Randy Goebel
email: rgoebel@ualberta.ca

Ajay Chander
email: achander@us.fujitsu.com

Katharina Holzinger
email: kholzinger@sba-research.org

Freddy Lecue
email: freddy.lecue@inria.fr

Zeynep Akata
email: z.akata@uva.nl

Simone Stumpf
email: simone.stumpf.1@city.ac.uk

Peter Kieseberg
email: peter.kieseberg@fhstp.ac.at

Andreas Holzinger
email: a.holzinger@hci-kdd.org

Explainable AI: the new 42?

Keywords: artificial intelligence, machine learning, Explainability, Explainable AI

Abstract. Explainable AI is not a new field. Since at least the early exploitation of C.S. Pierce's abductive reasoning in expert systems of the 1980s, there were reasoning architectures to support an explanation function for complex AI systems, including applications in medical diagnosis, complex multi-component design, and reasoning about the real world. So explainability is at least as old as early AI, and a natural consequence of the design of AI systems. While early expert systems consisted of handcrafted knowledge bases that enabled reasoning over narrowly well-defined domains (e.g., INTERNIST, MYCIN), such systems had no learning capabilities and had only primitive uncertainty handling. But the evolution of formal reasoning architectures to incorporate principled probabilistic reasoning helped address the capture and use of uncertain knowledge. There has been recent and relatively rapid success of AI/machine learning solutions arises from neural network architectures. A new generation of neural methods now scale to exploit the practical applicability of statistical and algebraic learning approaches in arbitrarily high dimensional spaces. But despite their huge successes, largely in problems which can be cast as classification problems, their effectiveness is still limited by their un-debuggability, and their inability to "explain" their decisions in a human understandable and reconstructable way. So while AlphaGo or DeepStack can crush the best humans at Go or Poker, neither program has any internal model of its task; its representations defy interpretation by humans, there is no mechanism to explain their actions and behaviour, and furthermore, there is no obvious instructional value . . . the high performance systems can not help humans improve. Even when we understand the underlying mathematical scaffolding of current machine learning architectures, it is often impossible to get insight into the internal working of the models; we need explicit modeling and reasoning tools to explain how and why a result was achieved. We also know that a significant challenge for future AI is contextual adaptation, i.e., systems that incrementally help to construct explanatory models for solving real-world problems. Here it would be beneficial not to exclude human expertise, but to augment human intelligence with artificial intelligence.

Introduction

Artificial intelligence (AI) and machine learning (ML) have recently been highly successful in many practical applications (e.g., speech recognition, face recognition, autonomous driving, recommender systems, image classification, natural language processing, automated diagnosis, . . . ), particularly when components of those practical problems can be articulated as data classification problems. Deep learning approaches, including the more sophisticated reinforcement learning architectures, exceed human performance in many areas [START_REF] Moravčík | Deepstack: Expert-level artificial intelligence in heads-up no-limit poker[END_REF], [START_REF] Taigman | Deepface: Closing the gap to human-level performance in face verification[END_REF], [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF], [START_REF] Esteva | Dermatologist-level classification of skin cancer with deep neural networks[END_REF].

However, an enormous problem is that deep learning methods turn out to be uninterpretable "black boxes," which create serious challenges, including that of interpreting a predictive result when it may be confirmed as incorrect. For example, consider Figure 1, which presents an example from the Nature review by LeCun, Bengio, and Hinton [START_REF] Lecun | Deep learning[END_REF]. The figure incorrectly labels an image of a dog lying on a floor and half hidden under a bed as "A dog sitting on a hardwood floor." To be sure, the coverage of their image classification/prediction model is impressive, as is the learned coupling of language labels. But the reality is that the dog is not sitting.

The first problem is the naive but popular remedy about how to debug the predictive classifier to correct the error: augment the original labeled training set with more carefully crafted inputs to distinguish, say, a sitting from a laying dog might improve the incorrect output. This may or may not correct the problem, and doesn't address the resource challenge of recreating the original learned model.

The transparency challenge gets much more complex when the output predictions are not obviously wrong. Consider medical or legal reasoning, where one typically seeks not just an answer or output (e.g., a diagnostic prediction of Description: This is a large bird with a white neck and a black back in the water. Definition: The Western Grebe is has a yellow pointy beak, white neck and belly, and black back. Visual Explanation: This is a Western Grebe because this bird has a long white neck, pointy yellow beak and red eye.

Image Relevance Class Relevance

Description

Visual Explanation Definition Laysan Albatross Description: This is a large flying bird with black wings and a white belly. Definition: The Laysan Albatross is a seabird with a hooked yellow beak, black back and white belly. Visual Explanation: This is a Laysan Albatross because this bird has a large wingspan, hooked yellow beak, and white belly.

Description: This is a large bird with a white neck and a black back in the water. Definition: The Laysan Albatross is a seabird with a hooked yellow beak, black back and white belly. Visual Explanation: This is a Laysan Albatross because this bird has a hooked yellow beak white neck and black back. prostate cancer would require some kind of explanation or structuring of evidence used to support such a prediction). In short, false positives can be disastrous.

Laysan Albatross

Briefly, the representational and computational challenge is about how to construct more explicit models of what is learned, in order to support explicit computation that produces a model-based explanation of a predicted output.

However, this is one of the historical challenges of AI: what are appropriate representations of knowledge that demonstrate some veracity with the domain being captured? What reasoning mechanisms offer the basis for conveying a computed inference in terms of that model?

The reality of practical applications of AI and ML in sensitive areas (such as the medical domain) reveals an inability of deep learned systems to communicate effectively with their users. So emerges the urgent need to make results and machine decisions transparent, understandable and explainable [START_REF] Holzinger | Towards interactive machine learning (iml): Applying ant colony algorithms to solve the traveling salesman problem with the human-in-the-loop approach[END_REF], [START_REF] Holzinger | Towards the augmented pathologist: Challenges of explainable-ai in digital pathology[END_REF], [START_REF] Holzinger | A glass-box interactive machine learning approach for solving np-hard problems with the human-in-the-loop[END_REF]. The big advantage of such systems would include not only explainability, but deeper understanding and replicability [START_REF] Holzinger | What do we need to build explainable ai systems for the medical domain?[END_REF]. Most of all, this would increase acceptance and trust, which is mandatory in safety-critical systems [START_REF] Holzinger | Can we trust machine learning results? artificial intelligence in safety-critical decision support[END_REF], and desirable in many applications (e.g., in medical robotics [START_REF] Osullivan | Machine learning enhanced virtual autopsy[END_REF], Ambient Assisted Living [START_REF] Singh | Human activity recognition using recurrent neural networks[END_REF], Enterprise decision making [START_REF] Chander | Working with beliefs: AI transparency in the enterprise[END_REF], etc.). First steps have been taken towards making these systems understandable to their users, by providing textual and visual explanations [START_REF] Kulesza | Principles of explanatory debugging to personalize interactive machine learning[END_REF], [START_REF] Tulio Ribeiro | Why should i trust you?: Explaining the predictions of any classifier[END_REF] (see Figures 2 and3). 2 Current State-of-the-Art

Deep Finegrained Classifier

Explaining decisions is an integral part of human communication, understanding, and learning, and humans naturally provide both deictic (pointing) and textual modalities in a typical explanation. The challenge is to build deep learning models that are also able to explain their decisions with similar fluency in both visual and textual modalities (see Figure 2). Previous machine learning methods for explanation were able to provide a text-only explanation conditioned on an image in context of a task, or were able to visualize active intermediate units in a deep network performing a task, but were unable to provide explanatory text grounded in an image.

Existing approaches for deep visual recognition are generally opaque and do not output any justification text; contemporary vision-language models can describe image content but fail to take into account class-discriminative image aspects which justify visual predictions.

Hendriks et al. [START_REF] Lisa | Generating visual explanations[END_REF] propose a new model (see Figure 3) that focuses on the discriminating properties of the visible object, jointly predicts a class label, and explains why the predicted label is appropriate for the image. The idea relies on a loss function based on sampling and reinforcement learning, which learns to generate sentences that realize a global sentence property, such as class specificity. This produces a fine-grained bird species classification dataset, and shows that an ability to generate explanations which are not only consistent with an image but also more discriminative than descriptions produced by existing captioning methods.

Although, deep models that are both effective and explainable are desirable in many settings, prior explainable models have been unimodal, offering either image-based visualization of attention weights or text-based generation of posthoc justifications. Park et al. [START_REF] Huk | Multimodal explanations: Justifying decisions and pointing to the evidence[END_REF] propose a multimodal approach to explanation, and argue that the two modalities provide complementary explanatory strengths.

Two new datasets are created to define and evaluate this task, and use a model which can provide joint textual rationale generation and attention visu-

The activity is A: Mowing Lawn

… because he is kneeling in the grass next to a lawn mower.

… because he is pushing a lawn mower over a grassy lawn.

The activity is A: Mountain Biking … because he is riding a bicycle down a mountain path in a mountainous area. … because he is wearing a cycling uniform and riding a bicycle down the road.

A: Mowing Lawn A: Road Biking Q: Is this a zoo? A: No A: Yes

… because the zebras are standing in a green field.

… because there are animals in an enclosure.

Q: Is the water calm? A: No A: Yes

… because there are waves and foam.

… because there are no waves and you can see the reflection of the sun.

Fig. 4. Left: ACT-X qualitative results: For each image the PJ-X model provides an answer and a justification, and points to the evidence for that justification. Right: VQA-X qualitative results: For each image the PJ-X model provides an answer and a justification, and points to the evidence for that justification.

alization (see Figure 4). These datasets define visual and textual justifications of a classification decision for activity recognition tasks (ACT-X) and for visual question answering tasks (VQA-X). They quantitatively show that training with the textual explanations not only yields better textual justification models, but also better localizes the evidence that supports the decision. Qualitative cases also show both where visual explanation is more insightful than textual explanation, and vice versa, supporting the hypothesis that multimodal explanation models offer significant benefits over unimodal approaches. This model identifies visual evidence important for understanding each human activity. For example to classify "mowing lawn" in the top row of Figure 4 the model focuses both on the person, who is on the grass, as well as the lawn mower. This model can also differentiate between similar activities based on the context, e.g."mountain biking" or "road biking."

Similarly, when asked "Is this a zoo?" the explanation model is able to discuss what the concept of "zoo" represents, i.e., "animals in an enclosure." When determining whether the water is calm, which requires attention to specific image regions, the textual justification discusses foam on the waves.

Visually, this attention model is able to point to important visual evidence. For example in the top row of Figure 2, for the question "Is this a zoo?" the visual explanation focuses on the field in one case, and on the fence in another.

