Matteo Mancinelli
email: matteo.mancinelli@univ-poitiers.fr

Vincent Jaunet
email: vincent.jaunet@ensma.fr

Peter Jordan
email: peter.jordan@univ-poitiers.fr

Aaron Towne
email: towne@umich.edu

Screech-tone prediction using upstream-travelling jet modes

Keywords: Supersonic jets, screech, instability

, a new prediction approach is proposed where the feedback loop is closed by the upstream-travelling jet modes first discussed in

Introduction

Supersonic jets operating at off-design conditions include a shock-noise source in addition to the turbulent mixing noise that is usually dominant in subsonic and perfectly expanded supersonic jets. The shock-associated noise includes a broadband component and a tonal component known as screech [START_REF] Tam | Supersonic jet noise[END_REF]. Both are due to the interaction between the convected flow disturbances and the quasi-periodic shock-cell structure.

Screech has been broadly studied in the literature (see e.g. the review from [START_REF] Raman | Supersonic jet screech: half-century from powell to the present[END_REF]). In his seminal work, [START_REF] Powell | On the mechanism of choked jet noise[END_REF] proposed a phenomenological description of the screech mechanism. He asserted that screech involves the interaction between downstreamtravelling flow instabilities, which originate at the nozzle lip, and the shock-cell structure. This interaction was understood to generate acoustic waves that propagate back to the nozzle where they trigger new instabilities, thus closing the loop. [START_REF] Powell | On the mechanism of choked jet noise[END_REF] furthermore showed how screech is characterised by different stages: the tone frequency evolution with jet Mach number involves sudden frequency jumps that occur at given flow conditions. He detected four different stages, which he named modes A, B, C and D. Later, [START_REF] Merle | Nouvelles recherches sur les fréquences ultrasonores émises par les jets d'air[END_REF] showed, using Schlieren visualizations, that the A mode could be divided into two sub-modes, A1 and A2. According to [START_REF] Powell | Observations of the oscillation modes of choked circular jets[END_REF], A1 and A2 are axisymmetric modes, B and D are sinuous or flapping modes, and C is a helical mode. The staging behaviour was studied by Walker and Thomas (1997) on a rectangular jet using a high-order spectral analysis. Screech staging was found to occur for jet-flow conditions where peaks of bi-coherence were found, the frequency jump being thus associated with non-linear interactions between the different modes. Wavelet transforms were used by Walker et al. (1997) to show that the staging behaviour in a rectangular supersonic jet can involve a coexistence of several modes. While different aspects of screech staging have been discussed in the literature and some models have been proposed to account for this in prediction schemes [START_REF] Gao | A multi-mode screech frequency prediction formula for circular supersonic jets[END_REF], a satisfactory explanation of why staging occurs is still lacking.

A complete understanding of screech dynamics is necessary for the development of screech-frequency prediction models. Powell's simple model [START_REF] Powell | On the mechanism of choked jet noise[END_REF]) is based on the propagation time of downstream-travelling disturbances from the nozzle to the shock, on one hand, and, on the other, the propagation time of a free-stream acoustic wave from the shock to the nozzle. A modified version of this model was obtained by [START_REF] Tam | Proposed relationship between broadband shock associated noise and screech tones[END_REF] by considering the screech as a special case of broadband shock-associated noise. In this formulation the screech frequency is explicitly expressed as a function of the shock-cell wavelength. Later, [START_REF] Panda | An experimental investigation of screech noise generation[END_REF] proposed a modification of Tam's model that includes the wavelength of the standing wave formed by the superposition of the downstream-travelling instability wave and the upstream-travelling acoustic wave. Comparison of predictions made using the foregoing models with experimental data have provided rough agreement. We here explore improvements that can be obtained by more correctly modelling the guided, upstream-travelling acoustic jet modes that [START_REF] Edgington-Mitchell | Upstream-travelling acoustic jet modes as a closure mechanism for screech[END_REF] and [START_REF] Gojon | Oscillation modes in screeching jets[END_REF] show to be active in closing the screech loop.

Recently, it has been shown how these modes explain weak, forced resonance observed in high-speed subsonic jets [START_REF] Towne | Acoustic resonance in the potential core of subsonic jets[END_REF], resonance in impinging subsonic and supersonic jets [START_REF] Tam | Theoretical model of discrete tone generation by impinging jets[END_REF][START_REF] Bogey | Feedback loop and upwindpropagating waves in ideally expanded supersonic impinging round jets[END_REF] and high-amplitude tones observed when a subsonic jet grazes an edge, as in a jetflap interaction [START_REF] Jordan | Jet-flap interaction tones[END_REF].

The idea that screech involves the guided, upstreamtravelling jet modes evoked above was first suggested by [START_REF] Shen | Three-dimensional numerical simulation of the jet screech phenomenon[END_REF], who claimed that the feed-back loop of modes A1 and B was closed by free-stream acoustic waves, whereas the loop of modes A2 and C was closed by the acoustic jet modes. We here show that both the A1 and A2 modes are underpinned by resonance between downstream-travelling Kelvin-Helmholtz (K-H) instabilities and the said upstream-travelling jet modes. We do so by means of a novel linear screechtone prediction model based on resonance between the aforesaid waves, and in this we go beyond the work [START_REF] Gojon | Oscillation modes in screeching jets[END_REF] and [START_REF] Edgington-Mitchell | Upstream-travelling acoustic jet modes as a closure mechanism for screech[END_REF], both of whom provided evidence that the guided modes underpin screech, without using this information to perform screech-frequency prediction.

Finally, using a wavelet transform of the measured pressure data, we show how the staging between A1 and A2 modes involves mutually-exclusive switching between the two, and how this is underpinned by nonlinear interactions. Given the success of the linear model we use for tone-frequency prediction, this result demonstrates how non-linearity, whilst present and active in staging, and in the determination of screech amplitudes, does not have a strong impact on frequency selection.

The paper is organised as follows. A review of the previous screech frequency prediction models as well as the presentation of the new approach involving the upstream-travelling jet waves are reported in §2. The experimental setup and the instrumentation adopted are described in §3, and the main results are presented in §4. Conclusions are finally discussed in §5.

Theoretical background

Screech-tone frequency prediction models

Powell's original screech-prediction approach involves a downstream-travelling Kelvin-Helmholtz instability and an upstream-travelling free-stream acoustic wave [START_REF] Powell | On the mechanism of choked jet noise[END_REF]. With this assumption, the time taken for a flow disturbance to reach the reflection point (assumed to be the third or fourth shock cell) plus the time required for the resulting sound wave to travel back to the nozzle orifice can be written as,

T = dh U c + h c ∞ , (1)
where U c and c ∞ are the convection velocity and the ambient speed of sound, respectively, and h is the spacing between the nozzle exhaust and the downstream reflection position. This model allows the screech frequency f s to be written in terms of the number of cycles θ = N + p of the flow disturbance:

N + p f s = h U c + h c ∞ , (2)
where N and p are an integer and a constant, respectively. [START_REF] Tam | Proposed relationship between broadband shock associated noise and screech tones[END_REF] proposed the alternative version,

f s = k sc U c 2π 1 + Uc c∞ , (3)
where k sc is the shock-cell wavenumber. It is straightforward to show that Tam's formula is not very different from that obtained by [START_REF] Powell | On the mechanism of choked jet noise[END_REF] by considering that k sc = 2π λsc , with λ sc being the shock-cell wavelength, and h = nλ sc . The screech frequency formula can thus be written,

n f s = h U c + h c ∞ . (4)
In the same work, [START_REF] Tam | Proposed relationship between broadband shock associated noise and screech tones[END_REF] also proposed a semi-empirical correction to equation (4) to account for temperature effects.

An alternative formulation has been proposed by [START_REF] Panda | An experimental investigation of screech noise generation[END_REF], where the standing wave that occurs due to superposition of the downstream-and upstreamtravelling waves is incorporated, leading to,

1 λ sw = 1 λ h + 1 λ a = f s U c + f s c ∞ =⇒ m f s = h U c + h c ∞ , (5)
where the substitution h = mλ sw has been performed to obtain an expression for the screech frequency as a function of the distance between the nozzle exit and the downstream reflection location. In all of the above formulae the convection velocity is usually taken as a constant and included between 0.6 and 0.8 of the jet velocity U j .

The resonance model

In this section we present a screech-frequency prediction model that is based on a resonance between two waves travelling in opposite directions. We make predictions based on downstream-travelling Kelvin-Helmholtz waves and two kinds of upstream-travelling wave: (i) free-stream acoustic waves; (ii) guided acoustic jet modes. Following [START_REF] Towne | Acoustic resonance in the potential core of subsonic jets[END_REF] and [START_REF] Jordan | Jet-flap interaction tones[END_REF], we use the terms downstream-and upstreamtravelling to designate the sign of the group velocity.

Accordingly, the downstream-travelling modes are denoted with the superscript +, whereas the upstreamtravelling modes are indicated with the superscript -.

The notation used throughout the manuscript is reported in the following for the sake of clarity. The Kelvin-Helmholtz mode is denoted k KH , the guided acoustic jet modes k p , and the free-stream acoustic wave k a .

