implications for design of biomimetic ankle prostheses[END_REF][START_REF] Frossard | Automated characterization of ankle stiffness of prosthetic feet fitted to bone-anchored transtibial prosthesis[END_REF] The results also support that parameters extracted from this curve are very useful to quantify the adaptation of MPA. [START_REF] Williams | Prosthetic anklefoot mechanism capable of automatic adaptation to the walking surface[END_REF] Indeed, these parameters are synthetic of the role of the ankle-foot complex, which allow the comparison of different technological design. [START_REF] Versluys | Prosthetic feet: state-of-the-art review and the importance of mimicking human anklefoot biomechanics[END_REF] The Propriofootä was the first MPA. The electric actuator is able to modify the ankle position during the swing phase toward dorsiflexion during slope ascent and toward plantarflexion during slope descent. It results in a shift of the ankle MAC on the angle axis that could be observed between the different conditions. This adaptation is higher during slope ascent than during slope descent. The global pattern of the curve remains the same, showing that the behavior of the foot is not modified during the stance phase. [START_REF] Fradet | Biomechanical analysis of ramp ambulation of transtibial amputees with an adaptive ankle foot system[END_REF] This is consistent with the design of the foot as the observed range of motion is due to the foot structure deformation under loading (like ESR feet). The results also show that the ankle angle adaptation allows to decrease the energy return during slope descent and to increase it during slope ascent in an order of magnitude close to the value obtained with ESR feet.

The Elanä foot adapts to varying terrain by modifying the damping coefficient of the ankle unit accounting for 9°of flexion extension. [START_REF] Struchkov | Biomechanics of ramp descent in unilateral trans-tibial amputees: comparison of a microprocessor controlled foot with conventional ankle-foot mechanisms[END_REF][START_REF] Koehler-Mcnicholas | The influence of a hydraulic prosthetic ankle on residual limb loading during sloped walking[END_REF] The ankle MAC is not shifted on the angle axis but the hysteresis is adapted to the slope to dissipate more energy during slope descent or less during slope ascent. The increase of the range of motion in slope, consecutive to the increase of plantarflexion in descent and dorsiflexion in ascent is limited compared to the other feet tested in this study. Finally, two profiles of MAC could be observed, corresponding to a variable adaptation of the foot depending on the individual setting. In particular, the setting of the hydraulic valve can impact the possible range of motion of the ankle.

The behavior of the Meridiumä is also adapted to varying terrain by modifying the hydraulic ankle behavior but on a wider range of motion than the Elanä and is able to hydraulically lock the ankle at a given angle. [START_REF] Ernst | Standing on slopes-how current microprocessor-controlled prosthetic feet support transtibial and transfemoral amputees in an everyday task[END_REF][START_REF] Schmalz | Lower limb amputee gait characteristics on a specifically designed test ramp: preliminary results of a biomechanical comparison of two prosthetic foot concepts[END_REF] The ankle MAC was shifted along the angle axis toward dorsiflexion during slope ascent until 15 degrees of maximal dorsiflexion and toward plantarflexion during slope descent until 12.7 degrees. These amplitudes allowed the highest global range of motion observed in the study giving a wide ability to adapt to the different walking conditions. The hysteresis of the curve during stance is also modified showing an increase of the dissipated energy during slope descent and a decrease of the dissipated energy during slope ascent. However, the returned energy during propulsion is the smallest among the feet tested in this study. The Meridium is the foot that presents the highest differences of hysteresis of the MAC between the different walking conditions. During the descent, more energy is lost compared to the other tested feet, which helps the subject in controlling his descent. In ascent, the hysteresis is decreased compared to level ground and descent. Thus, the dissipation of energy is limited in this condition where more energy is needed to go up the slope. However, it results in a low available power for the propulsion compared to the other feet. This trend is consistent with the functioning of the foot as the net external energy loss is directly linked to the energy that can be returned and used for propulsion.

Suggestive feedbacks and clinical functional test have been investigated in the companion article published in 2019 by Thomas-Pohl et al. [START_REF] Thomas-Pohl | Microprocessor prosthetic ankles: comparative biomechanical evaluation of people with transtibial traumatic amputation during standing on level ground and slope[END_REF] Basically, the participants found the MPAs heavier and less reactive for the propulsion.

Study limitations

The first limitation of the present study is the sample size which limits the power of the statistical analysis. Also, the population recruited was young (four of the participants were younger than 35 years old) and very active (military population).

The definition of the ankle center for the prosthetic feet can be also discussed. Indeed, for carbon-leaf foot design, there is no mechanical axis and the position of an ankle center is questionable. [START_REF] Prince | A new technique for the calculation of the energy stored, dissipated, and recovered in different ankle-foot prostheses[END_REF] On the contrary, for the 3 MPAs tested in the study, the mechanical axis could be visually identified, which ensures a consistent comparison between the feet.