There are also other approaches to explanation that formulate heuristics for creating what have been called "Deep Visual Explanation" [START_REF] Khalifa | An introduction to deep visual explanation[END_REF]. For example, in the application to debugging image classification learned models, we can create a heat map filter to explain where in an image a classification decision was made. There are an arbitrary number of methods to identify differences in learned variable distributions to create such maps; one such is to compute a Kullback-Leibler (KL) divergence gradient, experiments with which are described in [START_REF] Khalifa | Using kl-divergence to focus deep visual explanation[END_REF], and illustrated in (see Figure 5). In that figure, the divergence for each input image and the standard VGG image classification predictor is rendered as a heat map, to provide a visual explanation of which portion of an image was used in the classification.

Conclusion and Future Outlook

We may think of an explanation in general as a filter on facts in a context [START_REF] Chander | Evaluating explanations[END_REF]. An effective explanation helps the explainer cross a cognitive valley, allowing them to update their understanding and beliefs [START_REF] Chander | Working with beliefs: AI transparency in the enterprise[END_REF]. AI is becoming an increasingly ubiquitous co-pilot for human decision making. So AI learning systems will require explicit attention to the construction of problem domain models and companion reasoning mechanisms which support general explainability. Figure 6 provides one example of how we might bridge the gaps between digital inference and human understanding. Deep Tensor [START_REF] Maruhashi | Learning multi-way relations via tensor decomposition with neural networks[END_REF] is a deep neural network that is especially suited to datasets with meaningful graph-like properties. The domains of biology, chemistry, medicine, and drug design offer many such datasets where the interactions between various entities (mutations, genes, drugs, disease) can be encoded using graphs. Let's consider a Deep Tensor network that learns to identify biological interaction paths that lead to disease. As part of this process, the network identifies inference factors that significantly influenced the final classification result. These influence factors are then used to filter a knowledge graph constructed from publicly available medical research corpora. In addition, the resulting interaction paths are further constrained by known logical constraints of the domain, biology in this case. As a result, the classification result is presented (explained) to the human user as an annotated interaction path, with annotations on each edge linking to specific medical texts that provide supporting evidence.

Explanation in AI systems is considered to be critical across all areas where machine learning is used. There are examples which combine multiple architectures, e.g., combining logic-based system with classic stochastic systems to derive human-understandable semantic explanations [START_REF] Lécué | Semantic explanations of predictions[END_REF]. Another example is in the case of transfer learning [START_REF] Sinno | A survey on transfer learning[END_REF], where learning complex behaviours from small volumes of data is also in strong needs of explanation of efficient, robust and scalable transferability [START_REF] Chen | Transfer learning explanation with ontologies[END_REF].

Fig. 1 .

 1 Fig. 1. Segment of an example from LeCun, Bengio,Hinton, Science[START_REF] Lecun | Deep learning[END_REF]

Fig. 2 .

 2 Fig. 2. The goal is to generate explanations that are both image relevant and class relevant. In contrast, descriptions are image relevant, but not necessarily class relevant, and definitions are class relevant but not necessarily image relevant.

Fig. 3 .

 3 Fig.3. A joint classification and explanation model[START_REF] Lisa | Generating visual explanations[END_REF]. Visual features are extracted using a fine-grained classifier before sentence generation; unlike other sentence generation models, condition sentence generation on the predicted class label. A discriminative loss function encourages generated sentences to include class specific attributes.

Fig. 5 .

 5 Fig. 5. Explaining the decisions made by the VGG-16 (park bench, street sign, racket, cockatoo, traffic light and chihuahua), our approach highlights the most discriminative region in the image.

Fig. 6 .

 6 Fig. 6. Explainable AI with Deep Tensor and a knowledge graph

Acknowledgements

The authors thanks their colleagues from local and international institutions for their valuable feedback, remarks and critics on this introduction to the MAKE-Explainable-AI workshop.


Thomas Brunet
email: thomas.brunet@u-bordeaux1.fr

Kevin Zimny

Benoit Mascaro

Olivier Sandre

Olivier Poncelet

Christophe Aristégui

Olivier Mondain-Monval

Tuning Mie Scattering Resonances in Soft Materials with Magnetic Fields

Keywords: numbers: 43.35.+d, 43.20.+g, 47.65.Cb, 82.70.Kj

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

Since the pioneer works of Gustav Mie [1], wave scattering has aroused a growing interest in physics [START_REF] Sheng | Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena[END_REF], in particular with the intention of controlling wave propagation by taking benefit from scattering resonances as sought for metamaterials [START_REF]Physics of Negative Refraction and Negative Index Materials[END_REF]. As predicted by theories on resonant multiple scattering of light [START_REF] Lagendijk | [END_REF] or sound waves [5] in the Mie scattering regime, i.e., when the wavelength within the particles is comparable to their diameter, the effective properties of random media are deeply altered nearby the particle frequency resonances. Since the size and the shape of the particles fix them, these resonant modes cannot be easily tuned with rigid particles [6,7]. By contrast, the use of all-fluid structures should be more appropriate to tune the scattering resonances, as fluid objects may easily be deformed under various external stimuli. Since a long time, it is indeed well known that immiscible fluid drops suspended in a fluid matrix can elongate under extensional hydrodynamic flows [START_REF] Taylor | Proc. R. Soc. Lond. A[END_REF], electric fields [START_REF] O'konski | [END_REF] or magnetic fields [10]. Such changes in the particle shape should drastically affect the effective properties of random media as predicted for light [11] and for sound waves [12], paving the way for the realization of tunable and adaptive multifunctional materials.

For experimental studies on resonant wave scattering by an assembly of deformable particles, ultrasonic techniques present the advantages to readily detect the wave field (not just the intensity as in optics) and to resolve the measurements in both time and space. Moreover, the characteristic length scales (between 1 µm and 1 mm) of particles make the synthesis of systems of disordered resonant scatterers rather convenient over a broad range of scattering contrasts: bubbly media [13] or suspensions of solid spheres [14]. Other contrasted materials are emulsions made of fluorinated-oil droplets randomly dispersed in a water-based gel [15]. They were shown to exhibit a large collection of multipolar Mie resonances due to the sound-speed contrast between the particles and the host matrix. Such a model system of disordered resonant particles is easily achievable by means of microfluidics, which allows an accurate control of particle parameters: size, size dispersity, shape, and volume fraction [16,17].

In this letter, we tuned the effective acoustic properties of resonant emulsions using external low induction magnetic fields. The latter are sufficient to elongate initially spherical ferrofluid droplets into prolate spheroids whose axis of rotational symmetry is along the magnetic field direction [18]. To do so, we doped fluorinated-oil droplets with superparamagnetic γ-Fe 2 O 3 nanoparticles according to an original process leading to a stable fluorinated ferrofluid. Briefly, the proper dispersion of iron oxide nanoparticles in fluorinated oil involves the adsorption of a perfluoropoly(ether) surfactant onto the nanoparticles followed by a chemical grafting of a perfluorinated silane on iron oxide. The grafting efficiency and the colloidal stability of the nanoparticles were investigated by several methods including FT-IR and X-ray photoemission spectroscopy, and light and neutron scattering techniques [19]. As illustrated in Fig. 1, a single droplet of such fluorinated ferrofluid embedded in a water-based gel can elongate by a factor 2.5 under a magnetic field induction of 43 mT. During the application of a cycle of increasing and decreasing magnetic field inductions, the axial aspect ratio a/b describes a hysteretic loop. This is due to the relaxation time of the interface between the droplet and the host gel matrix. However, the deformation is fully reversible as the droplet recovers its initial spherical shape after a sufficient time (∼ 30 min) after cancellation of the magnetic field. Materials and methods. -Robotics is the most appropriate method to produce highly monodisperse emulsions of such magnetic droplets [15]. In our experiments, the fluorinated ferrofluid is continuously injected through a fused silica capillary with internal/outer diameters of 75/150 µm, directly into a water-based gel (Carbopol R ), which behaves like an acoustically transparent host matrix. In addition, the low yield stress (∼ 1.5 Pa) of this Bingham fluid circumvents the issue of sedimentation of the fluorinated ferrofluid droplets (ρ 1 = 1.9 g.cm -3 ), which are denser than the host matrix (ρ 0 = 1 g.cm -3 ). The injecting capillary moves within the gel matrix at a constant velocity of about 10 mm.s -1 giving birth to perfectly identical spherical droplets of about 100 µm in radius as shown in Fig. 2(a). The droplet-size distribution of the emulsion is optically characterized before applying the magnetic field providing a mean radius < a > of 105 µm and a coefficient of variation of 4% (Fig. 2(b)). The sample is then confined into a 5 mm-thickness acoustic measurement cell with small lateral dimensions (30x30 mm 2 ), on which a piezoelectric transducer of 5 MHz central frequency and of 0.50 inch diameter has been stuck as illustrated in Figs. [START_REF]Physics of Negative Refraction and Negative Index Materials[END_REF]. Since its surface is sufficiently large [20], the piezoelectric transducer measures the wave field averaged over its face. Moreover, the incoherent part of the acoustic field is negligible as we only consider dilute emulsions with volume fractions Φ V of about 1%, in order to avoid coalescence between droplets when they elongate under the external magnetic field. Thus, the remaining detected signal is the coherent wave [7,14]. The cell-transducer ensemble just takes up the width of the air gap (40 mm) of an electromagnet that generates a homogenous magnetic field of which induction can be precisely tuned up to B = 43 mT. The measurement cell can also be turned along with its vertical axis to vary the angle ζ between the direction of the magnetic field B and the acoustic wave vector k 0 (Fig. 3(a)). Acoustic experiments are then performed using multi-echo ultrasound spectroscopy techniques allowing the accurate measurement of the effective acoustic attenuation coefficient of the emulsion [15]. Results.-A first acoustic experiment is performed on the fluorinated ferrofluid droplet emulsion without applying any magnetic field (thickest blue lines in Figs. 4). The attenuation spectra clearly exhibit several peaks that are due to the multipolar Mie resonances of the spherical droplets [15]. From such an acoustic resonant response, an inverse procedure [21] provides an acoustically measured mean radius < a > of 106 m and a coefficient of variation of 5%, in excellent agreement with optical microscopy measurements (Fig. 2(b)). Then, the attenuation spectra are recorded for a cycle of increasing and decreasing magnetic field inductions with a 20-second delay between two acoustic measurements. When the direction of the applied magnetic field B is parallel to the acoustic wave vector k 0 (Fig. 4(a)), the attenuation spectrum tends to shrink down towards lower frequencies (Fig. 4(b)). By contrast, the attenuation peaks clearly shift towards higher frequencies (Fig. 4(e)) when the magnetic field B is applied perpendicularly to the acoustic wave vector k 0 (Fig. 4(d)). In both configurations, the initial attenuation spectra are fully recovered after cancellation of the magnetic fields (Figs. 4(c) and (f)). As suggested by the hysteretic loop shown in Fig. 1, the initially spherical droplets become spherical again after being elongated into prolate spheroids with an axial aspect ratio of 2.5 for the highest magnetic field induction. Therefore, the effective acoustic parameters of the emulsion can be reversibly tuned over a broad range of values. Model. -Since the volume fraction of droplets for the considered emulsion is quite low (Φ V ∼ 1%), the experimental results are analyzed within the framework of the Independent Scattering Approximation. Indeed, crosscorrelations between scatterers have not to be taken into account contrary to more concentrated media [22] or random media made of strongly resonant particles such as air bubbles [13]. Thus, the effective attenuation coefficient α ef f of the coherent pressure wave propagating in our dilute emulsion is given by [START_REF] Ishimaru | Wave propagation and scattering in random media[END_REF]:

α ef f = 2π k 0 a η(a)Im [F a (0)] da (1)
where k 0 is the incident wave-number in the host matrix, η(a) is the number of a-radius droplets per unit volume, Φ = a η(a) × (4πa 3 /3)da the total volume fraction of droplets, and F a (0) is the forward scattering function of a single droplet that depends on both the material properties of the particles and those of the host matrix. For a given couple of materials, the frequency locations of the resonant attenuation peaks are inversely proportional to the droplet size [15]. As the coefficient α ef f depends on the forward scattering function F a (0), one can get an intuitive understanding of the evolution of the attenuation frequency spectra as function of the magnetic field induction (Figs. 4) by only considering the droplet size along with the incident acoustic wave vector k 0 . When the magnetic field direction is parallel to the incoming acoustic waves, the droplets elongate along that direction (Fig. 4(a)) and the resonant attenuation peaks shift towards lower frequencies (Figs. 4(b) and (c)). Inversely, when the magnetic field is applied perpendicularly to the incoming acoustic waves, the droplet size become smaller along that direction (Fig. 4(d)) and the attenuation peaks shift towards higher frequencies (Figs. 4(e) and (f)).

To go beyond such a qualitative analysis, the forward scattering function F a (0) of the prolate droplets has to be derived in order to retrieve the effective attenuation coefficient measured in our emulsions. Wave scattering by spheroidal objects has been the subject of many theoretical works [START_REF] Flammer | Spheroidal Wave Functions[END_REF] and the exact solution of the acoustic wave scattering by a liquid prolate spheroid was obtained many decades ago [START_REF] Yeh | [END_REF]. From the latter theoretical work, the forward scattering function F a (0) of a prolate fluorinated ferrofluid droplet, whose axial aspect ratio a/b is 2, is calculated providing the effective attenuation coefficient of our emulsions submitted to an external magnetic induction B 0 of 25 mT (see Fig. In conclusion, the resonant attenuation in our emulsion can be widely tuned (by a factor 5) by controlling both the flux density and orientation of external magnetic fields. Such a tunability of the resonant properties of scattering media should be of the utmost relevance for metamaterials, of which unusual properties are driven by scattering resonances [START_REF]Physics of Negative Refraction and Negative Index Materials[END_REF]. As reported for electromagnetic waves, the use of magnetic fields turned out to be efficient to tune the effective permeability of metamaterials made of split ring resonators [26]. This external stimulus should also be appropriate to tune the properties of locally resonant materials in acoustics [27], providing large enough mechanical contrasts between the resonant particles and the host matrix as expected with soft acoustic metamaterials [28].

FIG. 1 .

 1 FIG.1. Axial aspect ratio a/b of a single fluorinated ferrofluid droplet embedded in a water-based gel matrix, submitted to a cycle of increasing and decreasing magnetic field inductions, with a 20-s delay between each step (a movie is available in the supplementary materials).

FIG. 2 .

 2 FIG. 2. (Color online) (a) Optical microscopy picture of fluorinated ferrofluid droplets embedded in a water-based gel matrix, achieved by means of robotics (ΦV ∼ 1%). (b) Corresponding histogram of the droplet-size distribution. Mean radius < a > = 105 µm and coefficient of variation CV = 4%.

FIG. 3 .

 3 FIG. 3. (Color online) (a) Top and (b) side view of the experimental setup dedicated to acoustic measurements on fluorinated ferrofluid droplet emulsions under magnetic fields with various inductions (up to 43 mT) and orientations. The angle ζ between the direction of the magnetic field B and the acoustic wave vector k0 can be varied between 0 • and 90 • .

FIG. 4 .

 4 FIG. 4. (Color online) Evolution of the attenuation frequency spectra of fluorinated ferrofluid droplet emulsions submitted to a cycle of increasing (b and e) and decreasing (c and f) magnetic field inductions (from 0 mT to 43 mT). The direction of the magnetic field B is parallel (a, b and c) or perpendicular (d, e and f) to the incident acoustic wave vector k0. Thickest curves refer to the reference emulsion made of spherical droplets (no magnetic field). Pictures (a and d) show the orientation of the fluorinated ferrofluid droplets along the direction of the magnetic field B (movies are available in the supplementary materials).

  1) for various orientations ζ. Theoretical predictions and experimental measurements are compared for five angles ζ between the direction of the magnetic field B and the acoustic wave vector k 0 : ζ = 0 • (B 0 is parallel to k 0 ), 22.5 • , 45 • , 67.5 • , and 90 • (B 0 is perpendicular to k 0 ) revealing an excellent quantitative agreement as shown in Fig. 5.

FIG. 5 .

 5 FIG. 5. (Color online)Comparison between the measured attenuation coefficients (circles) and those predicted in the framework of the Independent Scattering Approximation (solid lines) for emulsions made of prolate fluorinated ferrofluid droplets with an axial aspect ratio of 2. Various orientations between the direction of the magnetic field (of B0 =25 mT induction) and the acoustic wave vector k0 are investigated (ζ = 0 • , 22.5 • , 45 • , 67.5 • , and 90 • ). The top figure refers to the reference emulsion made of spherical droplets (no magnetic field).


José Alberto Galicia

Olivier Sandre

Fabrice Cousin

Dihya Guemghar

Christine Menager

Valérie Cabuil

Designing magnetic composite materials from aqueous magnetic fluids

Keywords: numbers: 82.70.Dd, 75.50.Mm, 82.35.Np, 75.80.+q, 87.16.Dg

In this paper, we report how to take advantage of the good knowledge of both the chemistry and the stability of an aqueous magnetic colloidal suspension to realize different magnetic composites. The osmotic pressure of the magnetic nanoparticles is set prior to the realization of the composite to a given value specially designed for the purpose of each hybrid material: magnetic particles in polymer networks, particles as probes for studying the structure of clay suspensions and shape modification of giant liposomes.

At first, we show that the introduction of magnetic particles in polyacrylamide gels enhances their Young modulus and reduces their swelling by water. The particles cause both a mechanical and an osmotic effect. The latter is strongly dependant on the ionic strength and attributed to an attraction between particles and polymeric matrix.

In the second part, we determine the microscopic structure of suspensions of laponite as a function of concentration, by combining SANS and magneto-optical experiments with the probes. This study requests conditions for including the magnetic particles as probes without disturbing the clay suspensions.

The third part presents giant magnetoliposomes, which encapsulate magnetic nanoparticles. Shape transitions are obtained with either a magnetic field or an osmotic stress.

Overview

Smart materials, which mean materials that respond to an external stimulus, can be obtained by associating magnetic nanoparticles to a polymeric or a lyotropic matrix. The resulting composite materials exhibit a response when they are submitted to a magnetic field of low intensity (typically less than 0.1 Tesla) or to a magnetic field gradient. Different procedures can be imagined to produce such materials: the magnetic particles can be either synthesized directly inside a host matrix, or synthesized first, then mixed with the other component of the composite. These last years, magnetic nanoparticles have been successfully introduced in glass [1], polymeric gels [2,3], lyotropic systems (nematics [4], smectics [5]), microscopic colloids (emulsions [6], latexes [7], liposomes [8]). They can be used as probes, in order to characterize dynamics (and subsequently structure) of the medium through the analysis of their magneto-optical response [9], or they can be introduced as a magnetic load in order to obtain field dependant materials [5,10,11].

Aiming to improve the homogeneity of the resulting composite material, the colloidal stability of both components of the composite is of uppermost importance. The colloidal dispersion of magnetic particles has thus to be stable in the chemical and physicochemical stability domains of the second system. An eventual chemical incompatibility between the nanometric magnetic particles and the host colloid has to be examined first. A modification of the pH, an increase of the ionic strength, adsorption or desorption of the charge determining species or of the surfactants, can occur during the mixing process or few weeks after, the latter case being especially harmful, because it can be unnoticed and leads to important interpretation errors. Chemistry of magnetic colloids is now sufficiently well developed to succeed in preventing such problems. As soon as the chemical stability of both colloidal systems is controlled, interactions in the binary system have to be monitored. As a matter of fact, each colloidal system is characterized by its own osmotic pressure Π. Thus it can be roughly said that the system that has the higher osmotic pressure will impose its own pressure to the other one that can then be destabilized [12]. The osmotic pressures of the two components should thus be of the same order of magnitude for the realization of the binary system. The aim of this paper is to illustrate this comment by describing how it has been possible during recent years to design various magnetic composite systems with always the same well-defined magnetic material: an aqueous dispersion of citrate-coated maghemite nanoparticles, that will be denoted hereafter CitMF [13]. Three examples are presented resulting from the association of CitMF with several hosts, the latter being i/ a polymeric network, ii/ a gel of inorganic particles and iii/ a lyotropic system. In the first case, the polymer is a polyacrylamide cross-linked network. The point was to trap the nanoparticles inside the mesh of the network and to compare the composite material with the undoped polymer. In the second case, the nanoparticles have been introduced in aqueous dispersions of a clay (laponite) in order to test the structure of those inorganic gels and test the hypothesis of microscopic liquid pockets coexisting with solid domains [14]. In the third case, CitMF has been encapsulated inside liposomes, thus enabling to elongate them under a magnetic field or generate their migration under a field gradient. Among the three composite systems, laponite clay suspensions and magnetoliposomes have already been described extensively in former publications, whereas the results about the thermodynamics of ferrogels (swelling and elasticity) are unpublished before and therefore presented in more details in this article.

I.