Cylindrical vortex-sheet model

The linear dynamics of the waves are modelled using a cylindrical vortex-sheet [START_REF] Lessen | On the inviscid stability of the laminar mixing of two parallel streams of a compressible fluid[END_REF][START_REF] Michalke | A note on the spatial jet-lnstability of the compressible cylindrical vortex sheet[END_REF][START_REF] Towne | Acoustic resonance in the potential core of subsonic jets[END_REF]. Following the procedure used in [START_REF] Jordan | Jet-flap interaction tones[END_REF] the normal mode ansatz is:

q (x, r, θ, t) = q (r) e i(kx+mθ-ωt) , ( 6
)
where m is the order of the azimuthal mode, k is the streamwise wavenumber normalised by the nozzle diameter D and ω is a non-dimensional frequency ω = 2πStM a , with St = f D/U j the nozzle diameter-based Strouhal number and M a = U j /c ∞ the acoustic Mach number. The vortex-sheet dispersion relation is,

D (k, ω; M a , T, m) = 1 1 -kMa ω 2 + + 1 T I m γi 2 γo 2 K m-1 γo 2 + mK m γo 2 K m γo 2 γi 2 I m-1 γi 2 -mI m γi 2 = 0 , (7)
with

γ i = k 2 - 1 T (ω -M a k) 2 , (8a)
γ o = k 2 -ω 2 , (8b)
where I and K are modified Bessel functions of the first and second kind, respectively, and T is the jet-toambient temperature ratio T j /T ∞ , so that the relation between the acoustic and jet Mach numbers is given by

M j = U j /c j = M a / √ T . We assume isothermal condi- tions in the modelling, that is T = 1.
Frequency/wavenumber pairs (ω, k) that satisfy equation (7) define eigenmodes of the vortex sheet for given values of m, M a , and T . To find these pairs, we specify a real frequency ω and compute the associated eigenvalues k according to equation (7). It is straightforward to show that, because of the normalisation adopted, the free-stream acoustic wave is simply given by k ± a = ±2πStM a . The upstream-travelling guided jet waves belong to a hierarchical family of modes characterised by their azimuthal and radial order (m, j). We restrict attention to azimuthal mode m = 0 due to the axisymmetry property of screech modes A1 and A2. The radial order of the k p waves is varied in the range j = 1, 2. Figure 1 shows an eigenspectrum comprising the k KH and k p modes for azimuthal mode m = 0. The acoustic wave, k - a , as well as a line with slope corresponding to a phase speed equal to 0.8 U j , an approximation frequently made for the K-H mode, are also reported. As an example, we consider the jet flow condition M j = 1.1. We note the following features of the k - p jet modes. Unlike the acoustic waves, they are dispersive. They only exist as propagative waves in a narrow frequency band delimited by the branch-and saddle-points B (m, j) and S (m, j), respectively. Their phase velocity is subsonic but very close to the speed of sound, particularly at the lower frequency end of the branch where the eigenvalues coincide almost exactly with those of free-stream sound waves. Furthermore, as pointed out by [START_REF] Tam | Theoretical model of discrete tone generation by impinging jets[END_REF], the branch point B (0, 1) for azimuthal mode m = 0 and radial order j = 1 in the k r -St plane coincides with the origin. Finally, we note that the k + KH mode is slightly dispersive, and its phase velocity is a little higher than the usually adopted 0.6-0.8 U j. These trends are consistent with the findings of [START_REF] Michalke | Survey on jet instability theory[END_REF].

Resonance criteria

In this section we discuss the conditions that the k + and k -waves must satisfy in order for resonance to occur. Resonance can clearly only exist in the frequency range where both waves coexist and are propagative. It is therefore clear that, where the k - p guided jet modes are concerned, the eligible frequencies for resonance lie in the band delimited by the branch-and saddle-points, as the waves are evanescent outside of this range.

We assume that the waves exchange energy upstream at the nozzle exit, where the k + KH mode is generated, and at some downstream location, where a determinant interaction between the K-H mode and the shock-cell pattern occurs. This location is frequently considered to lie somewhere between the third and the fourth shock cells [START_REF] Mercier | Experimental characterisation of the screech feedback loop in underexpanded round jets[END_REF]. Hence we can infer that the nozzle exit plane and a location around the third and fourth shock cell represent the end conditions for resonance. Following [START_REF] Pack | A note on prandtl's formula for the wavelength of a supersonic gas jet[END_REF], the first shock-cell length is given by,

L 1 (M j ) = π 2.4048 M 2 j -1 . (9)
Taking into account the shock-cell length decrease due to mixing layer growth, the s th shock-cell location is given by:

L s (M j ) = L 1 ((1 -α) s + α) , ( 10
)
where α is the rate of decrease of the shock-cell length with the downstream distance, and which takes a value of 0.06 according to [START_REF] Harper-Bourne | The noise from shock waves in supersonic jets-noise mechanism[END_REF].

As reported by [START_REF] Jordan | Jet-flap interaction tones[END_REF] (see also [START_REF] Landau | Course of theoretical physics[END_REF]), the conditions required for resonance involve both magnitude and phase constraints:

e ∆kiLs = |R 1 R 2 | , ( 11a
)
∆k r L s + φ = 2pπ , (11b)
where R 1 and R 2 are complex reflection coefficients at the boundaries, φ is the phase of the complex product R 1 R 2 and p is an integer. Following [START_REF] Jordan | Jet-flap interaction tones[END_REF], we neglect the magnitude constraint, which is related to the imaginary part of the eigenvalues. The phase component relation (11b) then completely determines the resonance conditions. Given that the true phase of reflection is unknown, following [START_REF] Jordan | Jet-flap interaction tones[END_REF], we explore the two extremes φ = 0 and φ = π, which lead to two resonance criteria,

k + -k -= ∆k r = 2pπ L s , (12a)
k + -k -= ∆k r = (2p + 1) π L s . ( 12b
)
We consider resonance predictions by assuming the k -wave active in resonance to be, on one hand, a free-stream sound wave, and, on the other, a guided jet mode. We allow the downstream reflection location to vary between the second and fifth shock cells. The best agreement was obtained by considering downstream reflection to occur at the fourth shock cell, i.e. s = 4, which is consistent with the observations of [START_REF] Mercier | Experimental characterisation of the screech feedback loop in underexpanded round jets[END_REF]. All results presented in what follows correspond to this value. Also, the out-of-phase reflection condition (eq. ( 12b)) provided best agreement with data, and so this is what is considered in the following analysis. Figure 2 • to k - p for the radial order j = 1, 2 to k + p for j = 1, to k - p for j = 2, × to k + p for j = 2, dash-dotted line to a non-dispersive wave whose phase speed is 0.8 U j , dashed line to free-stream acoustic wave. The branch-and saddle-points of the guided jet waves for each pair of (m, j) orders are indicated as well with letters B and S, respectively. KH and k - p and identification of the resonance frequency for the jet Mach number M j = 1.1 for azimuthal mode m = 0. Solid line refers to radial order j = 1, dash-dotted line to j = 2, horizontal dashed lines to resonance criteria in the case of out-of-phase reflection condition.

of a compressed dry-air duct at 200 bar. An electrically driven valve permits regulation of the jet velocity by controlling the pressure of the incoming flow. The inflow conditions are continuously monitored by a thermocouple and a pressure transducer which provide the stagnation temperature and pressure, respectively, at the inlet section of the nozzle. A heating system is installed in order to keep the stagnation temperature at the nozzle inlet constant and equal to 295 K. A settling chamber with a honeycomb panel and mesh grids is positioned upstream of the nozzle in order to have the desired inflow quality. The jet exit conditions are obtained by means of isentropic flow relations between the stagnation and ambient conditions at the nozzle exit. The supersonic under-expanded jet issues from a simple convergent nozzle of diameter D = 0.01m. Experimental tests were carried out for a stagnation pres-sure range p 0 = [1.89, 2.77] with corresponding fully expanded jet Mach number range M j = [1, 1.3] and a nozzle diameter-based Reynolds number range Re = U j D/ν = 2.86 • 10 5 , 4.3 • 10 5 . The tests were performed with a very fine Mach-number resolution, ∆M j = 0.005, in order to capture the fine details of the Mach-number dependence of the screech tones.

Pressure fluctuations were measured by GRAS 46BP microphones, whose frequency response is flat in the range 4 Hz-70 kHz. Data were acquired by a National Instruments PXIe-1071 acquisition card with a sampling frequency of 200 kHz, which provides a maximum resolved Strouhal number range [2.6, 3.2] well above the St of interest in this paper. The acquisition time was set equal to 30 s, which is six orders of magnitude larger than the longest convective time, thus ensuring statistical convergence of the quantities presented in the paper. An azimuthal array of 6 microphones was placed in the nozzle exit plane and radial distance r/D = 1. Such a device allowed to resolve the most energetic azimuthal Fourier modes: m = 0, ±1, ±2. A schematic representation of the experimental setup and microphones disposition is depicted in figure 3.

Additional experiments were conducted in the far field to verify that the close proximity of the microphone array to the nozzle did not impact the screech dynamics. The results of this analysis are reported in appendix A. Table 1 Summary of the parameters adopted to obtain screech-frequency predictions.

Screech frequency prediction

Figure 4 shows the Sound Pressure Spectrum Level SP SL [START_REF] Pierce | Acoustics: An Introduction to Its Physical Principles and Applications[END_REF], in dB/St, as a function of M j for azimuthal mode m = 0. Specifically,

SP SL = 10 log 10 P SD p 2 ref U j D , ( 13
)
where P SD is the Power Spectral Density computed through the Welch's method and p ref is the reference pressure, equal to 20µP a. The signature of the A1 and A2 screech modes is clearly detectable as well as the mode switch that occurs in the vicinity of M j = 1.12. The screech frequency prediction obtained using Tam's formula ( 4) is superimposed on the plot. It provides only a very rough agreement with the experimental data, and the staging behaviour is not captured. Furthermore, the model predicts screech at Mach numbers and frequencies for which no tones are measured. Screech-tone predictions obtained using the resonance model presented in §2.2 are shown in figure 5. Prediction using both the free-stream sound waves and the guided jet modes are shown. The k - p predictions are made assuming k - p modes of radial order j = 2 and values of p in equation (12b) equal to 3 and 4 for modes A1 and A2, respectively. A summary of the parameters used is reported in table 1. Figure 5 shows, in addition to the screech-tone predictions, the branch-and saddlepoint tracks of the guided jet modes. As recently discussed by [START_REF] Edgington-Mitchell | Upstream-travelling acoustic jet modes as a closure mechanism for screech[END_REF] and [START_REF] Gojon | Oscillation modes in screeching jets[END_REF], the screech tones of both modes A1 and A2 are bounded by the branch-and saddle-points. The cutoff and cut-on frequencies of screech are thus explained by the fact that the guided jet waves, k - p , are evanescent outside the St-M region defined by the B (0, 2) and S (0, 2) tracks. This is in contrast to the model involving free-stream sound waves which predicts screech tones for St-M regions where tones are not observed. Furthermore, the guided-jet-mode screech model provides a better description of the screech-tone Mach-number dependence in the vicinity of the high-frequency cut-off for both the A1 and A2 modes.