The marker placement between sessions could introduced biases on the computation of the joint angles and moments, even if it was limited by the protocol.

Finally, even with an adaptation time and a fitting performed always by the same expert prosthetist, different profiles with the use of the Elan can be observed that can be related to the individual needs of the patient that the prosthetist must have to fulfill.

Conclusion

The results of the present study show that the parameters that can be extracted from the moment/angle curve of prosthetic ankle foot are useful for the evaluation of their behavior in situ as it allowed to differentiate the different MPA. The main advantage of this curve is to synthetize the main parameters that have an impact on the gait and that are in relation with the design of the foot.

This independent study has allowed to compare microprocessor-controlled ankle with ESR foot by providing meaningful parameters in different walking conditions. This quantitative evaluation shows that every MPA adapts their range of motion to the condition but that these adaptations result in a modification of the available energy for the propulsion, which must be taken into account according to the activity of the person.

Thus, it confirms that the choice of the more adapted prosthetic foot to a given person is a trade-off between comfort/propulsion and project life/compensations. The present study will be completed by the investigation of the overlying segments adaptation to characterize immediate compensations that can be observed when wearing different prosthetic feet.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 1 .

 1 Figure 1. Ankle moment (Nm/kg) versus ankle angle (degrees) on level ground (dorsiflexion is positive and plantarflexion is negative)-Number 1: heel strike, Number 2: maximal plantarflexion-Number 3: equilibrium point-Number 4: maximal dorsiflexion-Number 5: toe off, the black triangle area correspond to the late stance energy release, the gray area to the hysteresis.

Figure 2 .

 2 Figure 2. Typical patterns of the ankle moment (Nm/kg) versus ankle angle (degrees) in three different conditions (ascent = red, level = blue, descent = yellow) for the different feet tested-each subfigure corresponds to the average of one participant describing the typical patterns obtained (one for each foot except the Elan which had two different patterns (b and c).[AQ: 1].

Table 1 .

 1 Population included in the study.

		TT01	TT02	TT03	TT04	TT05
	Age (years)	29	64	29	29	35
	Sex	M	F	M	M	M
	Amputated side	R	L	R	L	L
	Height (cm)	176	172	168	180	183
	Mass with the prosthetic (kg)	82	68	70	66	95
	Time since amputation (months) Habitual foot	57 Sierra Ò	35 Panthera Ò (Medi)	25 Panthera Ò (Medi)	19 Variflex Ò (Ossur)	76 Variflex Ò (Ossur)
		(freedom
		innovation)

M: male; F: female; R: right; L: left.

Table 2 .

 2 Description of the microprocessor prosthetic feet used and their technological principles.

	Foot name	Manufacturer	Amplitude claimed	Comment
	Propriofoot ä	Ossur Ò	29°with 18°DF	Motor to modify ankle position
	Meridiumä	Ottobock Ò	during the swing phase Hydraulic system allowing 14°D Can adapt the hydraulic
			F and 22°PF	response and the angle of the
	Elanä	Endolite Ò	Hydraulic block allowing 9°with	dorsiflexion stop Can adapt the hydraulic
			3°DF	response independently in DF
				and PF, fixed range of ankle
				motion

DF: dorsiflexion; PF: plantarflexion.

Table 3 .

 3 Mean values (standard deviation) for each foot of all participants for each parameter and the three different conditions.