Properties of aqueous dispersions of citrate-coated particles (CitMF)

A. Getting CitMF

The maghemite nanoparticles are chemically synthesized in water by coprecipitation of FeCl 2 and FeCl 3 in an alkaline solution [15]. Due to the strong absorption of short wavelength light by iron oxide, maghemite ferrofluids exhibit a characteristic orange color. The colloidal particles have a quasispherical shape and their diameter after synthesis range between 3 and 15 nm with a rather large polydispersity. Their size distribution is described by a log-normal law with a modal diameter d 0 around 7 nm ( ln d 0 = < ln d > ) and a standard deviation σ = 0.35. When necessary, polydipersity can be reduced by a size-sorting process to get suspensions with d 0 varying from 6 nm to 10 nm and σ = 0.1 [16]. In order to get stable suspensions from pH 4 to pH 10, particles are coated by citrate species.

The adsorption equilibrium of citrate leads to an inevitable residual ionic strength

∑ = i i i z c I 2 2
1 hence I = 6[Cit 3-] free due to the unadsorbed citrate species (Cit 3-) in equilibrium with the adsorbed ones and their Na + counterions. This equilibrium avoids decreasing the ionic strength under a given concentration that depends on the pH. At pH 7, the adsorption plateau is reached for a concentration of [Na 3 Cit] in solution equal to 2 10 -3 mol.L -1 [17]. The particle's surface charge is negative, saturated at a value of 2 charges.nm -2 . Above pH 10 citrate desorbs, while below pH 4 the surface charge density of these citrate-coated particles becomes insufficient to ensure electrostatic repulsion.

B. Phase behavior of CitMF

The stability of CitMF has been the object of numerous studies these last years [13,[18][19][20][21]. They exhibit indeed a very rich behavior due to two specific features: the presence of adsorbed citrate ligands and the magnetic dipolar interactions.

In such systems, the main interaction between particles is the electrostatic repulsion, which stabilizes the system in a wide range of salinity. In addition, the presence of citrate at the surface of the particles provides a steric repulsion at short range that ensures stability for high salinity [13] and prevents irreversible aggregation, which usually occurs in electrostatically stabilized colloidal systems. These two repulsive interactions ensure that all transitions are reversible whatever the experimental conditions. Magnetic dipolar interactions ensure that attractive interactions occur in the system on a larger range than Van der Waals ones and allow tuning the balance between repulsive and attractive interactions for long-range potentials.

Two regimes of interactions have been clearly identified:

i) At low ionic strength ([Cit] free < 10 -2 mol.L -1 ), electrostatic repulsion dominates inter-particle's interactions and the phase behavior is well described by the usual Fluid-Solid phase diagram of a repulsive system. The phase diagram of CitMF in the Π -Φ plane has been established and various iso-salinity lines have been plotted [13] allowing to set the osmotic pressure of CitMF for a given ionic strength within the fluid domain. This regime of interactions is clearly the most useful for the synthesis of composite materials as it ensures the CitMF stability. In this repulsive regime, a sample of CitMF remains a stable monophasic liquid for all intensities of magnetic field and magnetic field gradient.

ii) For a higher ionic strength ([Cit] free > 10 -1 mol.L -1 ), the inter-particle's potential is an attractive

Lennard-Jones like one and the phase behavior of the magnetic fluid is well described by a phase diagram like for an atomic system, including gas-liquid transitions [19], the existence of a critical point [20] and fluid-solid transitions [21]. Especially gas-liquid like transitions have to be kept in mind when making composite materials, as they may appear if the ionic strength strongly increases locally in the material, even if the average ionic strength is low.

Between these two regimes, one goes smoothly from the repulsive to the attractive regime by increasing salinity. The knowledge of the phase diagrams in the different salinity regimes allows choosing the best set of conditions (Π, Φ and I) for the precursor CitMF prior to the realization of a composite material.

II. Ferrofluids and polymer networks

When dealing with composites of polymers and ferrofluids, one commonly thinks about magnetic latexes used for biotechnological applications like cell sorting. Most commercial products are based on polystyrene beads filled with magnetic particles dispersed thanks to a hydrophobic coating [7,22].

About ten years ago, Zrínyi introduced the opposite approach of water-based polymers mixed with aqueous ferrofluids [2]. The composite material obtained by associating a hydrogel and a ferrofluid has been called a ferrogel. The purpose was to obtain soft magnetic gels easily deformed by a magnetic field gradient (magnetostriction). The matrix was for example poly(vinyl-alcohol) crosslinked by glutaraldehyde and the magnetic materials consisted in magnetite grains (Fe 3 O 4 ) about 10 nm in size dispersed in an acidic medium (HClO 4 ). Due to their high water content (more than 90% weight!), ferrogels are much more deformable than magnetic latexes. Indeed, our own estimation of the Young modulus is about 10 4 Pa, which is 2 orders of magnitude lower than for classical rubbers.

The goal of our study is to determine the influence of a charged ferrofluid properly dispersed in a polymer network on both the osmotic swelling equilibrium and on the mechanical elasticity of the gel.

We chose to mix a citrate-stabilized ferrofluid (CitMF) with acrylamide monomer (AM) that is polymerized and cross-linked in the pre-formed colloidal suspension. Acrylamide is polymerized thermally in the presence of a low amount of free radical initiator such as persulfate (peroxodisulfate) ions. Despite its simplicity, acrylamide is very useful to build a neutral hydrophilic network.

This section is organized as follows. In the first part, we describe the synthesis of ferrogels. The second and the third parts present mechanical and osmotic measurements respectively, with ferrogels of varying composition. Finally, we discuss possible interactions between ferrofluids and polymer networks that can explain the experimental data.

A. Synthesis

The cross-linker used was N,N'-methylene-bis-acrylamide (BA) and the initiator ammonium persulfate (APS). Because APS is a 2:1 electrolyte that contributes to the ionic strength, the minimum possible concentration avoiding destabilization of the ferrofluid was used. The reactive mixture (2-3 mL) contained monomer (0.5 mol.L -1 AM), cross-linker (5•10 -4 or 2.5•10 -4 mol.L -1 for 1% or 0.5% BA/AM respectively), initiator (5•10 -4 mol.L -1 APS), tri-sodium citrate electrolyte (Na 3 Cit) and ferrofluid (CitMF) at a volume fraction of magnetic nanoparticles denoted Φ 0 . The [Na 3 Cit] concentration was either 5•10 -3 or 8•10 -3 mol.L -1 for the two series of experiments which will be presented later in the text. The solution was degassed for 5 min before polymerization to eliminate oxygen. Then temperature was raised up to 70°C for 2 hours to achieve completion of the reaction.

Although the mixture already gelled after 15 min, this long reaction time was used to assure about 96-98% of reacted monomer (measured yield). After careful removal, the ferrogels kept the cylindrical shape of the glass vessel (sample tube or Pasteur pipette for the swelling and the elasticity experiments respectively). After washing with deionized water to eliminate unreacted species, the ferrogels were immersed into a large volume of solution which was either pure water or a solution of Na 3 Cit with a concentration ranging from 5•10 -4 mol.L -1 to 4•10 -1 mol.L -1 .

B. Elasticity measurements

Traditionally with hydrogels, the stress-strain measurements are performed in compression experiments of gel disks by using a tensile testing machine [23]. We preferred to use a home-build setup to apply a controlled elongation stress on ferrogels at equilibrium swelling, thereby visualizing directly their stretching. Moreover, our experiment has the advantage to keep the sample in direct contact with the solvent. Of course the Young modulus measured at low strain should be the same for elongation and compression experiments.

Long cylindrical samples of ferrogel were obtained by polymerizing the AM/CitMF mixtures in Pasteur pipettes of d 0 = 5 mm inner diameter and 50 mm length. The ferrogels were synthesized at different volume fractions Φ 0 of magnetic particles (from 1 to 7%) at a given ionic strength [Na 3 Cit] 0 = 8•10 -3 mol.L -1 as described in the part A. Synthesis. The two extremities of the ferrogel cylinders were reinforced by polymerizing them at a higher cross-linker ratio (BA/AM=5%) than the body of the ferrogel (BA/AM=1%). In practice, the ferrogel was built in three steps corresponding to each section, added successively to the previous one still freshly polymerized (at 10 min interval). After polymerization, the ferrogels were carefully removed from the Pasteur pipettes. Special attention was paid to avoid making any crack in the body of the ferrogels, which could decrease their mechanical strength. Then they were allowed to swell in a solution at [Na 3 Cit] = 8•10 -3 mol.L -1 . Once the swelling equilibrium was reached, the ferrogels were attached by their reinforced ends to two plastic nuts, the lower one static, the upper one mobile and connected to the arm of a counterweight balance. The system was immersed in a transparent reservoir containing an aqueous solution of citrate salt at [Na 3 Cit] = 8•10 -3 mol.L -1 , thus enabling a direct observation of the colored ferrogel under extension with a video camera mounted with a 75 mm zoom lens.

The stress was applied by loading the pan of the balance with calibrated weights (M=10 g maximum).

We checked that both ends of the sample were held firmly and without sliding by the nuts during the whole elongation test. The axial dimension L of the ferrogel was recorded from the initial state under zero-load L 0 up to a maximum elongation state always below rupture. Usually a change of the load is followed by mechanical oscillations. Therefore a delay of 1 min between two consecutive measurements was always respected to achieve static equilibrium of the sample.

The strain is defined as:

0 0 L L L - = ε
where L 0 is the length of the gel between the two anchoring points in the unloaded state (see Fig. 1a) and L is the length when a weight M is placed on the pan of the balance. The cross-section area of the cylinder is noted A 0 under zero-load and A under load. Assuming a constant volume of the sample under deformation, we have The Young modulus E is simply given by the slope of σ versus ε and can be plotted as a function of Φ 0 (Fig. 1c). These data show that the mechanical strength of ferrogels increases significantly with the L 0 L volume fraction of inorganic nanoparticles introduced at preparation. Therefore ferrogels can be considered as composite materials where the polymer matrix is reinforced by the solid component.

However the elastic modulus remains around 10 4 Pa, which is still two orders of magnitude lower than usual values for elastomers (E~10 6 Pa).

C. Swelling and release

The ferrogels were allowed to reach their swelling equilibrium in Na 3 Cit for approximately three weeks. The immersion bath was changed several times in order to get rid of free particles that were not trapped within the ferrogel. The swollen ferrogel at equilibrium was weighted (m swollen ) then dried at 70°C to obtain also its dry weight (m dry ). Finally, the iron content remaining in the dried ferrogel was measured by atomic absorption spectroscopy with a hollow cathode lamp in a Pelkin Elmer AAnalyst 100 apparatus. Thus we can calculate the mass of iron oxide (m Fe2O3 ) remaining after release of some of the magnetic particles and compare it to the mass of maghemite initially introduced in the ferrogel during the synthesis ( 0 Q is the swelling degree commonly used for hydrogels defined as the amount of water m H2O absorbed by the gel quoted by the weight of polymer network m polymer . The water content m H2O is given by the difference of weights between the swollen gel and the dry gel. Please note that in the case of ferrogels, the dry weight consists of polymer, particles and citrate salt all together. The mass of polymer only m polymer has thus to be computed from the initial concentration of monomer assuming a yield of 100%.