We also include the predictions of [START_REF] Shen | Three-dimensional numerical simulation of the jet screech phenomenon[END_REF] using the k - p modes. The authors claimed that mode A1 was underpinned by a free-stream sound wave, and mode A2 by a guided jet mode. Figure 5 shows that their prediction agrees poorly with the experimental data.

To sum up, a linear, vortex-sheet model has been used to provide screech-tone predictions of modes A1 and A2 using upstream-travelling guided jet waves as the closure mechanism. The predictions provide better agreement with experiments than does the usual approach based on free-stream sound waves. In the next section we explore non-linear aspects of the staging dynamics of screech modes A1 and A2.

Staging dynamics

We perform a time-frequency analysis to explore the screech dynamics associated with the staging process. This is achieved via a wavelet transform of the pressure signal p (t) [START_REF] Farge | Wavelet transforms and their applications to turbulence[END_REF]Mancinelli et al., 2017b). This provides wavelet coefficients which are a function of time, t, and of scale, s, which is inversely proportional to the frequency. The Continuous Wavelet Transform (CWT) is given by (Mancinelli et al., 2017a),

w (s, t) = C -1/2 ψ s -1/2 +∞ -∞ p (τ ) Ψ * t -τ s dτ , (14)
where Ψ * t-τ s is the complex conjugate of the dilated and translated mother wavelet Ψ (t) which satisfies the admissibility condition [START_REF] Meneveau | Analysis of turbulence in the orthonormal wavelet representation[END_REF]:

C ψ = +∞ -∞ Ψ (ω) 2 dω ω < ∞, (15)
where ω is the angular fequency. The CWT was computed using a complex bump wavelet kernel, whose expression in the Fourier domain is [START_REF] Jiang | Instantaneous frequency estimation based on synchrosqueezing wavelet transform[END_REF]:

Ψ (ω) = e 1- 1 1-σ 2 (ω-µ) 2 F (ω) , (16)
F (ω) =    1 if µ - 1 σ ≤ ω ≤ µ + 1 σ 0 else , (17)
where µ and σ are parameters chosen in order to have the desired frequency resolution and time localisation [START_REF] Jordan | Jet-flap interaction tones[END_REF].

In order to explore the screech dynamics in the staging process we focus on flow conditions where the switch from mode A1 to A2 occurs, i.e. M j = 1.115, 1.12, 1.125 and 1.13. Figure 6 shows the time-frequency scalogram for these jet Mach numbers, the amplitude of the wavelet coefficients has been normalised by the maximum amplitude at each wavelet scale/frequency. Frequency is expressed in terms of St and the plot shows only the first 10 s of the acquisition, that is five orders of magnitude larger than the characteristic flow time scale (the results do not change for the other time lapses). For M j = 1.115 (and in general up to this flow condition) only the screech frequency associated with mode A1 is detected. As M j increases to the value of 1.12, jumps occur between modes A1 (St 1 ) and A2 (St 2 ). The jumps are mutually exclusive. As the jet Mach number is further increased (M j = 1.125), the time lapses over which the mode A2 appears become larger. For M j = 1.13 (and in general beyond this flow condition) only the component St 2 is detected, the screech having definitively switched to mode A2. We emphasize that the two modes A1 and A2 are mutually exclusive. No coexistence of the two modes was observed, in contrast to the observations of [START_REF] Shen | Three-dimensional numerical simulation of the jet screech phenomenon[END_REF] and Walker et al. (1997) in a rectangular jet.

Finally we consider the jet flow condition M j = 1.125, where the mutually exclusive mode switching was most evident. We extract the time evolution of the amplitude of the wavelet coefficients corresponding to the screech frequency of mode A1, i.e. St 1 = 0.63. We then compute the P SD of |w p (St 1 , t) |, which is shown in semi-logarithmic scale in figure 7. The P SD has been normalised multiplying by U j /D and dividing by p 2 ref .

We observe that the amplitude is modulated at a Strouhal number St d ≈ 0.069, which is close to the difference frequency between that of mode A2 St 2 = 0.7 and that of mode A1 St 1 = 0.63. This indicates that a quadratic, non-linear interaction occurs between modes A1 and A2. Indeed, the weak presence of the St d component can also be observed in the pressure spectrum of azimuthal mode m = 0 for the same flow condition M j = 1.125, as shown in figure 8. We point out that the St d component appears in the pressure spectra only for the jet Mach numbers where the switch from mode A1 and A2 occurs, thus confirming that switching is underpinned by non-linear dynamics. This result supports that of Walker and Thomas (1997), that the staging process is an inherently non-linear process. Further analysis is necessary in order to more satisfactorily clarify the nature of the non-linear dynamics.

Conclusions

The screech of a supersonic jet issuing from a simple convergent nozzle has been characterised and modelled. Near-field pressure measurements were performed at the nozzle exhaust using an azimuthal array for jetflow conditions typical of the axisymmetric screeching modes A1 and A2. The main contribution is a new approach, following [START_REF] Jordan | Jet-flap interaction tones[END_REF], for screech frequency prediction, on one hand, and, on the other, a time-frequency analysis of the staging process that indicates its underpinning by non-linearity dynamics. Despite the role played by non-linearities in mode switching, the linear modelling framework for screech-frequency predictions that we propose captures the evolution of screech with jet Mach number for both modes A1 and A2. This suggests that non-linearity, while present, is not important for frequency selection.

A critical review of the state-of-the-art screech prediction models has been carried out underlining their limitations. A novel approach for the prediction of the screech frequency is proposed in the framework of the resonance between downstream-travelling Kelvin-Helm-holtz wavepackets and upstream-travelling, guided jet modes. Both were computed using a cylindrical vortexsheet model. The resulting prediction is in closer agreement with the experimental data than what is obtained by assuming the upstream-travelling component of the screech loop to comprise free-stream acoustic waves. The screech tones of both modes A1 and A2 only occur in the frequency-Mach number region, bounded by the branch-and saddle-point tracks, where the upstreamtravelling guided jet modes are propagative.

A time-frequency analysis using wavelet transform was performed in order to explore the screech dynamics associated with the staging process. The time-frequency scalogram of azimuthal mode m = 0 showed that the A1 and A2 modes are mutually exclusive during staging. We observed, furthermore, that the amplitude of the wavelet coefficients at the scale/frequency corresponding to mode A1 is modulated at the difference frequency between modes A1 and A2. This behaviour suggests a quadratic, non-linear interaction between A1 and A2 modes during staging. Figure 9 shows the spectral contour map for all M j . As for the near-field measurements, we restrict the attention on the frequency band where modes A1 and A2 live. The signature of the two modes is the same one arising in the near field and shown in figures 4 and 5. Hence, the close positioning of the microphone array in the near field has no effects on the emergence of the axisymmetric screech modes.

Fig. 1

 1 Fig.1Eigenvalues of the k KH and k p modes for the jet-flow condition M j = 1.1 for azimuthal mode m = 0. correspond to k + KH , • to k - p for the radial order j = 1, 2 to k + p for j = 1, to k - p for j = 2, × to k + p for j = 2, dash-dotted line to a non-dispersive wave whose phase speed is 0.8 U j , dashed line to free-stream acoustic wave. The branch-and saddle-points of the guided jet waves for each pair of (m, j) orders are indicated as well with letters B and S, respectively.

Fig. 2

 2 Fig.2Value of ∆k between k + KH and k - p and identification of the resonance frequency for the jet Mach number M j = 1.1 for azimuthal mode m = 0. Solid line refers to radial order j = 1, dash-dotted line to j = 2, horizontal dashed lines to resonance criteria in the case of out-of-phase reflection condition.

Fig. 3

 3 Fig. 3 Schematic representation of the experimental set-up and microphones disposition.

Fig. 4

 4 Fig. 4 Spectral contour map of azimuthal mode m = 0 and screech frequency prediction using Tam's formula (4).

Modem

  Shock cell Reflection condition p j of k -

Fig. 5

 5 Fig. 5 Spectral contour map of azimuthal mode m = 0 and screech-frequency predictions using the resonance model presented in §2.2: white dotted lines refer to the prediction obtained using the free-stream sound waves k - a , red bold lines to the guided jet modes k - p . The branch-and saddle-point tracks B (0, 2) and S (0, 2) are indicated with white dashed lines. Black solid line refers to prediction obtained by Shen and Tam (2002) using the guided jet modes.

Fig. 6 Fig. 7

 67 Fig. 6 Time-frequency scalogram for the jet Mach numbers: (a) M j = 1.115, (b) M j = 1.12, (c) M j = 1.125, (d) M j = 1.13. The screech frequencies related to modes A1 and A2 are indicated as St 1 and St 2 , respectively.

Fig. 8

 8 Fig. 8 Pressure spectrum of azimuthal mode m = 0 for jet Mach number M j = 1.125.

Fig. 9

 9 Fig. 9 Spectral contour map of the far-field microphone at the polar position ψ = 120 • .

Acknowledgements M.M. acknowledges the support of Centre National d' Études Spatiales (CNES) under a post-doctoral grant.