	Variable	Foot	Down	Level	Up
	Speed (m/s)	ESR	1.3 (0.2)	1.2 (0.2)	1.2 (0.2)
		Elan	1.3 (0.1)	1.3 (0.2)	1.3 (0.2)
		Propriofoot	1.3 (0.1)	1.2 (0.1)	1.3 (0.2)
		Meridium	1.3 (0.2)	1.3 (0.2)	1.3 (0.2)
	Max DF (°)	ESR	7.9 (1.6)	9.2 (1.8)	10.4 (3.0)
		Elan	7 (0.7)	8.3 (0.7)	9 (0.2)
		Propriofoot	9.6 (2.2)	10.5 (2.2)	13.5 (1.1)
		Meridium	9.9 (3.9)	9 (2.5)	15 (3.3)
	Max PF (°)	ESR	11.4 (1.6)	9.6 (1.4)	7.1 (0.6)
		Elan	11.9 (0.5)	10.6 (0.6)	4.9 (2.7)
		Propriofoot	11 (1.5)	10.3 (2.0)	4.6 (0.7)
		Meridium	12.7 (2.7)	11.3 (2.1)	4.5 (1.0)
	Range of motion (°)	ESR	19.3	18.8	17.5
		Elan	18.9	18.9	13.9
		Propriofoot	20.6	20.8	18.1
		Meridium	22.6	20.3	19.5
	Equilibrium point (°)	ESR	7 (1.9)	6.2 (1.2)	5.4 (0.8)
		Elan	5 (1.3)	7.1 (1.9)	2.5 (2.8)
		Propriofoot	6.2 (1.0)	6.6 (1.8)	3 (0.0)
		Meridium	11.2 (2.)	9.6 (2.2)	4.8 (1.2)
	Hysteresis (J/kg)	ESR	4.2 (1.7)	3.7 (1.4)	3.0 (1.8)
		Elan	5.2 (2.2)	5.4 (1.9)	1.5 (1.5)
		Propriofoot	3.3 (0.6)	3.8 (1.6)	4.1 (1.8)
		Meridium	15.2 (2.8)	10.4 (2.4)	7.1 (1.7)
	Energy propulsion (J/kg)	ESR	5.6 (1.5)	7.3 (3.1)	9.1 (4.2)
		Elan	4.0 (0.3)	5.4 (0.4)	6.1 (0.8)
		Propriofoot	5.6 (1.3)	6.7 (0.8)	8.0 (0.9)
		Meridium	2.2 (0.5)	3.7 (0.9)	4.0 (1.1)
	Quasi-stiffness (Nm/kg/°)	ESR	0.08 (0.01)	0.09 (0.01)	0.09 (0.01)
		Elan	0.08 (0.01)	0.11 (0,00)	0.09 (0.02)
		Propriofoot	0.07 (0.02)	0.08 (0.02)	0.08 (0.02
		Meridium	0.08 (0.01)	0.09 (0.01)	0.10 (0.01)
	Range of motion global including	ESR	22 (3.3)
	the three walking conditions (°)	Elan	20.5 (0.9)
		Propriofoot	24 (1.9)
		Meridium	27.8 (4.1)

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.


Wenjuan Wang

Elena S Chamkina

Eduardo Guisasola Cal

Desire Di Silvio

Marta Martínez Moro

Sergio Moya

Jean-René Hamon

Didier Astruc
email: didier.astruc@u-bordeaux.fr

Zinaida B Shifrina
email: shifrina@ineos.ac.ru

Ferrocenyl-terminated polyphenylene-type "click" dendrimers as supports for efficient gold and palladium nanocatalysis

Whereas dendrimer supports are known as key parts of nanocatalysts, the capability of rigid dendrimers for this function has not yet been reported. Here, the study is focused on ferrocenylmethylenetriazolyl-terminated dendrimers (FcMTPD) as supports of remarkably efficient nanogold and nanopalladium catalysts. A biphasic system is elaborated to evaluate the catalytic activity of FcMTPD-supported Au and Pd nanoparticles (NPs) for the reduction of 4-nitrophenol to 4-aminophenol by NaBH4 at 20 °C, and FcMTPD-supported PdNPs are found to be the best nanocatalyst with a rate constant kapp= 7.8×10 -2 s -1 . Excellent catalytic results are also obtained in this reaction for FcMTPD-supported AuNPs with a rate constant kapp= 5.6×10 -2 s -1 . For both Pd NPs and AuNPs, the kinetic results are shown to strongly depend on the method of preparation of these NPs that influences the NP size, thus their catalytic efficiency. The FcMTPD-stabilized PdNPs are easily recovered and reused at least 13 times, and their catalytic performance displays only a slight decrease during the first seventh runs.

Introduction

The ability of dendrimers [START_REF] Tomalia | [END_REF][2][3][4] to stabilize transition-metal nanoparticle catalysts [5][6][7][8][9] has been well recognized. Dendrimers constructed with rigid tethers such as polyphenylene dendrimers 10,11 or poly(azomethine) dendrimers 12,13 present specific structures and properties that have attracted much attention from researchers. Yamamoto's group has exploited the properties of phenylazomethine dendrimers to stabilize nanoclusters or very small nanoparticles (NPs) that are very active in catalysis, 14,15 but Müllen-type poly(phenylene) dendrimers have not been much utilized for the preparation of active nanocatalysts. Functionalization with pyridyl groups 16 has provided first attempts to coordinate transition metal cations and NPs., 17,18 with special attention to prion trapping. 19,20 Recently, ferrocene terminated dendrimers with rigid cores have been obtained via the Diels-Alder approach with ferrocene containing cyclopentadienone, 21 and polyphenylene dendrimers containing the pyridyl units and terminated with ethynyl groups have been "clicked" with azidomethyleneferrocene according to the CuAAC reaction to form 1,2,3-triazolylmethylene-ferrocene-terminated poly(phenylene) dendrimers. 22 The later dendrimers possess the 1,2,3-triazole groups near their termini allowing to coordinate transition-metal cations [23][START_REF] Cotton | Advanced Inorganic Chemistry[END_REF][25][26][27] and smoothly stabilize late transition-metal NPs. Ferrocene-terminated dendrimers are a well-documented family [28][START_REF] Casado | Designing Dendrimers[END_REF][START_REF] Ornelas | [END_REF][31] with rich redox properties related to the location of the ferrocene groups in the dendrimers that is favorable toward the use of redox-related processes. 25 Here, the role of the ferrocene termini is to provide bulk at the dendrimer periphery in order to inhibit or at least minimize NP agglomeration, and therefore improve the performances of the nanocatalysts. On the other hand, the ferrocene group does not play any redox role in these catalytic processes, because its reduction would be far too negative to be observed under the reaction conditions. Given the ability of gold [32][33][34] and palladium 35- ferrocenylmethylene-triazolyl-poly(phenylene) dendrimer (FcMTPD, Fig. 1) and its catalytic properties. The selected reaction in an environmentally-useful process, the prototypical reduction by sodium borohydride of the pollutant nitrobenzene to the nitroaniline dye, an industrial intermediate in the manufacture of analgesic and antipyretic drugs. 38,39 The kinetic of this standard reaction, discovered by Pal and his group upon Ag NP catalysis, 40,41 has been deeply examined by Ballauff and his group, 42- 44 and nanocatalysis of nitroarene reduction has been reviewed. [41][42][43][44][45]