The amount of water being known precisely in the synthesis vessel, an initial value of the swelling ratio is calculated. This Q 0 value ranges from 25 to 27 depending on the volume fraction Φ 0 of solid iron oxide. R is the release parameter specific for ferrogels that we define as the fraction of magnetic particles which are not trapped by the ferrogel and are released in the swelling bath.

We performed two series of swelling experiments with ferrogel samples:

-We varied the volume fraction Φ 0 of magnetic particles at preparation from 1 to 9% while we kept the ionic strength at a low value identical in the swelling bath and during synthesis [Na 3 Cit] = [Na 3 Cit] 0 = 8•10 -3 mol.L -1 . For this series, the cross-linker ratio BA/AM was 1%. The measurements of Q and R versus Φ 0 are presented on Fig. 2.

-For a given volume fraction Φ 0 =3.8%, we kept the citrate concentration at preparation constant [Na 3 Cit] 0 =5•10 -3 mol.L -1 , but we increased the ionic strength [Na 3 Cit] in the swelling bath from 0 to 0.4 mol.L -1 . The cross-linker ratio BA/AM was 0.5% for all those samples. Figure 3 compares the swelling Q of ferrogels prepared at Φ 0 =3.8% to the case of undoped hydrogels (Φ 0 =0%) swollen at various concentrations of citrate. The release R of the magnetic content is plotted on Fig. 3 as a function of [Na 3 Cit] on a secondary axis.

Although the degree of cross-linking are different for the two series of experiments, they remain in the regime of low cross-link density, where the elastic modulus of the hydrogels grows linearly with the ratio BA/AM. Only at higher cross-linker ratio (above 2%) and higher polymer concentration hydrogels start to exhibit a heterogeneous distribution of chemical nodes concomitant with a maximum of their shear modulus [24]. In Figure 2, we observe that the swelling Q decreases continuously as a function of the volume fraction Φ 0 of magnetic particles in the ferrogel during polymerization. For the higher content of particles (Φ 0 =9%), we see that Q=20 becomes smaller than the initial water content after synthesis Q 0 =25, which means that the ferrogel actually contracted slightly in the swelling bath. Concerning the release, we note that the network systematically lost a large fraction of the particles present at preparation (R=35-45%, except for the lower values of Φ 0 where R~15%). But in other words, more than half of the particles were efficiently trapped in all the cases.

Role of the initial particle's volume fraction

Role of the ionic strength during swelling

Fig. 3: Swelling degree Q (filled circles) and particle's release R (diamonds) versus sodium citrate concentration [Na 3 Cit] in the swelling bath for ferrogels prepared with a volume fraction of magnetic particles Φ 0 =3.8% and for undoped hydrogels (empty circles). For all those ferrogels, the cross-link ratio was BA/AM=0.5 % and the swelling ratio at preparation Q 0 =27. For visualization purpose, the horizontal scale is dilated in the region of low salinity (<10 -2 mol.L -1 ) and the vertical axis is broken to represent the first point concerning the hydrogel, which is far above the other ones (Q=308).

In Figure 3, the case of the undoped hydrogel and of the ferrogel both prepared in [Na 3 Cit] 0 =5•10 -3 mol.L -1 then swollen in pure water is particular because the corresponding values of the swelling are far above the rest of the plot: Q=308 and Q=78.5 for Φ 0 =0% and 3.8% respectively. For the other samples immersed in a non-zero citrate concentration, we observe a different variation of Q vs.

[Na 3 Cit] for iron oxide loaded ferrogels and unloaded hydrogels. Without particles, the swelling Q decreases smoothly as a function of salinity, then saturates to a value Q~65, which is still twice larger than Q 0 =27. The plots look different for ferrogels. They exhibit a minimum value of Q near the concentration [Na 3 Cit]= 1•10 -2 mol.L -1 , which is followed by a maximum of Q located around 5•10 -2 mol.L -1 for Φ 0 =3.8%. After this maximum, the swelling reaches a plateau value Q~50 for Φ 0 =3.8%, smaller than the plateau Q~65 for the unloaded hydrogel. Starting from R~30% at the lowest salt concentration [Na 3 Cit]=5•10 -3 mol.L -1 , R raises significantly for higher citrate salt concentrations for the ferrogels initially loaded at Φ 0 =3.8%. In that case, a maximum of particle's release R=93% is reached for 0.3 mol.L -1 citrate. This loss of particles is twice as large as for the ferrogel approximately at the same initial load Φ 0 =4% but swollen in [Na 3 Cit]=8•10 -3 mol.L -1 instead (Fig. 2). All these features of the curves will be discussed in part D. Interpretation. In the first part of this paper, we have seen that the citrate concentration is a control parameter in the phase diagram of ferrofluids, the other parameter being the volume fraction. This series of ferrogels at varying salinity is also aimed to explore possible shifts of the boundaries of the phase diagram when the colloidal particles are dispersed in a polymer matrix rather than in a pure solvent. All those ferrogels at Φ 0 = 3.8% were prepared from the same CitMF ferrofluid characterized by a size distribution with mean diameter d 0 =9 nm and σ=0. 25. In the ferrofluid at Φ 0 = 3.8% volume fraction (without polymer), the gas-liquid transition mentioned in Part I.B of this article occurs at [Na 3 Cit]=0.19 mol.L -1 . Above this threshold concentration, the continuous gas-like phase coexists with micron-sized droplets of a liquid-like phase, which is more concentrated in particles. The same phase separation of the particles was also observed by optical microscopy in the ferrogels prepared at Φ 0 =3.8% and swollen in Na 3 Cit above a threshold concentration of 0.25 mol.L -1 (Fig. 4). At this salt concentration, the ferrogel looked homogeneous during the first hours of swelling (Fig. 4a). However, the application of a strong magnetic field (1Tesla) initiated a visible roughness of the sample (Fig. 4b).

After a longer time in the swelling bath, the sample became clearly phase-separated, as droplets concentrated in particles had appeared (Fig. 4c). Being embedded in the polymer matrix those droplets neither elongate nor chain when a magnetic field is applied, unlike the regular case of a fluid CitMF.

D. Interpretation

When the polymerization of BA/AM is achieved in presence of CitMF, all the magnetic particles initially introduced are located inside the polymer network because all the reactive mixture has gelled (despite a negligible volume of liquid supernatant). Hence the volume fraction of particles in the ferrogel is initially equal to Φ 0 as in the liquid mixture. As soon as the ferrogel is plunged into the swelling bath, this volume fraction of particles starts to decrease. The particle's concentration after some time in the swelling bath is equal to Φ, which is inferior to Φ 0 due to two phenomena occurring simultaneously. On the one hand, the ferrogel exhibits a significant volume increase due to water absorption by the polymer. This "inflation" contributes to dilute the particles by a factor Q Q 0 . On the other hand, a fraction R of the particles has been released into the external solution during the swelling process. Thus a fraction ( )

R - 1
remains in the swollen ferrogel. Therefore we can estimate the volume fraction of particles in a state characterized by a release fraction R and a swelling ratio Q by using a simple conservation law:

( ) Q Q R Φ Φ 0 0 1 - =
We notice an important difference between the first series of experiments at low citrate concentration and the second series where this salt concentration was varied from low to high values. In the low salinity case, the ferrogel always reached a static state where the weight of the ferrogel did not vary anymore and the release of iron oxide in the outer solution stopped. Thus the particle's volume fraction Φ had reached an equilibrium value. In the series of experiments at varying salt concentration during swelling, we noticed for some high salinity cases that the release never stopped even though the weight of the swollen ferrogel was constant. In particular, this absence of equilibrium occurred for the initial particle's volume fraction Φ 0 =3.8% and for citrate concentrations around the destabilization threshold at 0.25 mol.L -1 . Therefore we comment on the two types of experiments separately.

1.

Role of the particle's volume fraction Φ 0 at low sodium citrate concentration identical during Although it is calculated rather than measured in situ by an independent experiment, this estimate of the volume fraction Φ 0 leads to the following statement: the more particles we introduced at the synthesis, the more concentrated ferrogel we got after the swelling and release equilibrium. This result is not trivial because the increase of the release fraction R for increasing values of Φ 0 (see Fig. 2) tends to diminish Φ while the decrease of the swelling ratio Q produces the antagonist effect. The effect of Q is stronger than the effect of R because in the end, Φ increases when Φ 0 increases. Realized for the same low citrate concentration, the mechanical elongation test with a series of ferrogels at increasing Φ 0 shows that the rigidity of ferrogels also increases continuously with the solid volume fraction at preparation Φ 0 . On Fig. 5b, we plot the measured values of the Young modulus as a function of the estimate of the actual particle's volume fraction Φ in the swollen ferrogels. There were two ways to compute those values of Φ. The conservation law states that

0 Φ Φ is the product of Q Q 0 and ( ) R - 1
. The ratio of the swelling degree Q compared to its value Q 0 right after synthesis can be either computed from the weight measurements or estimated geometrically by measuring the relative change of diameter of the cylindrical samples (assuming an isotropic swelling):

3 0 0       = d d Q Q
Even though they were applied on two different series of samples, the two methods to compute Φ give similar results for the plot of E vs. Φ. Thus we can deduce that the elastic strength of the studied ferrogels increase almost linearly with the volume fraction of solid particles in the swollen state. The nanoparticles can thus be considered as reinforcement fillers.

Coming back to the decrease of the swelling degree Q as a function of the particle's volume fraction Φ 0 (Fig. 2), we can explain this behavior by the mechanical reinforcement of ferrogels compared to the undoped hydrogel. In the standard Flory-Rehner theory of hydrogel swelling indeed, the swelling degree Q is determined by a competition between the osmotic pressure of the polymer which is the driving force for water absorption and the elastic energy resisting to network deformation due to volume increase [START_REF] Flory | Principles of Polymer Chemistry[END_REF]. More precisely, the swelling degree scales with the Young modulus like 5 3 -∝ E Q in the limit of high Q values. Usually this law is tested for rubbers by varying the crosslink density. Here with ferrogels we varied the concentration of entrapped particles instead. We find a semi-quantitative agreement between our measurements and the theory of swelling, because Q and E are respectively a decreasing and an increasing function of the particle's volume fraction Φ in the swollen state. In other words, the limitation of ferrogel swelling by the particles is due in part to a mechanical reinforcement.