A Far-field measurements

Pressure measurements were performed in the far field in order to verify that the screech dynamics of modes A1 and A2 was not affected by the close positioning of the near-field microphone array with respect to the nozzle. The far-field microphone was placed at a radial distance r/D ≈ 90 at a polar position ψ = 120 • , with the polar angle measured from the downstream axis of the jet. A coarser jet Mach number


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email: niki.baccile@upmc.fr

Biocompatible Glyconanoparticles by Grafting of Sophorolipid Monolayers on Monodisperse Iron Oxide Nanoparticles

Keywords: sophorolipid, glyconanoparticle, nanoparticle surface functionalization, small angle neutron scattering, small angle X-ray scattering, lipid shell, iron oxide nanoparticle, core-shell nanoparticle, colloidal stability

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Introduction

Superparamagnetic iron oxide nanoparticles are used in applications such as drug delivery, MRI or hyperthermia, for which iron oxide cores smaller than 20 nm in diameter are coated with weakly adsorbed polymers (often dextran [START_REF] Hong | Synthesis, Characterization and MRI Application of Dextran-Coated Fe3O4 Magnetic Nanoparticles[END_REF][START_REF] Lacava | Magnetic Resonance of a Dextran-Coated Magnetic Fluid Intravenously Administered in Mice[END_REF][START_REF] Tassa | Dextran-Coated Iron Oxide Nanoparticles: A Versatile Platform for Targeted Molecular Imaging, Molecular Diagnostics, and Therapy[END_REF] ) or lipids. [START_REF] Boni | Design and Optimization of Lipid-Modified Poly(Amidoamine) Dendrimer Coated Iron Oxide Nanoparticles as Probes for Biomedical Applications[END_REF] However, physisorbed shells lead to low dispersant densities on the particle surface and low colloidal stability over time. Controlled grafting of chemically linked dispersants yields denser and more stable shells; therefore, such approaches have received increasing attention. [START_REF] Amstad | Stabilization and Functionalization of Iron Oxide Nanoparticles for Biomedical Applications[END_REF][START_REF] Frey | Magnetic Nanoparticles: Synthesis, Functionalization, and Applications in Bioimaging and Magnetic Energy Storage[END_REF] With improvements in the synthesis, monodisperse (SD < 5 %) iron oxide nanoparticles have been developed, [START_REF] Park | Synthesis of Monodisperse Spherical Nanocrystals[END_REF] but their hydrophobic (mostly oleic acid) shell of weakly adhering ligands is not compatible with biomedical applications. Consequently, the original ligands must be replaced by chemisorbed ligands that provide a water-soluble and sterically stabilizing shell, crucial for colloidal stability in biological fluids. Ligand exchange protocols for highly hydrated and chemically grafted ligands, mainly based on poly(ethylene glycol) (PEG), have therefore been developed. [START_REF] Lassenberger | Evaluation of High-Yield Purification Methods on Monodisperse Peg-Grafted Iron Oxide Nanoparticles[END_REF] PEG provides excellent colloidal stability and long circulation times of the particles in the body due to limited opsonization (protein binding and elimination of the particles by the reticuloendothelial system), [START_REF] Lassenberger | Superparamagnetic Nanoparticles with Controlled Shell and Size Leading to Exceptional Stealth Properties and High Relaxivities[END_REF] but PEG does not provide targeting specificity and has increasingly been claimed to be subject to antibody production. [START_REF] Yang | Anti-PEG Immunity: Emergence, Characteristics, and Unaddressed Questions[END_REF] Coating of nanoparticles with biological or biomimetic ligands could address both these drawbacks; to this end, other surface ligands are tested, including carbohydrates.

Carbohydrate-grafted nanoparticles are generally referred to as glyconanoparticles [START_REF] Bernardi | Multivalent Glycoconjugates as Anti-Pathogenic Agents[END_REF][START_REF] Marradi | Glyconanoparticles as Multifunctional and Multimodal Carbohydrate Systems[END_REF] and they are constituted by a nanoparticle core (e.g. gold or iron oxide) and a shell composed of a glycoconjugate, a term which refers to a molecule composed of a carbohydrate on one side and a binding group on the other. Since specific carbohydrates are known to selectively bind proteins, [START_REF] Lee | Carbohydrate-Protein Interactions: Basis of Glycobiology[END_REF][START_REF] Lis | Lectins: Carbohydrate-Specific Proteins That Mediate Cellular Recognition[END_REF][START_REF] Cecioni | Glycomimetics Versus Multivalent Glycoconjugates for the Design of High Affinity Lectin Ligands[END_REF] glyconanoparticles generally contain mannose, galactose, fucose or sialic acid, which are well-known saccharides targeting carbohydrate receptors on tumor cells. [START_REF] Lis | Lectins: Carbohydrate-Specific Proteins That Mediate Cellular Recognition[END_REF][START_REF] El-Boubbou | Magnetic Glyco-Nanoparticles: A Tool to Detect, Differentiate, and Unlock the Glyco-Codes of Cancer Via Magnetic Resonance Imaging[END_REF] The binding group must be selected with the type of core particle surface in mind. Typically, thiols are used to graft to gold nanoparticles while silanes are used to graft to oxide nanoparticles. [START_REF] Marradi | Glyconanoparticles as Multifunctional and Multimodal Carbohydrate Systems[END_REF][START_REF] El-Boubbou | Magnetic Glyco-Nanoparticles: A Tool to Detect, Differentiate, and Unlock the Glyco-Codes of Cancer Via Magnetic Resonance Imaging[END_REF][START_REF] Gallo | Water-Soluble Magnetic Glyconanoparticles Based on Metal-Doped Ferrites Coated with Gold: Synthesis and Characterization[END_REF] The main drawback of these fully synthetic systems is the complex synthesis of the glycoconjugate ligands, mainly due to the classically tedious sugar chemistry, and for this reason alternative routes to prepare glyconanoparticles are worth exploring.

In the past fifteen years, a number of research groups has shown the potential of using natural capping agents for metallic nanoparticles. [START_REF] Dumur | Controlled Spontaneous Generation of Gold Nanoparticles Assisted by Dual Reducing and Capping Agents[END_REF][START_REF] Duan | Green Chemistry for Nanoparticle Synthesis[END_REF] However, the field is still in its infancy due to the poor control over both particle size distribution and composition of the shell. A promising group of novel capping agents are glycoconjugates obtained through microbial synthesis. This class of molecules, in particular sophorolipids (SL), is the most studied in the field of nanoparticle stabilization. SL are bolaform, non-toxic, bio-based glycolipids produced by the yeast Starmerella bombicola and characterized by a bulky sophorose headgroup and a free carboxyl group. [START_REF] Manet | Structure of Bolaamphiphile Sophorolipid Micelles Characterized with SAXS, SANS, and MD Simulations[END_REF] SL are known to have natural targeting abilities, anti-cancer [START_REF] Chen | Production, Structure Elucidation and Anticancer Properties of Sophorolipid from Wickerhamiella Domercqiae[END_REF] and anti-bacterial [START_REF] De Rienzo | Sophorolipid Biosurfactants: Possible Uses as Antibacterial and Antibiofilm Agent[END_REF] properties. SL were previously used to stabilize metal nanoparticles (Ag, Co) [START_REF] Kasture | Multiutility Sophorolipids as Nanoparticle Capping Agents: Synthesis of Stable and Water Dispersible Co Nanoparticles[END_REF][START_REF] Singh | A Direct Method for the Preparation of Glycolipid-Metal Nanoparticle Conjugates: Sophorolipids as Reducing and Capping Agents for the Synthesis of Water Re-Dispersible Silver Nanoparticles and Their Antibacterial Activity[END_REF][START_REF] Kumar | Continuous Flow Synthesis of Functionalized Silver Nanoparticles Using Bifunctional Biosurfactants[END_REF] and iron oxide nanoparticles (IONP). [START_REF] Baccile | Sophorolipids-Functionalized Iron Oxide Nanoparticles[END_REF] The interaction between SL and the nanoparticles was attributed to the complexing of the accessible COO -group to the surface; however, low grafting densities, poor control over polydispersity, shell composition and even nanoparticle structure show that further enhancement of SL-coated iron oxide nanoparticle synthesis and structure are required for applications. Here, we propose a new approach based on the use of size-controlled monodisperse IONP and SL having the COOH group modified with nitrodopamine (NDA) via an amide bond. NDA is an anchor molecule that has been used to bind dispersants strongly to IONP. [START_REF] Amstad | Influence of Electronegative Substituents on the Binding Affinity of Catechol-Derived Anchors to Fe3O4 Nanoparticles[END_REF][START_REF] Amstad | Ultrastable Iron Oxide Nanoparticle Colloidal Suspensions Using Dispersants with Catechol-Derived Anchor Groups[END_REF] We demonstrate grafting of a monolayer SL shell by a combination of SANS and synchrotron SAXS. Furthermore, we show the resulting excellent colloidal stability of the SL-IONP in physiological buffers and protein concentrations, paired with absent cytotoxicity. This work opens opportunities for the application of glycosylated IONP obtained from natural glycoconjugates, combining strong colloidal stability and water solubility with the imaging, tracking and therapeutic abilities contributed by the IONP core.

Experimental Section

Materials. All Chemicals were purchased from Sigma-Aldrich and all solvents from Roth. Chemicals were used as received without further purification (see supporting information for details). Sophorolipids (Sopholiance, batch number: 11103A, dry content: 60 ± 6 %) are purchased from Soliance, France.

Synthesis of sophorolipids (SL).