Results and discussion

Synthesis and characterization of the metal nanoparticles (MNPs).

FcMTPD was fabricated as described in the literature, 22 and it was used as a stabilizing support of Au(III) and Pd(II) upon reactions with HAuCl4 and Na2PdCl4, respectively. The intradendritic triazoles and pyridyls that are present in stoichiometric amount vs. Au(III) displace a chloride ligand from the Au(III) coordination sphere in the mixed solvent system used (CH2Cl2/MeOH), so that the main species in aqueous solution is the neutral Au(III) square-planar species [AuCl3(triazole)] or [AuCl3(py)], respectively, as shown earlier with ferrocenyl triazole derivatives. [23][START_REF] Cotton | Advanced Inorganic Chemistry[END_REF][25][26][27] Likewise, substitution of a chloride ligand by an intradendritic triazole or pyridyl in [PdCl4] 2-presumably leads to d 8 Pd(II) square-planar species [Pd(triazole)Cl3] -or [PdCl3(py)] -, respectively. [23][START_REF] Cotton | Advanced Inorganic Chemistry[END_REF][25][26][27] The lability of the ligands due to the dendritic bulk is not involved, because in such rigid dendrimers the branch termini carrying these ligands are maintained far from one another, unlike in flexible dendrimers. Indeed, the colors and UV-vis. spectra of these solutions were stable for several days. One hour after addition of the transition-metal salts to the ferrocenylmethylenetriazolylterminated dendrimers (FcMTPD)-coordinated Au(III) and Pd(II), addition of NaBH4 rapidly leads to formation of AuNP-1 and PdNP-1 (Scheme 1a). Alternatively, HAuCl4 or Na2PdCl4 are added to a mixture of FcMTPD and NaBH4 (Scheme 1b) in the same mixture of solvents, which led to AuNP-2 and PdNP-2. The FcMTPD-supported NPs prepared using these two methods are compared for their plasmon band in the case of the Au NPs and for their size (from TEM measurements) and catalytic activities. In these reduction reactions, the neutral Fe II ferrocenyl groups remain unchanged, because their reduction to Fe I would occur only at extremely negative redox potentials, i. e. around -3 V vs. SCE. 25 This is confirmed by comparison of the XPS analysis of the Fe 2p3/2 orbital of ferrocene in the dendrimer before complexation, after coordination of the dendrimer to Pd(II) and after reduction of Pd(II) by NaBH4 to the Pd(0) NPs. In these three situations, the XPS value for the Fe 2p3/2 orbital remains constant at 707.8 ± 0.1 eV (Table S1, Fig. S1-3), showing that the ferrocene termini, unlike the triazole groups (vide infra), are not electronically perturbed by the coordination and reduction processes. The role of the ferrocene termini is to provide bulk at the dendrimer periphery in order to form a shell around the dendrimer inhibiting encapsulated NP escape. Stabilization of NPs by bulky dendrimer periphery was already observed when three first generations of a dendrimer did not inhibit NPs to escape from inside dendrimers, whereas the fourth generation providing a sufficiently bulky periphery inhibited small NP escape. 17 During the process of preparation of AuNPs, the color of the CH2Cl2 solution changed from light yellow to red-brown for AuNPs-1 and from light yellow to purple for AuNPs-2. The surface plasmon band (SPB) of AuNPs-1 is found at 511 nm and that of AuNPs-2 is observed at 524 nm (Fig. 2). Compared with AuNPs-1, the SPB of AuNPs-2 shows a red shift, qualitatively indicating that AuNPs-2 have a larger size than AuNP-1. For PdNPs, the color of solution changed from yellow-brown to brown for PdNPs-1 and from yellow-brown to golden yellow for PdNPs-2 (Fig. S4). The XPS results show that the FcMTPD-coordinated metal cations have been reduced to metal (0) NPs (Fig. 3). Partial (minor) oxidation to Pd(II) found by XPS (Fig. 3a) is believed to results from some aerobic oxidation occurring between the time of the synthesis and that of the XPS record. Au(0) state in all the FcMTPD-supported AuNPs samples already observed by XPS (Fig. 3b) is confirmed by the presence of the Au plasmon band around 520 nm (vide supra, Fig. 2). MNPs with low polydispersity resulting from stabilization by the "click" dendrimer FcMTPD are observed (Fig. 4). The mean sizes of PdNPs-1 and AuNPs-1 are 2.0 nm and 3.6 nm, respectively, and those of PdNPs-2 and AuNPs-2 are 3.7 nm and 7.5 nm, respectively. Compared with AuNPs, PdNPs are smaller, which might be part of the reason explaining why PdNPs show a better catalytic performance than AuNPs. The difference of NP size between the Au and Pd NP synthesized under the same conditions is due to difference of aggregation rates of Pd and Au atoms including the relativistic effect of Au that favors their aggregation in clusters and NPs. 27 In addition, MNPs-2 are larger than MNPs-1, indicating that direct reduction of FcMTPDsupported metal cations to MNPs-1 by NaBH4 is the optimized way to fabricate smaller, more catalytically active MNPs.