2.

Variation of the ionic strength [Na 3 Cit] in the swelling bath for a given salinity during synthesis [Na 3 Cit] 0 =5•10 -3 mol.L -1 for undoped hydrogels and ferrogels at Φ 0 =3.8%

The variation of the swelling ratio Q with the [Na 3 Cit] concentration in the swelling bath is rather complicated (Fig. 3). Poly(acrylamide) hydrogels are indeed neutral networks, and thus are supposed to be insensitive to charge screening effect by an external electrolyte. We report here two effects of the tri-sodium citrate electrolyte both on undoped hydrogels and on ferrogels. On the one hand, the presence of citrate during polymerization increases the swelling in pure water and leads to an influence of [Na 3 Cit] on the swelling ratio even for undoped hydrogels. On the other hand, the differences of swelling between the ferrogels and the undoped hydrogel taken as reference demonstrate the influence of citrate on the particle's interactions, stability and release.

-

Influence of citrate on network swelling

When prepared in [Na 3 Cit] 0 =5•10 -3 mol.L -1 and swollen in pure water, a hydrogel containing no particles or particles at Φ 0 =3.8% absorbs a much larger quantity of water (Q=308 and 78.5 respectively) than when swollen in any concentration of salt. This enhancement of the swelling is reminiscent of the polyelectrolyte effect obtained with charged super-absorbent hydrogels [START_REF] Philipova | [END_REF].

Ionization of poly(acrylamide) has been reported in literature, but only at pH higher than 12 [27],

which is not the case here because tri-sodium citrate is a pH7 buffer. Thus we can only conclude that some unidentified electrostatic charges are present on the polymer backbone in our conditions of polymerization. When tri-sodium citrate is also present in the swelling solution, the swelling ratio of the undoped hydrogel decreases slightly from Q~75 for [Na 3 Cit]=5•10 -3 mol.L -1 to Q~65 for [Na 3 Cit]=4•10 -1 mol.L -1 . This variation is low enough to consider that the residual charges of the network are screened for all electrolyte concentrations used during swelling. In the following, we use this curve of Q vs. [Na 3 Cit] for the bare hydrogel as the reference level to discuss the influence of the particles.

-Influence of citrate on the interactions, stability and release of particles

The difficulty to address the issue of the osmotic role of particles during the swelling of ferrogels comes from the particle's release that varies a lot as a function of the ionic strength (Fig 3). Therefore the particle's volume fraction is far from constant when salinity is varied. Nevertheless, this concentration of particles in the swollen state of the ferrogel can be estimated from the measurements of Q and R and the conservation law (Fig. 6). Apart from the case of pure water where the particles are diluted by the strong water absorption, the volume fraction of entrapped particles remains constant and approximately equal to Φ=2.2% on this whole range of salinity (Fig. 6). Thus we can really discuss the osmotic contribution of particles on the network swelling at a constant Φ. In this range of ionic strength, the swelling of the undoped hydrogel is always larger than the swelling of the ferrogel, as shown on the left part of Fig. 3. This low salinity regime corresponds to strong electrostatic repulsions between the particles associated with a high osmotic pressure of the ferrofluid. It also corresponds to a strong osmotic pressure of the hydrogel, as the latter swells more in this regime than in the domain of high ionic strength. Nevertheless comparing the swelling of the hydrogel and the one of the ferrogel, the swelling degree of the latter is noticeably lower. This indicates that the osmotic pressure of the composite is smaller than the osmotic pressure of the hydrogel and therefore smaller than the sum of the osmotic pressures of the two components individually. From this negative cross-term in the total osmotic pressure, we can conclude on the existence of attractive interactions between the polymer and the particles.

The adsorption of polyacrylamide chains onto ferric oxide surfaces was indeed reported in the literature [28]. This hypothesis of a (weak) binding between particles and network is also supported by the efficient entrapment of a fraction (1-R) of the nanoparticles while the remaining ones (R) escape from the ferrogel. One may wonder what are the processes at the microscopic scale leading to this partial entrapment. The kinetics must be limited by the diffusion of the nanoparticles through the pores of the polymer network. The volume increase caused by water swelling enlarges the polymer meshsize and liberate particles that were initially trapped. However, the swelling does not completely wash out the particles. The remaining particles cannot leave the ferrogel once the release equilibrium is attained, which means that the particles are not free to diffuse in the polymer network. Thus the immobilization of a large fraction of particles is neither simply due to steric hindrance nor slow kinetics of diffusion. Therefore an attractive interaction must exist between the polymer chains and the iron oxide nanoparticles.

b) at high salinity [Na 3 Cit]>1•10 -1 mol.L -1

We know from past studies with CitMF ferrofluids that the sign of the second Viriel coefficient changes from positive (repulsion) to negative (attraction) at a citrate concentration about 1•10 -1 mol.L -1 [13]. For this salinity, the particles behave like an ideal gas. Above this threshold, the osmotic pressure of a ferrofluid at constant volume fraction and increasing ionic strength decreases because the interparticle's potential becomes more and more attractive.

For particles embedded in a ferrogel, we observe that the swelling at [Na 3 Cit]=1•10 -1 mol.L -1 is approximately the same for a blank hydrogel (Q=68) and a ferrogel prepared at Φ 0 =3.8% (Q=61). At this salt concentration and above, the discrepancy in the swelling degree of the ferrogel and the hydrogel has almost disappeared compared to the regime of low salinity, even though a gap remains between the Q levels for the hydrogel and the ferrogel. At the same time, the particle release fraction R increases strongly with the ionic strength (Fig. 3). The estimate of the particle's volume fraction (Fig. 6) shows indeed a deep decrease down to a minimum Φ=0.15% at [Na 3 Cit]=3•10 -1 mol.L -1 . Being more dilute and having their electrostatic repulsions screened by the electrolyte, the nanoparticles by their own must have a much lower osmotic pressure than at low ionic strength. Their negative contribution to the osmotic pressure of the composite also disappears, as seen from the much larger swelling of the ferrogels in the salinity range 5•10 -2 -3•10 -1 mol.L -1 compared to the low salt domain 5•10 -3 -1•10 -2 mol.L -1 . This feature is the signature of the decrease of the supposed attractions between the particles and the polymer network when the ionic strength increases.

In spite of the previous statement, we cannot conclude that the polymer becomes totally "transparent" for the interactions between particles at high ionic strength. The study of particle's destabilization shows indeed that the threshold ionic strength for gas-liquid like phase separation is shifted toward a higher salinity in the ferrogel prepared at Φ 0 =3.8% compared to the ferrofluid at the same volume fraction ([Na 3 Cit]=0.25 and 0.19 mol.L -1 respectively). This observable shift of the boundary in the phase diagram is not simply caused by the lower volume fraction in the ferrogel compared to the ferrofluid, because it occurred after a time about 24 hours (Fig. 4) much lower than the waiting time before the measurements of Fig. 3 (three weeks), so that the ferrogel was still concentrated in particles at that time. Therefore this shift of the onset of phase separation shows that the polymer network somehow hampers the attractive interactions between particles. Moreover, the decrease of particle's release R at 0.4 mol.L -1 compared to its maximum at 0.3 mol.L -1 can be explained by a larger amount of the liquid-like phase. The high viscosity of this concentrated phase certainly causes a kinetic blockage of further particle's release (please remember that no real equilibrium of particle's release was reached for those two highest values of the ionic strength).

E. Conclusions

This study has shown the possibility to include charged magnetic nanoparticles in a polyacrylamide hydrogel, along with maintaining repulsive interactions between the particles. The advantage of polymerizing the hydrogel directly in a stable colloid (CitMF) consists in realizing a homogenous dispersion of nanoparticles without clusters. The main control parameter determining the entrapment of particles in the polymer matrix and the swelling degree is shown to be the ionic strength during swelling. We were indeed able to obtain swollen ferrogels at final particle's volume fraction up to Φ=6.5% at low ionic strength (8•10 -3 mol.L -1 ) and Φ=2.2% at a larger ionic strength (5•10 -2 mol.L -1 ).

We identified two different effects of the particles on the water absorption by the ferrogel. On the one hand, the swelling of the network Q is limited by the increase of the stretching modulus E, which is proportional to the volume fraction Φ of particles behaving as hard fillers. On the other hand at constant Φ, we noted that the swelling degree Q is also limited by a decrease of the osmotic pressure of the composite ferrogel compared to the osmotic pressure of the hydrogel alone. This negative crossterm is attributed to an attraction between the particles and the polymer network, which still needs to be clarified (coordination bonds between the amide moieties of the monomer and the ferric cations?).

The lowering of this interaction between the polymer and the inorganic colloids when salt concentration increases is responsible for the minimum of the curve of Q vs. [Na 3 Cit] for the ferrogel on Figure 3. Such a minimum of the swelling ratio as a function of salinity has been reported for polyampholite hydrogels, which are made of copolymers bearing both positive and negative charges [29]. Therefore ferrogels and polyampholites are analogous in the sense that the network is submitted to a combination of attractive and repulsive interactions, which both are screened by the ionic strength.

A last point remaining to be completed is the mechanism by which tri-sodium citrate can induce the presence of charges on the polyacrylamide chains during polymerization. This residual charge of polyacrylamide networks can be estimated to a few percent of monomers or less. When prepared in a tri-sodium citrate solution, a hydrogel swollen in pure water absorbs a large quantity of water (Q~300), but this value is still lower than for a real polyelectrolyte hydrogel made of a copolymer of AM and 10 mol% of negatively charged sodium acrylate (SA): in that case the swelling is even higher (Q~1000 for 10% of charged comonomers, data not shown).

Finally, the most direct practical application of ferrogels consists in their macroscopic response to a magnetic field or field gradient. Different configurations can be imagined to test the properties of "magnetoelastics". Recently the enhancement of the Young modulus by application of a magnetic field was demonstrated in a stretching geometry with a sample made of a magnetic powder and a silicone rubber [START_REF] Nikitin | Translated from 2001 Vysokomolekulyarnye[END_REF]. This strengthening under a magnetic field was also reported in a compression experiment with a poly(vinyl-alcohol) based ferrogel and attributed to a demagnetizing effect of the cylindrical sample [31]: the compression modulus increases (respectively decreases) under an applied field perpendicular (respectively parallel) to the cylinder axis. The variation would be quite the opposite for the elongation modulus. Our ferrogels are very promising for such magneto-elastic experiments, because their elastic modulus remains low (maximum E=1.6•10 4 Pa for a relatively high magnetic load Φ=6.5%).