Acidic sophorolipids have been prepared from a commercial batch of a sophorolipid mixture using alkaline hydrolysis to convert the crude lactonic/acidic mixture into a fully acidic sophorolipid compound. Extraction and purification have been performed using the method N°2 described earlier, [START_REF] Baccile | Practical Methods to Reduce Impurities for Gram-Scale Amounts of Acidic Sophorolipid Biosurfactants[END_REF] to which one should refer for a typical 1 H solution NMR fingerprint. The compound used here is majorly (> 80%) composed of the acidic subterminal C18:1-cis form that forms micelles. [START_REF] Dhasaiyan | Micelles Versus Ribbons: How Congeners Drive the Self-Assembly of Acidic Sophorolipid Biosurfactants[END_REF] Synthesis of nitrodopamide-SL (SL-NDA) ligands. 6-Nitrodopamine-hemisulfate (NDA-HSO 4 ) was synthesized according to literature with slight modifications. [START_REF] Napolitano | A New Oxidation Pathway of the Neurotoxin 6-Aminodopamine. Isolation and Characterization of a Dimer with a Tetrahydro[3,4a]Iminoethanophenoxazine Ring System[END_REF] SL-NDA was synthesized by (1-cyano-2-ethoxy-2-oxoethylidenaminooxy)dimethylamino-morpholinocarbenium hexafluorophosphate (COMU) mediated peptide-coupling reactions. [START_REF] Bixner | Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles[END_REF][START_REF] El-Faham | Comu: A Safer and More Effective Replacement for Benzotriazole-Based Uronium Coupling Reagents[END_REF] Briefly, 100 mg (0.16 mmol) of SL were pre-activated with 1.5 eq COMU and 1 eq Nmethylmorpholine in 7 mL dimethylformamide (DMF) at RT for 10 minutes. The mixture was cooled to 0 °C and a mix of 1eq NDA and 1eq N-methylmorpholine in 5 mL DMF was slowly dropped to the activated acid. The mixture reacted for 1 h at 0 °C and subsequently 3 h at RT. The solvent was evaporated and 4 mL of Milli-Q were added to the crude product. The product was transferred into butanol (BuOH) and extracted thrice with Milli-Q, once with 1.5 M HCl and finally washed with pure Milli-Q. BuOH was evaporated and the product was vacuum-dried. The coupling of SL to NDA was confirmed by FTIR and by solution [START_REF] Hong | Synthesis, Characterization and MRI Application of Dextran-Coated Fe3O4 Magnetic Nanoparticles[END_REF] H NMR (see Figure S1 for details), showing the coexisting 1:1 ratio between SL and NDA together with the downfield shift, from 3.05 ppm to 3.47 ppm, attributed to the -CH 2 in NDA and respectively in an amine and amide environment. [START_REF] Bixner | Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles[END_REF][START_REF] Kurzhals | Synthesis and Magneto-Thermal Actuation of Iron Oxide Core-Pnipam Shell Nanoparticles[END_REF] One can also observe the parallel upfield shift, from 2.30 ppm to 2.18 ppm of -CH 2 in SL for respectively an amine and an amide environment. NMR excludes the presence of unreacted free NDA, but we must acknowledge the presence of residual COMU and unreacted SL (between 10 and 20 mol% with respect to SL-NDA), which due to similar physico-chemical properties were not removed by washing the sample. However, COMU and unreacted SL do not have the affinity to the iron oxide nanoparticle surface to displace oleic acid or interfere with the ligand displacement by SL-NDA.

Synthesis of iron oxide nanoparticles (IONP).

Iron oxide NP (3-10 nm in diameter) coated with oleic acid (OA) were synthesized by thermal decomposition of iron pentacarbonyl according to a heat-up procedure originally proposed by Hyeon et al. [START_REF] Hyeon | Synthesis of Highly Crystalline and Monodisperse Maghemite Nanocrystallites without a Size-Selection Process[END_REF] that was slightly modified as described in [START_REF] Lassenberger | Evaluation of High-Yield Purification Methods on Monodisperse Peg-Grafted Iron Oxide Nanoparticles[END_REF] . Details for the molar ratios of reactants can be found in the supporting information (Table S1). Larger, 14.1 nm IONP were synthesized via a modified two-step method introduced first by Park et al. [START_REF] Park | Ultra-Large-Scale Syntheses of Monodisperse Nanocrystals[END_REF] and previously by us. [START_REF] Lassenberger | Superparamagnetic Nanoparticles with Controlled Shell and Size Leading to Exceptional Stealth Properties and High Relaxivities[END_REF] IONP cores with diameters of 3.1, 4.6 and 14.1 nm were used for functionalization with sophorolipids and further experiments.

Ligand exchange and purification. SL-IONP were synthesized according to a slightly modified method published earlier. [START_REF] Lassenberger | Evaluation of High-Yield Purification Methods on Monodisperse Peg-Grafted Iron Oxide Nanoparticles[END_REF] For 4.6 nm cores, 0.9 g of as-synthesized IONP coated with oleic acid were dispersed in 20 mL DMF. 0.183 g of SL-NDA were added and the mixture was sonicated for 28 h at slightly elevated temperature. Amounts of ligand ACS Paragon Plus Environment ACS Applied Bio Materials were adjusted for the smaller 3.1 nm IONP to account for the difference in surface area and the same surface area to ligand ratio was used. However, for the 14.1 nm cores we used a much larger excess of ligand (10x with respect to surface area), supposing that a larger excess of ligand will aid in achieving a high surface coverage. After ligand exchange, the SL-IONP were washed three times with n-hexane to remove released OA.

In a final step, the solvent was evaporated and the IONP were lyophilized. The lyophilized SL-IONP were redispersed in Milli-Q and dialysed in a 12-14 kDa MWCO dialysis bag against 5 L Milli-Q to remove excess SL-NDA ligands. Alternatively, SL-IONP were purified by repeated (5x) membrane centrifugation in 50 kDa MWCO Amicon filter units.

The purified SL-IONP were lyophilized and could be stored for more than two years as a dark-brown powder. The yield was 96 % calculated with respect to the initial amount of IONP cores. SL-IONP were analyzed by TEM, TGA, ATR-FTIR and DLS.

The samples were named according to their core diameter measured by TEM: 3.1 nm SL-IONP (diameter 3.1 nm), 4.6 nm SL-IONP (diameter 4.6 nm) and 14.1 nm SL-IONP (diameter 14.1 nm) Cell growth. U937 cells were grown under conditions reported in [START_REF] Lassenberger | Superparamagnetic Nanoparticles with Controlled Shell and Size Leading to Exceptional Stealth Properties and High Relaxivities[END_REF] .

Toxicity test. Toxicity measurements were performed with the PrestoBlue® Cell Viability assay. Briefly, 2x10 4 cells were seeded on 96-well plates using 200 µl medium per well and incubated for 16 h (each 6 repeats for sample and control). 5 µl nanoparticle dispersion (1 mg Fe/ml) were added and incubated for either 2 or 20 h. As control 5 µl Milli-Q water were added. After incubation, 20 µl PrestoBlue ® were added and plates were incubated for one hour. A Tecan infinite F200 plate reader with excitation filter 560 ± 20 nm and emission filter 595 ± 35 nm was used to read the plates. The background was determined by measuring medium with presto blue at 10 % (v/v).

Viability was calculated as:

(1) and the cells were incubated for 20 hours. The control well was incubated with 50 µL Milli-Q water. After incubation, cells were centrifuged and consequently washed three times with PBS to remove IONP that were not taken up the cells. Iron quantification was done by a modified Ferrozine test as described previously. [START_REF] Lassenberger | Superparamagnetic Nanoparticles with Controlled Shell and Size Leading to Exceptional Stealth Properties and High Relaxivities[END_REF] For each type of SL-IONP at least 5 wells were prepared in parallel and 3 independent repetitions were performed, resulting in a minimum of 9 data points for each type of SL-IONP.

Protein quantification. The Roti tm -NanoQuant protein detection assay was used for protein quantification according to the manufacturer's protocol. BSA dissolved in 50 mM

NaOH was used as a standard. sample holder, was filled with Milli-Q grade water, used as solvent, and then with the sample dispersion. To eliminate errors in the background subtraction process due to in homogeneities of the capillary walls, great care was taken to analyze both the water and sample solutions at the same position. Solvent contribution was subtracted during the data treatment. Data were corrected for the transmission of the direct beam and presented in absolute scale. The q-range calibration was made using a silver behenate standard sample ( 𝑑 𝑟𝑒𝑓 = 58.38 Å) found at on the developers' homepage. 39 The following parameters (Table 1) characterize the fitting function: (X-ray) = 40.0 x 10 -6 Å -2 and (neutron) = 6.9 x 10 -6 Å -2 refer to the X-ray and neutron 𝜌 𝑐 SLD of iron oxide respectively, for which we have used the bulk density value of 5.17 where the lower and upper limits consider plausible molecular bending and stretching; meanwhile, 9.6 < (X-ray) (10 -6 Å -2 ) < 12 and 1 < (neutron) (10 -6 Å -2 ) < 5 reasonable 𝜌 𝑠 𝜌 𝑠 identify the range for both the X-ray and neutron shell SLD values, which can vary between a highly hydrated shell and a poorly hydrated organic layer.

Small Angle Neutron Scattering (SANS). SANS was performed at the

Results and Discussion

IONP synthesis, ligand exchange and purification. Spherical, monodisperse and singlecrystalline iron oxide nanoparticles with diameters of 3.1 ± 0.3 nm ( = 8.0 %), 4.6 ± 0.3 𝜎 nm ( = 7.0 %) and 14.1 ± 0.9 nm ( = 6.9 %) were synthesized and characterized by 𝜎 𝜎 HR-and LR-TEM. Figure S2 shows TEM micrographs of as-synthesized monodisperse oleic acid-coated iron oxide cores.

The exchange of hydrophobic oleic acid for sophorolipid-nitrodopamide ligand was performed using a method established earlier [START_REF] Lassenberger | Evaluation of High-Yield Purification Methods on Monodisperse Peg-Grafted Iron Oxide Nanoparticles[END_REF] and yielded well-dispersed SL-NDA coated IONP (SL-IONP) with three different core sizes (Figure 1). Single-crystallinity of the IONP cores was revealed by HR-TEM (inset in Figure 1C and Figure S3) and the lattice spacing in the (220) direction was measured to be 0. The functionalization of the IONP with SL-NDA through ligand replacement was first evaluated using ATR-FTIR. Figure 2 shows the FTIR spectra of the compounds and products. NDA has a characteristic C-O stretch band at 1272 cm -1 , [START_REF] Gulley-Stahl | Surface Complexation of Catechol to Metal Oxides: An ATR-FTIR, Adsorption, and Dissolution Study[END_REF] which can be found in the product of the purified SL-NDA but not in pure SL. Likewise, the "sugar bands" corresponding to C-O and C-O-C stretch modes at 1021 cm -1 and 1069 cm -1 , [START_REF] Valotteau | Biocidal Properties of a Glycosylated Surface: Sophorolipids on Au(111)[END_REF] respectively, from the sophorolipid are also strong in the SL-NDA product. Finally, the bands of the amide bond formed between SL and NDA are clearly visible in SL-NDA.