The click dendrimers stabilize the NPs through their interaction with the intradendritic triazole rings near their periphery and with pyridines, acting as ligands for the nanoparticle surface. This is beneficial for catalysis, because large agglomerated NPs would be less catalytically active. 4 NPs Indeed, earlier comparison between click dendrimers containing triazole ligands near their periphery and dendrimers of similar size that did not contain triazole groups showed that only triazole-containing dendrimers near their periphery stabilized such small nanoparticles, whereas other dendrimers stabilized only very large nanoparticles (like 10 nm). 46,47 By analogy, the fact that relatively small NPs were characterized here confirm the existence of these dendrimer-NP interactions that occur necessarily at the dendrimer peripheries, given the closely related sizes of the dendrimer and NPs. Nevertheless, since the dendritic triazoles and pyridines appear to be the ligands stabilizing the NPs, this implies a small penetration of the NPs near the external part of the dendrimers. These tether extremities can bend (unlike the rigid interiors), because the triazolyl ferrocenes are the only flexible fragments of the dendrimer. 46,47 XPS analysis of the N atoms provides useful information on the coordination of the Ncontaining intradendritic ligands by Pd(II) upon reaction with Na2PdCl4 and Pd(0) NPs formed upon reduction of the former by NaBH4. 48 The compared XPS data of the N 1s orbital of FcMTPD alone, Pd(II)-FcMTPD complexes and Pd(0)NPs-FcMTPD are shown in Figure 5. In the Pd(II)-dendrimer complex, the very significant shift of the N 1s binding energy to a higher value shows the electron-donating effect from N to Pd(II) due to the N atoms sharing their lone pairs with Pd(II). With the Pd(0) NP complex, this shift is much weaker as expected due to the much weaker electronic donation from N to Pd(0) than with Pd(II), although it can still clearly be observed.

Catalysis by the metal NPs of 4-nitrophenol (4-NP) reduction.