III. Composite suspensions of laponite discs and maghemite spheres: probing a colloidal system by another one

Laponite is a synthetic clay of general formula Si 8 M g5 , 45 Li0 4 H 4 O 24 Na 0,7 . Particles are discotic (diameter around 30 nm, thickness of 1 nm) and make stable suspensions when dispersed in aqueous media for convenient conditions of pH (9 < pH < 10.5 : below pH 9, the magnesium ions dissolve in solution; above pH 10, dissolution of silica appears) and ionic strength (if the ionic strength is higher than 2 10 -2 mol.L -1 , attractions in the system lead to flocculation). For these experimental conditions, particles are chemically stable and have a negative average surface charge.

For ionic strength ranging between 10 -4 mol.L -1 and 2 10 -2 mol.L -1 , laponite suspensions exhibit a rheological transition over a given volume fraction range, the nature of which is still a subject of debate [32,33,34,35,36,37]. The transition is related to the appearance of a pseudoplateau in the equation of state of the system and the end of the pseudoplateau may be related to an ill-defined

The pseudoplateau of the equation of state still exists for the composite dispersion. Neither its border nor its value were shifted. The three parts of the equation of state (before, along and after the pseudoplateau) will be denoted hereafter parts 1, 2 and 3 respectively. This result indicates that the inclusion of a few maghemite particles changes neither the interactions nor the structure of the system.

These maghemite particles can be considered indeed as non-invasive probes.

C. Probing laponite gels heterogeneity, using magneto-optical probing and SANS

Particles have an intrinsic optical anisotropy, such that a CitMF become birefringent when submitted to a magnetic field as particles orientate along the field. The measurement of temporal birefringence relaxation after the application of a magnetic pulse (0.017 T) enables to measure a relaxation time τ of the probes, which is characteristic of their rotational diffusion. Knowing the diameter of the particles (from magnetic measurement) and using Stokes-Einstein relation, the viscosity of the mixture in the vicinity of the probes can be attained by such a measurement [9].

It appeared that this time τ is comparable for maghemite particles in water and in laponite whatever Φ Laponite , except for region 3 of the equation of state where τ is shorter. It shows that the particle's dynamics is not slowed down in the region of the pseudoplateau even though suspensions are solid. In addition, no aggregates are formed, as they would increase the relaxation time. The ratio between birefringence in solid suspensions and in solution for the same volume fraction of maghemite particles gives the percentage of freely rotating particles at 0.017 T and is presented on Fig. 8. It departs smoothly from 1 in the middle of the equation of state to reach 0.75 in region of equation 3. Thus some probes begin to be mechanically blocked only at the end of the pseudoplateau and become more and more numerous although laponite suspensions are solid since the beginning of the plateau. This result is in good accordance with the hypothesis of microscopic heterogeneities in laponite gels, liquid pockets coexisting with solid domains. Fig. 8: Ratio of the free maghemite probes in mixtures when increasing the volume fraction of laponite particles. The three domains correspond to the three regions of the equation of state [14].

The spatial repartition of the maghemite probes is studied by SANS. In such an experiment, the solvent was a H 2 O/D 2 O mixture, which neutron scattering length density exactly matches the value of laponite particles. Indeed, the measured intensity only comes from the contribution of maghemite particles. The perfect extinction of laponite enables to get an effective structure of the probes. It is obtained by dividing absolute intensities by the form factor of the maghemite particles in dilute solution in pure solvent. The scattering vector ranged from 1.6 10 -3 Å -1 to 3 10 -2 Å -1 . It appeared that at low Φ Laponite , the structure factor is close to one (part 1), indicating that the probes are homogeneously distributed. Along the pseudoplateau of the Π vs. Φ Laponite plot, the effective structure factor increases a lot with Φ Laponite at small q, revealing an increasing heterogeneity. This suggests that the probes are located in liquid-like pockets. In other words, they are excluded from the dense regions where Laponite particles are localized and share strong attractions. When Φ Laponite increases, the size of these large solid-like clay domains grows, while liquid pockets shrink and the effective structure factor increases further. For the largest Φ Laponite (part 3), the structure factor decreases again and even shows a pronounced depletion at low q. The probes are again homogenously dispersed with Laponite, but the presence of Laponite particles filling all the space prevent the probes from localizing and moving freely. Fig. 9: Effective structure factor of magnetic probes in hybrid systems. Φ probes is constant (0.05%). Φ laponite correspond respectively to part 1 of the equation of state (Φ = 0.18%), beginning (Φ = 0.59%) and end of part 2 (Φ = 1.48%), and part 3 (Φ = 2%) [14].

Thus SANS results are in agreement with local mechanical measurements and allow giving an illustration of the hybrid system for the different parts of the equation of state (Fig. 10). This was possible because first the chemical conditions of the mixture have been found and second because the presence of maghemite particles has not disturbed the equation of state of laponite. The small spheres represent the maghemite nanoparticles and the disks the laponite clay platelets. Picture (2a) and picture (2b) correspond respectively to the beginning and to the end of the pseudoplateau where solid-like domains of clay coexist with liquid-like pockets. Pictures (1) and (3) depict the pure liquid phase and the pure solid phase (gel) respectively [14].

The population of the liposomes obtained by spontaneous swelling is heterogeneous in size and in color, indicating that the concentration of magnetic particles is not the same in all liposomes. Because of the swelling process, these two characteristics cannot be calculated using a simple dilution factor, but both the volume fraction of magnetic particles and the concentration of tri-sodium citrate inside liposomes can be determined after all. Magnetophoresis experiments, i.e. migration in a controlled magnetic field gradient, allow an estimation of the volume fraction Φ of magnetic particles encapsulated inside the liposomes (ranging between 0.002 and 0.005%). The concentration of trisodium citrate encapsulated in the liposomes is obtained from the observation by optical microscopy of a liposome in a solution of known salinity. When the ionic strength is the same inside and outside the liposome, the latter appears as a sphere with a fluctuating membrane.

C. Deswelling of giant magnetoliposomes

Shape transitions are well-known consequences of an osmotic stress on red blood cells or on liposomes [44]. An increase of the osmotic pressure outside liposomes induces a decrease of their diameter that is related to the flow of water toward the outside of the liposomes across the lipid membrane. The same kind of phenomenon was observed with magnetoliposomes, the osmotic stress being induced by an increase of the salt concentration outside the liposomes [45]. Quantitative characterization of the deswelling process was performed by direct measurement of the vesicle radius as a function of time for different values of the concentration gradient across the phospholipid membrane (∆c) (Fig. 13a). The permeability of the DOPC bilayer to water measured for ∆c ranging between 7 and 70 mmol.L -1 has been found equal to 34 µm/s in good agreement with the values found in other studies. It has to be underlined that all along the deswelling process, at the same time that the diameter of the liposomes decreases, the latter becomes more and more orange colored indicating an increase of its particle's volume fraction. This indicates that the nanoparticles are unable to permeate the liposome surface, thereby suggesting the absence of mesoscopic pores during the osmotic stress inducing the deswelling process. Magnetic nanoparticles appear here as possible probes to test the formation of mesoscopic pores in a membrane. In most cases, the deswelling process leads to a drop of concentrated magnetic fluid stuck to a phospholipid membrane without any apparent release of magnetic material in solution. This drop exhibits an important deformation when a magnetic field of 0.03 Tesla is applied, attesting of the high concentration of magnetic material and of the presence of an excess of phospholipid membrane (Fig 14). Decreasing the osmotic pressure in the surrounding medium by water dilution, this object begins to swell again. In the end, a spherical liposome filled with the magnetic fluid is recovered, with almost the same size as before the osmotic stress (Fig 13b).

The re-swelling process appears here as a proof that the membrane is not dramatically damaged during the deswelling process.

D. Deformation of giant magnetoliposomes

An illustration of the importance of the encapsulated ferrofluid composition is the effect of the ionic strength upon the magnetic field induced deformations of liposomes. At high ionic strength, the application of a magnetic field of low intensity (0.04 Tesla) on a giant magnetoliposome elongates the latter in the direction of the field (prolate ellipsoid, Fig. 15a). Conversely at low ionic strength, the same magnetic field compresses the liposome at their poles (oblate ellipsoid, Fig. 15b). The relevant experimental parameters to explain this shape transition are the initial radius R 0 of the liposome, the magnetic susceptiblity χ and the salt concentration C s in the encapsulated ferrofluid. Two domains corresponding to both types of deformation are defined on a shape phase diagram, the oblate one being in the region of low values of R 0 , χ and C s [START_REF] Sandre | Cebers A in Giant Vesicles[END_REF]. A model comparing the magnetic energy and the bending energy of the membrane enabled to establish the sensitivity of the shape on C s [START_REF] Sandre | [END_REF]. The main result of this description is an anisotropic distribution of particles at the neighborhood of the membrane when a magnetic field is applied. This shape transition triggered by the ionic strength is explained by an electrostatic interaction between the weakly charged phospholipid bilayer and the ionic encapsulated species (particles and Na 3 Cit electrolyte) Fig. 15: Optical pictures of the two kinds of shape exhibited by a magnetolipsome under the application of a magnetic field [START_REF] Sandre | [END_REF]: a) prolate ellipsoid for a high ionic strength ferrofluide; b) oblate ellipsoid for a low ionic strength ferrofluid. Length of the bar is 10 µm.

E. Conclusion

This last part illustrates that the inclusion of a citrate-stabilized ferrofluid (CitMF) in liposomes allows probing some properties of the latter and helps for the interpretation of their behavior. Again the composition of the ferrofluid and especially the ionic strength is a key parameter as it controls the osmotic pressure of the systems. Giant liposomes are useful objects as they allow a direct observation of the effect of a physical control like the magnetic field, or a chemical modification of the system. For example mesoscopic pores or complete solubilization of the phospholipid membrane can be observed by addition of a detergent on giant magnetoliposomes. Once again the magnetic nanoparticles appear as possible probes. At a lower scale, small magnetoliposomes (LUV, 200 nm in diameter) are now under study. In this case, a direct observation is not possible and only averaged quantities can be determined. Nevertheless, they have applications in the field of pharmacology and a parallel between the behavior of the magnetic giant and large vesicles is interesting to make.

V. General conclusion

This paper illustrates through three examples the versatility of CitMF for making magnetic composite materials in aqueous media. The main interest of the specific magnetic properties of nanoparticles for the composite material was to perform mechanical measurements on the other component of the system on a large range of scales: macroscopic (stretching test for ferrogels and possibility of magnetostriction), microscopic (deformation of giant liposomes under a magnetic field) and nanoscopic (local viscosity in laponite suspension).