Figure 2 shows that two characteristic bands of oleic acid, the C=O stretch at 1707 cm -1 (which is slightly higher than for sophorolipid) and the out-of-plane O-H stretch at 963 cm -1 are absent or insignificant compared to the characteristic bands of the sophorolipid and NDA. [START_REF] Bixner | Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles[END_REF] In summary, the ATR-FTIR results strongly support successful ligand replacement of the oleic acid by SL-NDA to form iron oxide nanoparticles with a shell of sophorolipid, strongly linked by nitrodopamide. The average grafting density of SL-NDA ligand irreversibly bound to the Fe-ions at the IONP surface was evaluated after purification by TGA. Typical TGA weight loss profiles for 3.1 nm SL-IONP, 4.6 nm SL-IONP and 14.1 nm SL-IONP are shown in Figure S4. The total organic content (TOC) was determined as the fraction of mass loss up to 650 °C. If all excess ligand is removed, the TOC can be converted into the dispersant grafting density using the known molecular weight of SL-NDA, the defined average iron oxide core area determined by TEM and a known iron oxide core density of 5.17 g/cm [START_REF] Tassa | Dextran-Coated Iron Oxide Nanoparticles: A Versatile Platform for Targeted Molecular Imaging, Molecular Diagnostics, and Therapy[END_REF] . We thus assume for this calculation that all oleic acid was replaced by SL-NDA during the rigorous ligand replacement and purification. Earlier studies have shown that ligand replacement of OA by hydrophobic ligands is challenging and can leave significant residues within the nanoparticle shell. [START_REF] Bixner | Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles[END_REF][START_REF] Shirmardi Shaghasemi | Host-Guest Driven Ligand Replacement on Monodisperse Inorganic Nanoparticles[END_REF] If this is the case, the amount of SL-NDA grafted to the IONP would be overestimated. However, we have previously investigated the ligand replacement and purification protocol used here and shown that the amount of residual OA is below the detection limit by ATR-FTIR. As discussed above, the ATR-FTIR data shown in Figure 2 supports this finding. Additionally, the calculation of the grafting density based on the TGA data can yield a higher value than the actual grafting density if there is also free ligand present in a sample. We therefore list the average number of ligands (

) per nm 2 in Table 2 calculated in the same way for differently sized IONP purified 𝑛 𝑙𝑖𝑔𝑎𝑛𝑑𝑠 by dialysis or membrane centrifugation (Amicon 50 kDa MWCO) to take into account the possible presence of free ligand. The limiting factor for ligand adsorption to the IONP surface is given by the number of surface iron sites (3.5 -5.9 depending on crystal plane) [START_REF] Santos-Carballal | A Dft Study of the Structures, Stabilities and Redox Behaviour of the Major Surfaces of Magnetite Fe3O4[END_REF] or the spatial requirements (footprint) of the ligand. The hydrated sugar headgroup and the unsaturated fatty acid structure of SL could sterically hinder achieving the maximum grafting density of NDA, but this steric blocking is reduced by the high curvature of the IONP that provides much larger volume for the headgroup than for the binding group. The grafting density of the deacetylated acidic form of sophorolipids (the same used in this work) varies according to the system under study; one finds between 2 and 3 molecules/nm 2 on a flat gold surface (evaluated by X-ray photoelectron spectroscopy and quartz crystal microbalance with dissipation monitoring), [START_REF] Valotteau | Antibacterial Properties of Sophorolipid-Modified Gold Surfaces against Gram Positive and Gram Negative Pathogens[END_REF] 0.96 molecules/nm 2 at the air/water interface (surface tension) [START_REF] Chen | Adsorption of Sophorolipid Biosurfactants on Their Own and Mixed with Sodium Dodecyl Benzene Sulfonate, at the Air/Water Interface[END_REF] and between 0.5 and 1.0 molecules/nm 2 in micelles respectively at the micelle/water and alkyl/sophorose interface (evaluated by SAXS). [START_REF] Manet | Structure of Bolaamphiphile Sophorolipid Micelles Characterized with SAXS, SANS, and MD Simulations[END_REF] The SL-IONP with a diameter of 4.6 nm purified by Amicon have a ligand density of 3.3 molecules/nm 2 , which is within the range of plausible grafting densities taking both the density of grafting sites and steric blocking during grafting into account. The other systems display values of SL-NDA/nm 2 that are higher than the number of possible grafting sites on the IONP surface, which sets an absolute upper bound on the grafting density. Hence, the observed values above 5 molecules/nm 2 (Table 2) must be due to excess ligand that is not grafted to the IONP surface. The excess ligand could not be removed with Amicon filters and dialysis could also not reduce the organic content of the samples. It has been reported that sophorolipids form micellar structures in water, [START_REF] Manet | Structure of Bolaamphiphile Sophorolipid Micelles Characterized with SAXS, SANS, and MD Simulations[END_REF] and cryo-TEM micrographs in Figure 3A and Figure S5 demonstrate that also SL-NDA self-assembles into both spherical and filamentous structures. Since it is not a goal of this work to describe the self-assembly properties of SL-NDA in water, we prefer not to go into descriptive details; we will simply refer to a general micellar and filamentous self-assembled phase of SL-NDA in coexistence with SL-IONP. This feature suggests why SL-NDA could not be fully removed by dialysis or by membrane centrifugation: the cut-off pore size of the membranes is larger than a single SL-NDA molecule, but smaller than their self-assembled phase. Dialysis should in principle allow for removal of excess lipid from the sample, but in practice, selfaggregating molecules with a low critical aggregation constant or very slow kinetics of desorption (low ) will make dialysis very inefficient; this is apparently the case for 𝑘 𝑜𝑓𝑓 dialysis of SL-NDA forming large and stable structures. An attempt to improve the dialysis with salt (NaCl) by shifting the critical micelle concentration failed for this system since SL-NDA micelles are insensitive to salt (cf. SANS data below). Interestingly, the small core sample (4.6 nm) had much less excess ligand after purification than the large core sample. This could tentatively be explained by that for the larger cores a larger excess of SL-NDA to IONP surface area was used, which favors growth of more and larger micelles during grafting or during resuspension. The 4.6 nm SL-grafted IONP presumably had a lower amount of excess SL-NDA in solution after grafting and consequently a negligible excess of SL-NDA in the dispersion after purification. This interpretation of the purification and TGA data is supported by cryo-TEM (Figure 3C this easily leads to inefficient grafting and sub-monolayer dispersant grafting density on the particle surface. Grafting with large SL-NDA excess is therefore recommended for applications where excess micelles can be tolerated but particle colloidal stability is of paramount importance.

Characterization of the SL-NDA ligand shell with SANS and SAXS. It is typically assumed that the high colloidal stability of coated nanoparticles is explained by the presence of a single layer of ligand; this argument may also hold for the SL-IONP presented here. However, most classical techniques, like DLS or TEM, on which this assumption is based, are generally not providing in situ or detailed enough data to quantitatively investigate the presence, structure and properties of the shell in support of this hypothesis. SAXS, which is sometimes used for this purpose, is mostly not suitable for hybrid inorganic-organic nanoparticles, because the contrast between the solvent and the electron-rich inorganic core generally masks the signal of the shell resulting from the poor contrast between the solvent and the shell. The combined use of X-ray and neutron scattering is the only method to probe the structural characteristics such as the thickness Page 30 of 62 ACS Paragon Plus Environment ACS Applied Bio Materials of the nanoparticle organic shell. In fact, neutrons, being scattered by the atom nuclei, are less sensitive to atoms with high atomic number. We therefore combined SAXS and SANS as a reliable method to estimate the extension of the SL-NDA shell for SL-IONP purified by Amicon filtration, that had a low excess of ligand in micelles.

SAXS was used to determine and confirm the size of the IONP cores. Under X-ray irradiation, the inorganic core of SL-IONP nanoparticles has a very high contrast (𝜌 𝑠𝑜𝑙𝑣 -= -30.60 x 10 -6 Å -2 , Table 3) if compared to the shell-solvent ( = -0.57 x 10 -6 𝜌 𝑐 𝜌 𝑠𝑜𝑙𝑣 -𝜌 𝑠 Å -2 , Table 3); for this reason, SAXS only provides structural information on the nanoparticle cores. Figure 4A (green circles) shows the SAXS profile for 4.6 nm SL-IONP.

The best fit using a core-shell sphere form factor can be obtained using an average nanoparticle core diameter of 4.8 ± 0.4 nm and a null value for the shell thickness. This is in very good agreement with the diameter obtained by TEM (4.6 ± 0.3 nm) within the experimental errors. The corresponding SANS pattern (Figure 4A, blue circles) is shifted towards the low-region, which signifies sensitivity to the larger size resulting from the 𝑞 much higher contrast of neutrons to the lipid shell.

The SANS pattern can be modeled using an imposed (from SAXS data) core diameter of = 4.8 ± 0.4 nm and a shell thickness of = 2.5 ± 0.2 nm obtained by fitting a core-𝑑 𝑡 shell model to the scattering data. This simple model assumes a uniform scattering length density throughout the shell, which is clearly a simplification, but it can be used to estimate the shell thickness by fitting the shift of the first minimum of the form factor. The calculated length of SL, considering the 120° angle due to the mono-unsaturation, can be estimated to 2.6 nm, where 1.6 nm are attributed to the fatty acid [START_REF] Baccile | Ph-Driven Self-Assembly of Acidic Microbial Glycolipids[END_REF] and 1 nm to sophorose, in analogy to the size of maltose, a common disaccharide. [START_REF] Abel | Molecular Simulations of Dodecyl-Β-Maltoside Micelles in Water: Influence of the Headgroup Conformation and Force Field Parameters[END_REF] The size of NDA is estimated to about 1 nm. [START_REF] Bergin | Structure of the Pyrocatecholamines. Ii. Crystal Structure of Dopamine Hydrochloride[END_REF] Under these conditions, the maximum expected size for SL-NDA is about 3.6 nm. The modeled thickness of = 2.5 ± 0.2 nm is shorter than the maximum 𝑡 monolayer thickness and demonstrates that the shell of monodisperse SL-IONP is comprised of a single layer of SL-NDA of less than maximum density. From the fit, one can also evaluate an average shell scattering length density of = 3.39 x 10 -6 10 -6 Å -2 , a 𝜌 𝑠 value which is reasonable for a hydrated (in D 2 O) organic lipid layer. [START_REF] Smith | Neutron Reflectometry of Supported Hybrid Bilayers with Inserted Peptide[END_REF] The lower density or slightly lower thickness that is observed can be explained in several ways. One can, e.g., consider that the shell could contain other smaller ligands than SL-NDA, such as palmityl-NDA ligand replacement of OA. [START_REF] Bixner | Complete Exchange of the Hydrophobic Dispersant Shell on Monodisperse Superparamagnetic Iron Oxide Nanoparticles[END_REF] Furthermore, our original attempts to replace OA with SL failed to produce water-soluble particles, strongly suggesting that replacement of OA will be driven by SL-NDA. Thus, although our data do not allow its exclusion, we do not expect significant amounts of unmodified SL on the IONP.