The catalytic activity of metal NPs (MNPs) for the 4-nitrophenol (4-NP) reduction to 4-aminophenol (4-AP) was evaluated using a standard reaction, the reduction of 4-NP to 4-AP by NaBH4. This reaction, disclosed by Pal group in 2002, has been much studied mechanistically, [42][43][44][45] and the intermediacy of nitrosophenol and 4hydroxyaminophenol has been shown. 41 Several mechanisms including the Langmuir-Hinshelwood mechanism with fast adsorption of both substrates on the catalyst, discussed through in-depth studies by Ballauff, 42 and the Eley-Rideal mechanism involving hydride adsorption 41 have been proposed. Indeed, metal NPs behave as electron reservoirs [49][50][51] with surface atom-hydrogen bond intermediates, 49,51 and the hydride donor NaBH4 has been shown to be able to transfer sequentially an electron and a hydrogen atom to delocalized electron-reservoir systems 51 such as late transitionmetal NPs. Likewise, the hydride transfer steps from the NP catalyst to 4-NP can proceed by a sequence of electron transfer followed by hydrogen atom transfer, coupled electron-hydrogen atom transfer 52 or direct hydride transfer. Activation of the NP surface-adsorbed nitrophenolate substrate in the rate-limiting step is then all the easier as the NP catalyst is negatively charged, which increases its reactivity. 53,54 The convenience of the 4-NP reduction reaction is due to its simple manipulation and obvious color change during the reaction process. In addition, whereas the reaction is usually conducted in water only, a biphasic system composed of CH2Cl2 and water was newly used here in order to carry out the catalytic reaction, since both the dendrimer and the MNPs are soluble in CH2Cl2. Therefore, in the reaction mixture, the MNP catalyst is located in the lower layer (CH2Cl2 phase) and the substrates are located in the upper layer (aqueous phase). The color of the aqueous solution containing 4-NP changes from pale yellow to dark yellow upon addition of NaBH4, owing to the formation of sodium 4-nitrophenolate. After the reaction is completely finished, the dark-yellow color vanishes, and therefore the reaction mixture becomes colorless. S2) for the calculation of the rate constant normalized to the surface of the particles in the medium. 42,43 As shown in Fig. 6a, with 0.5% mmol of PdNPs-1, the absorbance peak at 400 nm corresponding to the nitrophenolate anion decreases rapidly with time and disappears after 60 s, with a kapp= (7.8 ± 0.7) × 10 -2 s -1 (Fig. 7). A weak signal at 300 nm corresponding to 4-AP appears, and its intensity gradually increases with time. Under the same conditions, for AuNPs-1 (Fig. 6b), it takes 80 s to finish the catalytic reaction, and the value of the rate constant kapp is (5.6 ± 0.2) ×10 -2 s -1 (Fig. 7). In addition, no more absorption band at 400 nm is observed after 120 s for PdNPs-2 (Fig. 6c) and 480 s for AuNPs-2 (Fig. 6d), and their values of kapp are (4.0 ± 0.2) ×10 -2 s -1 and (0.95 ± 0.02) ×10 -2 s -1 (Fig. 7), respectively. Compared to the other MNPs, PdNPs-1 is the best catalyst for the reduction of 4-NP. The comparison between MNPs-1 and MNPs-2 shows the higher catalytic efficiency of MNPs-1. This efficiency difference between MNPs-1 and MNPs-2 is more marked for AuNPs-1 whose catalytic efficiency is around 6 times as much as that of AuNPs-2. This result signifies that the synthetic method of preparation of MNPs-1 by addition of NaBH4 into a solution containing both the dendrimer and the metal salt is superior to that involving addition of metal salt into a mixture of the dendrimer and NaBH4. The lower catalytic efficiency of MNPs-2 is attributed to the lack of complete coordination of the metal cation with the dendritic triazole during the short reaction time followed by rapid reduction to MNPs-2 in large part in solution outside the FcMTPD. This results in inter-FcMTPD NP stabilization of MNPs-2 rather than intra-FcMTPD NP stabilization in the case of MNPs-1. Outside the dendrimer, the reduced steric confinement let NP aggregation proceed further before inter-FcMTPD NP stabilization. As a consequence, the MNPs-2 are larger than the MNPs-1 and less catalytically active, because the total surface of MNPs-2 is smaller than that of MNPs-1 for the same mass amount. The presence of the bulky terminal ferrocenyl group apparently serves to optimize the balance between stabilization and catalytic activity.

The remarkably low polydispersity of the NPs and the NP stability and small size (2 to 4 nm) related to that of the dendrimer (4 nm) all confirm encapsulation near the periphery of the dendrimers (vide infra) and stabilization by coordination of the intradendritic triazole. The interaction of the NP with the bipyridine ligands did not lead to improvement of the catalytic reactions upon increasing the amount of metal precursor in order to account for pyridine coordination (Fig. S5-S7). As shown in Fig. S9, with 0.5% mmol of MNPs-3, no signal at 400 nm is observed after 80 s for PdNPs-3 (Fig. S6a) and 120 s for AuNPs-3 (Fig. S6b), and their kapp values are (7.1 ± 0.5) × 10 -2 s -1 and (4.4 ± 0.6) × 10 -2 s -1 (Fig. S6c), respectively. In addition, MNPs-3 will cluster and form precipitation after 2 h for AuNPs-3 (Fig. S7a andb) and 12 h for PdNPs-3 (Fig. S7c). These results suggest that the catalytic performance and stability of MNPs-3 are not as good as those of MNPs-1, and a weaker interaction between the pyridine ligands and MNPs. The comparison of the apparent rate constants kapp observed here with those recently reported in the literature shows the excellent efficiency of the present FcMTPDsupported Au and Pd NPs (Table 1).