The key point is the robustness of CitMF, which remains stable whatever the conditions of ionic strength and magnetic field in the pH stability range of nanoparticles. The perfect knowledge of interaction strength and range through osmotic pressure has allowed to set conditions of osmotic pressure for several purposes:

-For making stable ferrogels and tune their swelling and elastic properties through variation of the magnetic particle concentration.

-For using nanoparticles on an interaction range where they behave as non-invasive probes.

-For exploring the swelling and deswelling of liposomes in response to an osmotic stress.

One may wonder about the possibility to dope with magnetic nanoparticles some composite materials that are not stable within the same physicochemical range than CitMF. Other chemical conditions of colloidal stability of such particles can be found by coating their surface with other ligands than citrate, surfactants [48], silica [49], or simply by using "naked" particles (bare iron oxide). Controlling the initial osmotic pressure of the precursor suspension of nanoparticles is still the prerequisite for ensuring the stability of the particles in the final product.

.Fig. 1 :

 1 Fig.1brepresent the strain-stress measurements for ferrogels at the same polymer and cross-linker concentrations but varying volume fractions of nanoparticles Φ 0 during synthesis. We observe no significant deviation of the curves from linearity, meaning that the ferrogels exhibit a rubber-like elasticity over the whole domain of deformation studied here.

Fe2O3m).

  Two ratios are defined from those experimental measurements:

Fig. 2 :

 2 Fig. 2: Swelling ratio Q (filled squares) and particle's release R (circles) versus volume fraction Φ 0 of magnetic particles in the preparation mixture. The solid line represents the swelling ratio at preparation Q 0 , which varies from 27 to 25 depending on Φ 0 . All these ferrogels were prepared and swollen at low salinity [Na 3 Cit] = [Na 3 Cit] 0 = 8•10 -3 mol.L -1 and their cross-link ratio was always BA/AM=1%.

Fig. 4 :

 4 Fig. 4: Observation by optical microscopy of the gas-liquid like transition inside ferrogels prepared at an initial particle's volume fraction Φ 0 = 3.8% and a cross-linking degree BA/AM=0.5% swollen in a salt concentration [Na 3 Cit]=0.25 mol.L -1 a) 9 hours after beginning of swelling, b) after 9 hours of swelling and application of a magnetic field of 1Tesla for 10 min; c) after 24 hours of swelling. The bar length is 50 µm. The orange color is due to the light absorption spectrum of ferric oxide. The dots are microdroplets concentrated in particles (mentioned in text as "liquid-like" phase).

synthesis and swelling [Na 3

 3 Cit] = [Na 3 Cit] 0 = 8•10 -3 mol.L -1 a) b) Fig. 5: a) Final particle's volume fraction in the swollen ferrogel Φ as a function of the initial volume fraction Φ 0 during synthesis computed from the conservation equation with the data of Fig. 2; b) Elastic Young modulus from the data of Fig. 1c) plotted vs. the actual particle's volume fraction Φ calculated from Q and R where Q either comes from weight measurements (open circles) with the samples presented on Fig. 2 or Q is estimated from the relative increase of diameter (filled circles) using used for the elongation tests plotted on Fig. 1. All those ferrogels were prepared at BA/AM=1% and [Na 3 Cit] 0 = 8•10 -3 mol.L -1 .

Fig. 6 :

 6 Fig. 6: Final particle's volume fraction in the swollen ferrogel Φ as a function of the tri-sodium citrate concentration [Na 3 Cit] in the swelling bath, computed from the measurements of Q and R represented on Fig. 3. For visualization purpose, the horizontal scale is dilated in the region of low salinity (<10 -2 mol.L -1 ). All ferrogels were prepared at BA/AM=0.5% and [Na 3 Cit] 0 = 5•10 -3 mol.L -1 .

Fig. 7 :

 7 Fig. 7: Experimental state isotherm curve Π vs. Φ for pure laponite suspensions in a Na 3 Cit solution (2.5 10 -3 mol.L -1 ) at pH 10 (open dots) and for laponite doped with maghemite probes in the same chemical conditions (filled dots). The dotted lines separate the three characteristic domains of the equation of state considered in the text (before, along and after the pseudoplateau) [14].

Fig. 10 :

 10 Fig. 10: Schematic description of the laponite suspensions including magnetic probes (Φ = 0.05%).

  Fig 13: a) Optical microscopy of a magnetoliposome submitted to a concentration gradient ∆c=7 mmol.L -1 . The diameter of the liposome decreases due to a water flow toward the outer medium. The bar length is 10 µm. b) Reswelling of a magnetoliposome that has been previously submitted to an osmotic stress.

Fig 14 :

 14 Fig 14: Last stage of the osmotic stress. The inner phase becomes more and more contrasted and exhibits large deformation under a weak magnetic field (H=0.03 T).

Acknowledgements

All these results have been obtained thanks to a close collaboration with Emmanuelle Dubois, Pierre Levitz, Régine Perzynski, Jean-Claude Bacri and Jean Chevalet. The part of this work about ferrogels is supported by CONACYT Mexico.

isotropic-nematic transition [38]. Although this pseudoplateau in the equation of state could be associated to a first-order transition, the laponite suspensions stay macroscopically homogeneous and the existence of biphasic samples has never been reported. The hypothesis of an isotropic-nematic transition that occurs on a microscopic scale because of long-range electrostatic interactions preventing the system to explore the whole phase space can be formulated.

We have tested this hypothesis in reference [14] by including maghemite nanoparticles (CitMF) as probes in laponite suspensions in order to determinate their spatial repartition for different Φ laponite covering all parts of the laponite equation of state. Citrate-coated maghemite particles were the best candidates for probes as they have magneto-optical properties allowing local viscosity measurements [9]. They are spherical, with a size similar to the one of laponite particles; they have the same counterions as laponite (Na + ) and can be dispersed in the same conditions of pH and ionic strength as laponite. They have a neutron scattering length density that is very different from laponite particles thereby allowing a good contrast for SANS experiments.

A. Including probes in laponite suspensions

The suspensions including probes were obtained by stirring laponite particles (purchased from Laporte Industries Ltd) in a suspension of maghemite particles probes at Φ probes = 0.05 % with Na 3 Cit = 2.5 10 - 3 mol.L -1 and NaOH = 10 -4 mol.L -1 to set pH 10. The citrate concentration was above the critical concentration for citrate desorption and corresponded to an ionic strength of 1.5 10 -2 mol.L -1 below the destabilization threshold of laponite suspensions. The volume fraction of probes was kept constant at a very small value (0.05%) to avoid disturbing the laponite suspensions. Suspensions were let to stand for 10 days before performing any measurements.

B. Equation of state of the mixture

The inclusion of the probes did not shift the fluid/solid transition and did not modify the equation of state of laponite suspensions, as can be seen on Figure 7 which represents the osmotic pressure as a function of the volume fraction either with or without the probes, by analogy with the pressure-density isotherms for Van der Waals gases. This curve has been obtained by direct measurements of Π with a membrane osmometer for the lowest volume fractions and by osmotic compression (where Π is controlled by a solution of dextran) for the highest ones. For this latter experiment, the constant parameter is not Φ probes but the ratio Φ probes /Φ laponite . This ratio insures that Φ probes stays in the range 0.05% to 0.4% and the osmotic pressure of maghemite particles remains below 45 Pa (see part 1)

which is much inferior to the one of laponite suspensions. Laponite particles thus determine the osmotic pressure of the hybrid system to preset values.

IV. Ferrofluids and liposomes

"Magnetoliposomes" have been introduced by De Cuyper [39] to describe iron oxide nanoparticles wrapped by a lipid bilayer. Small and large magnetic liposomes have been studied during recent years for applications in the field of biotechnologies [40], because of their compatibility with biological media combined with their physical properties. In particular, their ability to move in a magnetic field gradient (a phenomenon called magnetophoresis) is useful for sorting processes. With a much larger size (10 µm and above), giant magnetoliposomes exhibit important deformations when a magnetic field is applied (Fig. 11). From the analysis of such shape modifications, it has been possible to get some information on the membrane properties. For example, the membrane bending modulus of the DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) has been estimated [11].

A. CitMF: a good candidate for encapsulation

Several procedures are possible to encapsulate the nanoparticles in liposomes but two conditions are always required. The particles have to be negatively charged in order to avoid a quick adsorption of the phospholipid molecules on their surface and coated by citrate species in order to be dispersed in water at pH 7. The residual tri-sodium citrate in solution is sometimes a problem for applications, but its concentration can be adjusted through dialysis of the magnetic fluid against a tri-sodium citrate solution of the desired concentration.

Here the total osmotic pressure of the encapsulated magnetic fluid (osmotic pressure due to the particles + osmotic pressure due to the ionic species) is a key factor for the synthesis of the magnetoliposomes as for their stability. The problem is not a problem of phase diagram, because liposomes are out of equilibrium objects, but is related to the properties of the membrane and to the swelling of the liposomes. The ionic strength especially has to be carefully controlled because it will affect the properties of the final magnetoliposome.

B. Encapsulation of CitMF in giant liposomes

Particles can be introduced in the liposomes either by a multiple emulsion process [8], or by a spontaneous swelling in water of phospholipid bilayers filled with magnetic particles [START_REF] Sandre | [END_REF], or by the swelling of the phospholipidic bilayers in a magnetic fluid followed by the separation of the non encapsulated particles [41]. The procedure is chosen according to the size required for the final liposomes.

Giant unilamellar magnetic liposomes have been obtained by spontaneous swelling in water of phospholipid bilayers pre-hydrated with an aqueous magnetic fluid. The phospholipid powder (1 mg) is mixed with 10µL of CitMF and sheared on a glass support. Thus an oily orange film is obtained, which is then swollen with distilled water (1 mL) at 45°C.

The first remark is that the swelling is more efficient when the film is pre-hydrated by a solution of charged particles and ions rather than pure water. Indeed, the water added in excess to the multilamellar film swells the system in order to dilute the material entrapped in the phospholipid bilayers (the charged magnetic particles and the unadsorbed tri-sodium citrate). The low diffusion coefficient of the particles enables their encapsulation while the swelling process of the lipid bilayers takes place, whereas the tri-sodium citrate electrolyte diffuses rapidly in the surrounding medium.

If water is added under flow and in a restricted volume (for example directly in the observation chamber, 200 µm thickness) liposomes connected to tubes are observed (Fig. 12). Such phospholipidic tubes have soon been described [42]. The originality of the present system lies in the action of the magnetic fluid on the tube itself but also on the liposomes ending each tube. Pearling instability has thus been induced on such tubes by the stress of the two ending liposomes due to the application of a magnetic field [43].