A more plausible explanation for the thin shell is that the SL-NDA is grafted on a highly curved surface, which provides a rapidly increasing conical volume to the SL-NDA even at the highest grafting density. [START_REF] Reimhult | Design Principles for Thermoresponsive Core-Shell Nanoparticles -Controlling Thermal Transitions by Brush Morphology[END_REF] This allows for a large tilt or bending of the molecules, i.e. a lower effective shell thickness. The extended length of SL is calculated according to the classical Tanford formula. However, SL is known to adopt a bent configuration, which yields an effectively thinner layer than theoretically calculated. For instance, XPS has shown that a single self-assembled monolayer of cysteamine-modified SL grafted onto flat gold has a thickness of only 3.0 ± 0.2 nm, [START_REF] Valotteau | Biocidal Properties of a Glycosylated Surface: Sophorolipids on Au(111)[END_REF] while small-angle X-ray and neutron scattering measurements showed that the total radius of an acidic SL micelle is generally below 4 nm, i.e, approximately the size of a single SL molecule. [START_REF] Manet | Structure of Bolaamphiphile Sophorolipid Micelles Characterized with SAXS, SANS, and MD Simulations[END_REF][START_REF] Penfold | Solution Self-Assembly of the Sophorolipid Biosurfactant and Its Mixture with Anionic Surfactant Sodium Dodecyl Benzene Sulfonate[END_REF] A layer grafted on a highly curved NP would be expected to yield a thickness in between these estimates.

Finally, one should not exclude that the simplification of assuming a uniform scattering length density, which could be invalidated by the conical ligand volume and the highly hydrated headgroup, would also lead to a fit predicting an effectively thinner shell.

Whichever the dominant of the two latter explanations, the SAXS/SANS data demonstrate a single thin SL-NDA layer serving as the stabilizing shell on the IONP. Similar results are obtained for the smaller 3.1 nm SL-IONP (Figure 4B). The SANS pattern can be modelled with a fixed (from SAXS data) core diameter, = 3.0 ± 0.2 nm 𝑑 and a fitted shell thickness of = 2.2 ± 0.2 nm. These data are summarized in which also contains the solvent-core and solvent-shell scattering length density contrasts fitted from the SANS data: = -0.57 x 10 -6 Å -2 while is in the order of 3.0 𝜌 𝑠𝑜𝑙𝑣 -𝜌 𝑐 𝜌 𝑠𝑜𝑙𝑣 -𝜌 𝑠

x 10 -6 Å -2 . This demonstrates that the shell has higher contrast than the iron oxide core, and therefore dominates the scattering signal of the core-shell particle. The absolute value of the shell scattering length density for 3.1 nm SL-IONP is = 3.45 x 10 -6 10 -6 Å -2 𝜌 𝑠 and in good agreement with what is found for the 4.6 nm core SL-IONP. The scattering curve of the 14.1 nm SL-IONP sample was radically different to those of the dispersions of the two smaller SL-grafted IONP and is shown in Figure 5. The typical SANS spectrum for 14.1 nm SL-IONP in D 2 O (blue filled circles) is relatively featureless in D 2 O, but it shows strong scattering with a characteristic slope in the low-region that 𝑞 is not present in the SANS spectra of the smaller SL-grafted IONP. This additional feature can be explained by comparing the data to the SANS spectrum of the pure SL-NDA ligand solution (Figure 5, grey filled circles), which nicely matches the spectrum of the 14.1 nm SL-IONP sample. Thus, in good agreement with the TGA data presented in Figure S4 and Table 2, the SANS signal of the 14.1 nm SL-IONP dispersion is dominated by SL-NDA in the form of filamentous structures instead of the core-shell particles. The higher contrast of SL-NDA to D 2 O than of iron oxide to D 2 O further contributes to the dominance of scattering from the SL-NDA micelles. These micelles were also prevalent in cryo-TEM images of the 14.1 nm SL-IONP sample (see Figure 3B). Nonetheless, SL-NDA is soluble in perdeuterated methanol, as shown by the corresponding poor SANS signal (grey empty circles) in Figure 5 5. As expected, the SANS pattern of 14.1 nm SL-IONP (blue empty circles) in MeOD-d4 loses the SL-NDA scattering profile and it rather presents the typical feature of spherical objects. A shell-free 14.1 nm diameter IONP nanoparticle would be expected to have the first minimum of the form factor around = 0.4 nm -1 , whereas the 𝑞 minimum of the oscillation of the form factor measured for the 14.1 nm SL-IONP falls between 0.2 nm -1 < < 0.3 nm -1 , suggesting a spherical object sized between 20 and 30 𝑞 nm. This is largely in agreement to what would be expected for a 14.1 nm iron oxide core, stabilized by a single SL-NDA layer even if the conditions of analysis (excess of SL-NDA, methanol) and likely presence of aggregates do not allow the quantification of the thickness of the SL-NDA layer. Colloidal stability and long-term stability. Removal of all monomeric free SL-NDA, is a good test of the colloidal stability of SL-NDA-grafted IONP. However, a biological environment is much more challenging for IONP colloidal stability, due to the higher concentration of biological colloids, displaying a larger variety of attractive interactions and leading to nanoparticle aggregation. [START_REF] Amstad | Stabilization and Functionalization of Iron Oxide Nanoparticles for Biomedical Applications[END_REF] Thus, colloidal stability of nanoparticles meant to perform functions in biotechnological or medical applications should be tested under conditions where they are exposed to full physiological ionic strength as well as to concentrations of protein similar to those that could be encountered during application.

Therefore, we suspended the SL-IONP in 10 % fetal calf serum (FCS), which has a lower concentration than full serum, but at which the colloidal stability can be monitored by DLS.

10 % serum also corresponds to the typical additive to cell culture media. We performed the measurements while heating from 20 °C to 70 °C and back. These conditions are known to weaken the hydration of the nanoparticle shell [START_REF] Amstad | Ultrastable Iron Oxide Nanoparticle Colloidal Suspensions Using Dispersants with Catechol-Derived Anchor Groups[END_REF] and thereby reduce the colloidal stability and decrease the ability to suppress adsorption of serum protein. Adsorption of denatured proteins leads to irreversible aggregation and precipitation of insufficiently stabilized nanoparticles [START_REF] Zirbs | Melt-Grafting for the Synthesis of Core-Shell Nanoparticles with Ultra-High Dispersant Density[END_REF] . Figure 6 shows the evolution of the volume weighted hydrodynamic diameter of 4.6 nm SL-IONP in water with 10 % FCS with temperature. 𝐷 𝐻 Volume weighed of 4.6 nm SL-IONP in water is shown in Figure S8A. The 𝐷 𝐻 hydrodynamic diameter of 4.6 nm SL-IONP was measured to be around 12 nm, which was stable after more than 1.5 years in storage. The SL-IONP with 3.1 nm and 14.1 nm core sizes appeared equally stable in dispersion over the same time period. However, the stability could not be quantitatively confirmed by the hydrodynamic diameter, as there were excess SL-NDA in these samples. All investigated SL-IONP have small diameters in the superparamagnetic range and they are stabilized predominantly by steric and hydration forces from the hydrophilic headgroup region of the sophorolipid. It is advantageous for many applications to have a thin stabilizing shell of this kind to reduce the overall hydrodynamic size. However, we note that the strength of the long-range attractive van der Waals forces increases if the inorganic nanoparticle core is made larger. It is likely that there is a maximum core size for which an SL-NDA shell can provide sufficient stabilization against aggregation by dipolar interactions.

The hydrodynamic diameter of the 4.6 nm SL-IONP is in reasonable agreement with the size of the core-shell nanoparticle determined by SANS, 9.2 nm, which might underestimate the steric or hydrodynamic size due to the fitting of a homogeneous shell.

The DLS result is also in good agreement with a theoretical size of a core-shell IONP calculated from the diameter of the core measured by TEM (4.6 nm) and the length of a SL-NDA molecule (3 nm), which implies a total steric diameter of 10.6 nm diameter. Thus, both DLS and SANS data strongly suggest a monolayer of SL-NDA ligands on the NP surface. The size distribution measured for the monodisperse iron oxide nanoparticles grafted with SL-NDA is narrower and with a smaller than the SL-coated iron oxide 𝐷 𝐻 nanoparticles reported in our earlier work. [START_REF] Baccile | Sophorolipids-Functionalized Iron Oxide Nanoparticles[END_REF] When heating up the SL-IONP in FCS, we observed a size distribution with the main peak corresponding to the abundant serum albumin, with a tail towards larger sizes contributed by the SL-IONP. Upon heating, the fraction of small objects (serum albumin) in the size distribution decreased and the volume fraction of larger objects (nanoparticles) increased. This results from partial denaturation and aggregation of serum proteins. This trend becomes even more obvious in Figure 6B where a temperature of 70 °C was held for 8 minutes to allow for more equilibration of the sample. Here, the apparent volume fraction of nanoparticles is even larger, which could be due to precipitation of serum protein. Importantly, no aggregation and precipitation of SL-IONP was observed at any temperature, with or without exposure to denatured serum protein. This can also be observed from the intensity weighted size distributions for the same temperature cycling experiment (Figure S11). Figure S9 shows a photograph of SL-IONP after temperature cycling. Aggregation of SL-IONP could not be induced by heating the samples in FCS at 70 °C for 3 h (Figure S10). Similar to the observations during temperature cycling, only a small shift in size is observed after heating for 3 h and a very small peak in the intensity weighted appears at large sizes, indicating the aggregation of the protein that 𝐷 𝐻 precipitated after 3 h heating (Figure S12). These data, showing the excellent stability of SL-IONP with temperature, can be explained by the small influence that temperature has on the dehydration of the carbohydrate moiety of sugar-based capping agents. Sugarbased dispersants are both hydrogen-bond donors and acceptors, which allows for a bulk water-like hydrogen-bonding network and thereby low sensitivity to dehydration upon increasing temperature.