Stability of PdNPs-1 in the reduction of 4-NP

To further assess the catalytic activity of MNPs, the best catalyst PdNPs-1 was selected to check its recyclability. After the catalytic reduction of 4-NP was completely finished, the biphasic system was kept still until the organic phase and aqueous phase were well separated. The catalyst PdNPs-1 in the lower CH2Cl2 phase was recovered by removing the aqueous solution with 4-AP. A fresh aqueous solution of 4-NP and NaBH4 was added into the reused catalyst solution for another round of reaction as shown in Fig. 8a. The reaction time for full conversion of 4-NP changed with increase of the number of recycling (Fig. 8b). The catalytic performance exhibited a slight decrease from the 1 st run to 7 th run, but showed an obvious decrease after the 11 th run, which is ascribed to the tendency of PdNPs-1 tend to aggregate. However, PdNPs-1 still display a good catalytic activity even after being reused 13 times.

After the 1 st cycle, the size of the AuNPs-1 displays a change from 4 nm to 7.46 nm but that of PdNPs-1 changes a little bit from 2 nm to 2.95 nm (Fig. S8). Besides, the UVvis. spectrum of PdNPs-1 keeps the same shape, but the SPB of AuNPs-1 shows a red shift from 511 nm to 540 nm (Fig. S9), revealing that AuNPs-1 with larger size tend to aggregate after the 1 st run, which is in concordance with the TEM images. Thus, the stability of PdNPs-1 is much better than that of AuNPs-1.

Experimental Section

Synthesis of MNPs-1 stabilized by FcMTPD.

FcMTPD was prepared according to the literature procedure by copper-catalyzed azidealkyne cycloaddition (CuAAC) reaction between a previously reported ethynylterminated dendrimer and azidomethylferrocene. 22 Then, a solution (VCH2Cl2/ V MeOH = 30:1, 6.8 mL) of Na2PdCl4 (or HAuCl4, 1.0 × 10 -3 mmol, nmetal:ntrz = 1:1) was mixed with a solution (VCH2Cl2/ V methanol = 30:1, 3 mL) of the dendrimer FcMTPD (6.25×10 -5 mmol) in a 20 mL flask with a stir bar. After the mixture was stirred for 30 min, then 5.0 × 10 -3 mmol of NaBH4 was added into the flask under vigorous stirring. After continuous stirring for 1 h at room temperature, the metal nanoparticles were obtained.

Synthesis of MNPs-2 stabilized by FcMTPD.

A solution (VCH2Cl2/ V methanol = 30:1, 3.2 mL) of FcMTPD (6.25 × 10 -5 mmol) and NaBH4 (5.0 × 10 -3 mmol), and a stir bar were introduced into a 20 mL flask, then a solution (VCH2Cl2/ V MeOH = 30:1, 6.8 mL) of the Na2PdCl4 (or HAuCl4, 1.0 × 10 -3 mmol, nmetal:ntrz = 1:1) was added dropwise under vigorous stirring. After continuous stirring for 1 h at room temperature, the MNPs were obtained.

Reduction of 4-NP to 4-AP catalyzed by MNPs-1 and MNPs-2

First, a fresh solution of MNP (0.5% mmol) was injected into a 20 mL flask, and CH2Cl2 was added until the volume of organic phase reached 3 mL. Then a 10 mL prepared aqueous solution of 4-NP (4.17 mg, 3.0 × 10 -2 mmol) and NaBH4 (113.5 mg, 3.0 mmol) were added into the flask. 57 Then, the reaction system was vigorously stirred at rt. The dark-yellow color of the mixture changed to colorless with time, and UV-vis. spectroscopy was applied to monitor the process of the reaction kinetics (40 s for each round).

Recycling of PdNPs-1 for 4-NP reduction

Catalytic reduction of 4-NP by PdNPs-1 was recorded according to the steps mentioned above. While the color of the mixture became colorless, the biphasic system was kept still until the organic phase and aqueous phase were completely separated. The CH2Cl2 phase with the catalyst PdNPs-1 was recovered by removing the aqueous solution with 4-AP. In order to keep the volume of CH2Cl2 at 3 mL, fresh CH2Cl2 was injected into the biphasic system to reach this volume. 10 mL of fresh aqueous solution of 4-NP and NaBH4 was added into the reused catalyst solution for another round of reaction.

Conclusion

In summary, the FcMTPD containing 1,2,3-triazolyl and pyridyl groups was used to stabilize PdNPs and AuNPs. Two preparation modes were compared for both metal NPs in order to optimize the FcMTPD-supported NP catalytic efficiency, and it was found that addition of NaBH4 addition to pre-coordinated metal cation leading to MNPs-1 provided the best results. MNPs-2 prepared by addition of the metal cation complex to a solution containing a mixture of FcMTPD and NaBH4 produced less efficient PdNPs-2 and AuNPs-2, respectively than the corresponding MNPs-1, which was assigned to increased aggregation of MNPs-2 outside FcMTPD. Whereas this reaction is usually conducted in water, a new biphasic system was elaborated here to evaluate the catalytic activity of FcMTPD-supported MNPs-1 and MNPs-2 in the reduction of 4-NP to 4-AP by NaBH4 at 20 °C. Such a new biphasic system involving hydrophobic nanocatalysts that are insoluble in water is extremely practical and could in principle be extended in the future to any other hydrophobic nanocatalyst. 58 For instance, the catalytic efficiency of AuNPs-1 was around 6 times superior to that AuNPs-2 in terms of rate constant kapp. This result indicates that the location of small MNPs supported by the nitrogen ligands inside the periphery of the FcMTPD plays a vital role for the NP catalytic efficiency.

Although the dendritic core of FcMTPD is rigid, the bulky terminal CH2Fc group can freely rotate around the triazole-CH2 bond to accommodate adequate coordination of the ligands to transition metal cations and, more smoothly, to NPs for their stabilization.

In this way a reasonable balance is obtained between NP stabilization and catalytic activity. As a result, the FcMTPD-stabilized PdNPs show excellent catalytic efficiency and stability, as indicated by recycling using the biphasic system. Indeed, the catalytic activity of these PdNPs-1 exhibits only a slight decrease, allowing the system to be reused many times.

Acknowledgements

Financial support from the China Scholarship Council (CSC, PhD grant to W. W.), the Universities of Rennes 1 and Bordeaux, the Centre National de la Recherche Scientifique (CNRS), the Ministry of Science and Higher Education of the Russian Federation using the equipment of Center for molecular composition studies of INEOS RAS, and CIC biomaGUNE is gratefully acknowledged.

Fig. 1 .

 1 Fig. 1. Structure of the ferrocenylmethylene-triazolyl-poly(phenylene) dendrimer, FcMTPD.

Scheme 1

 1 Scheme 1 Syntheses of Au and Pd NPs by a) addition of NaBH4 to FcMTPD-supported Au(III) or Pd(II) leading to the MNPs-1; b) addition of the complex HAuCl4 or Na2PdCl4 to a mixture of the dendrimer and NaBH4 leading to the formation of the MNPs-2.

Fig. 2 .

 2 Fig. 2. UV-vis. spectrum of FcMTPD-stabilized AuNPs-1 and AuNPs-2. Insert: photograph of AuNPs-1 (left) and AuNPs-2 (right).

Fig. 3 .

 3 Fig. 3. XPS spectra of the PdNPs-1(a) and AuNPs-1 (b).

Fig. 4 .

 4 Fig. 4. TEM images of PdNPs-1 (a), AuNPs-1 (c), PdNPs-2 (e) and AuNPs-2 (g); size distribution histogram of PdNPs-1 (b), AuNPs-1 (d), PdNPs-2 (f) and AuNPs-2 (h). The larger size of AuNPs compared to PdNPs is due to the gold aurophilicity involving the relativistic effect of Au atoms facilitating their aggregation.

Fig. 5 .

 5 Fig. 5. N 1s XPS of FcMTPD alone, Pd(II)-FcMTPD and Pd(0) NP@FcMTPD.

Fig. 6 .

 6 Fig. 6. Time-dependent UV-vis. spectrum of p-nitrophenol reduction in the presence of different catalysts (0.5% mmol of MNPs).

Fig. 7 .

 7 Fig. 7. Plots of the consumption rate of 4-NP: [-ln (Ct/C0)] vs. reaction time with 0.5% mmol of nanocatalyst. See ESI (eq. 7 and TableS2) for the calculation of the rate constant normalized to the surface of the particles in the medium.42,43

Fig. 8 .

 8 Fig. 8. (a) Schematic diagram for the re-use of PdNPs-1 in the reduction of 4-NP. Plots of reaction time for full conversion vs. recycling number of PdNP-1 (b).

Table 1

 1 Comparison of selected literature apparent rate constants kapp with the present results for the nanocatalyzed reduction of 4-NP to 4-AP by NaBH4.

	Entry	Catalyst	Catalyst amount (ug)	kapp (s -1 )	Reference
	1	Pure Pt	4.0	1.25×10 -4	55
	2	Raney Ni	4.0	1.48×10 -4	55
	3	NiPt NPs	4.0	1.93×10 -3	54
	4	PtPdFe	2.5	3.00×10 -2	56
	5	PdCuFe/RGO	2.8	8.90×10 -3	56
	6	Pd/RGO	2.5	4.52×10 -3	56
	7	PtCu/RGO	2.6	8.02×10 -3	56
	8	Pd	3.1	1.02×10 -3	56
	9	Pd/AC	3.0	2.58×10 -2	56
	10	AuNP-5	5.2	2.63×10 -2	57
	11	AuNP-5	1.3	1.33×10 -2	57
	12	PdNPs-1	0.7	(7.8 ± 0.7) ×10 -2	This work
	13	AuNPs-1	1.3	(5.6 ± 0.2)×10 -2	This work

NPs as catalysts, we have investigated and report here their stabilization by the