The excellent colloidal stability of the SL-IONP nanoparticles is further demonstrated by additional experiments performed in the presence of 1 M NaCl in D 2 O. The high ionic strength of 1 M NaCl was chosen for the ability of the NaCl ions to screen and reduce double layer repulsion, thereby increasing the propensity of nanoparticles to aggregate, as well as the ability of the mild kosmotropes to reduce hydration and thereby decrease stabilization due to steric and hydration forces. The data show that the SANS profiles of neither sample change when the ionic strength of the solvent is increased. The absence of change is true in both the mid/high-region 𝑞 characteristic of the core-shell structure and in the low-region characteristic of 𝑞 aggregation. This indicates that the SL-NDA shell has neither been removed upon salt addition, nor has its structure been modified. This contrasts to previous findings for sophorolipid coated nanoparticles, where aggregation was promoted by the addition of salt. [START_REF] Baccile | Sophorolipids-Functionalized Iron Oxide Nanoparticles[END_REF] The improved stability of our novel SL-IONP can be attributed to the NDA anchor chemistry that irreversibly grafts the SL coating densely to the cores. Furthermore, the SANS profiles do not show any sign of particle aggregation, since a structure factor corresponding to particle aggregation would appear in the low -range. There is also no 𝑞 optically visible increase in scattering nor does precipitation take place, which supports the SANS observation of excellent colloidal stability. This is in full agreement with the DLS data that showed retained size and no aggregation and precipitation (cf. Figure 6). The SANS measurements also show that micelles of excess ligand in the 3.1 nm SL-IONP sample were not altered by that addition of salt (no change in the slope at low ), which 𝑞 explains why dialysis at high ionic strength could not remove the excess ligand.

In-vitro cellular uptake and cytotoxicity of SL-IONP. To prove the applicability of SL-IONP in the biomedical field, we conducted cellular uptake and cytotoxicity tests on two different cell lines: U937 monocytes which are part of the reticuloendothelial system and responsible for clearance of pathogens and foreign bodies from the blood and MCF7, a human breast cancer cell line.

Differentiated monocytes, macrophages, are the cells in the body that are most exposed to toxins and foreign bodies. The response of these cells to exposure of SL-IONP is thus of highest relevance. If they detect and scavenge nanoparticles, the nanoparticles will be of limited use in applications that require circulation and/or targeting. It is, to the best of our knowledge, the first time that cellular uptake and toxicity are studied for sophorolipid coated core-shell nanoparticles. Figure 8 shows the results of the cellular uptake and cytotoxicity tests for 4.6 nm SL-IONP with U937 and MCF7 cells. SL-IONP show very low non-specific uptake by both monocytes and cancer cells. A slight trend to higher uptake of breast cancer cells over the phagocytic monocytes could not be statistically verified.

The low uptake is in the same order as previously shown for stealth poly(ethylene glycol)grafted IONP [START_REF] Lassenberger | Superparamagnetic Nanoparticles with Controlled Shell and Size Leading to Exceptional Stealth Properties and High Relaxivities[END_REF] and can be traced back to the good colloidal stability of the core-shell SL-IONP and their resistance against aggregation in presence of proteins and salts (cf.

Figure 6 and7).

Both sophorolipids and iron oxide nanoparticles have individually shown negligible toxicity at relevant concentrations to various cell lines. [START_REF] Ikeda | Toxicological Studies on Sophorolipid Derivatives. (I). Acute Toxicity, Eye Irritation, Primary Skin Irritation, Skin Sensitization, Phototoxicity, Photosensitization, Mutagenicity of Polyoxypropylene (12) [(2'-0-Beta-D-Glucopyranosyl-Beta-D-Glucopyranosyl)Oxy-] Fatty Acid Ester[END_REF][START_REF] Gal | Interaction of Size-Tailored PEGylated Iron Oxide Nanoparticles with Lipid Membranes and Cells[END_REF] Figure 8B shows that also SL- Design principles for using SL-NDA to stabilize IONP for applications. In summary, a range of challenging conditions for colloidal stability relevant for applications were tested; all results were consistent with excellent stability of the grafted SL-NDA shell translating to equally excellent colloidal stability. The low size dispersity, high grafting density and colloidal stability of the SL-IONP system developed here are comparable to those of synthetic glyconanoparticles [START_REF] Marradi | Glyconanoparticles as Multifunctional and Multimodal Carbohydrate Systems[END_REF][START_REF] El-Boubbou | Magnetic Glyco-Nanoparticles: A Tool to Detect, Differentiate, and Unlock the Glyco-Codes of Cancer Via Magnetic Resonance Imaging[END_REF][START_REF] Gallo | Water-Soluble Magnetic Glyconanoparticles Based on Metal-Doped Ferrites Coated with Gold: Synthesis and Characterization[END_REF][START_REF] Varela-Aramburu | Straightforward and Robust Synthesis of Monodisperse Surface-Functionalized Gold Nanoclusters[END_REF][START_REF] Reynolds | Influence of Ligand Presentation Density on the Molecular Recognition of Mannose-Functionalised Glyconanoparticles by Bacterial Lectin Bc2l-A[END_REF] rather than sophorolipid-capped nanoparticles. 23- 26 Our results demonstrate that the densely grafted SL-NDA shell provides a stable repulsive potential preventing both mutual aggregation and protein adsorption under highly challenging conditions (1 M NaCl, 70 °C with and without FCS). The colloidal stability is not adversely affected by temperature and kosmotrope salts that often have a destabilizing effect on polymer coated-core-shell nanoparticles. This is reached by the irreversible grafting of the SL ligand to the core in contrast to pure self-assembly and/or complexation. The expected main contribution to the repulsive interaction of the shell is the high and stable hydration of the lipid head-groups that is apparently strong enough to withstand weakening in the coordination of associated water under relevant challenging environmental conditions. This fact is confirmed by the literature on the micellization properties of sugar-based amphiphiles: the strength between the hydrogen bonding between the hydroxyl groups of the sugar unit and water is stronger than between ethylene oxide and water. [START_REF] Ruiz | Sugar-Based Surfactants; Fundamentals and Applications[END_REF] It is worth noting that stabilization through a grafted lipid is fundamentally different to the more commonly applied approach of a high-flexible polymer; the low thickness 𝑀𝑤 added by a lipid monolayer and its insignificant molecular flexibility makes it possible to design such shells much more compact and structurally precise than using solvated polymer. At the same time, it is impressive that equally high colloidal stability, as demonstrated here, can be obtained. The hydrophobic spacer part of the lipid shell is important to reduce core-core van-der-Waals attraction and likely cannot be made too thin without compromising colloidal stability. However, with a hydrophobic interior of the shell, a prerequisite for stability in biofluids is that the lipid shell (the lipid headgroup region) is dense enough to prevent hydrophobic molecules, such as protein denatured by temperature, to adsorb to shell defects exposing the alkyl part of the lipids. We achieved this by the stable NDA-coupling and efficient ligand exchange protocol used to graft the SL-NDA shell. As expected, in the absence of aggregates, the SL-IONP showed only weak interaction with cells in-vitro with negligible uptake and no resulting cytotoxicity, thus making these systems promising candidates for the development of IONP-based biomedical applications. These, so-called stealth, nanoparticles can be further functionalized or make use of specific interactions of the exposed saccharide motif to add targeting capability, for which structural and colloidal stability, as well as suppression of non-specific biomolecular interactions, is a prerequisite.

Conclusion

We have synthesized monodisperse, biocompatible, sophorolipid-grafted core-shell iron oxide nanoparticles with excellent colloidal stability in demanding application environments mimicking the conditions of biological fluids. As-synthesized, oleic acidcoated IONP with precisely tunable sizes and narrow size distributions were successfully grafted with a nitrodopamide-modified sophorolipid ligand by replacement of the oleic acid. Analysis of TGA and cryo-TEM highlighted the challenge of removing excess ligand as sophorolipid forms very stable aggregates of similar size as the grafted nanoparticles and with the same physico-chemical characteristics. Cryo-TEM revealed the coexistence of individual, monodisperse, SL-grafted IONP with large and stable SL-NDA aggregates formed by excess ligand that could not be completely removed by excessive purification.

However, also close to pure SL-grafted IONP product was obtained for 4.6 nm IONP cores. The core-shell structure of SL-IONP was analyzed by SAXS and SANS. The resulting data were successfully fitted with a core-shell model. SANS revealed the thickness of the shell, which was found to be in the order of 2.5 nm, in good agreement with a shell composed of a monolayer of SL-NDA grafted to a highly curved surface.

The stable, grafted core-shell architecture presenting the equivalent of a dense sophorolipid membrane at the nanoparticle surface was shown to translate into excellent colloidal stability under demanding conditions such as in dense protein dispersions (serum) at high temperature and at high ionic strength, as shown by DLS and SANS. The resulting colloidally stable and biocompatible SL-IONP are promising materials in the biomedical field through their combination of IONP imaging and therapeutic properties with natural presentation of functional glycosylation, whereas carbohydrate-rich

3 𝜔 = 5 .

 35 Institut Laue-Langevin (ILL, Grenoble, France) on D16 and D33 beamlines. The spectrometer configurations were adjusted as follows. D16 beamline (3.5 . 10 -2 Å -1 < < 0.5 Å -1 ): neutron 𝑞 wavelength, , sample-to-detector distance = 955 mm, sample and detector 𝜆 = 4.5 Å rotation angles: and , acquisition time = 60 min. D33 beamline (5.0 . 10 -5°2𝜃 = 11°Å -1 < < 0.3 Å -1 ): neutron wavelengths: and sample-to-detector 𝑞 𝜆 1 = 4.6 Å 𝜆 2 = 13.0 Å distances = 2 m, 10 m, acquisition time = 10 min (in D 2 O), 45 min (in MeOD-d4). For both spectrometers: neutron absorber: Boron Carbide (B4C), thickness of quartz Hellma cells: 1 mm, temperature (controlled): , background: 99.9 % D 2 O. Direct beam, empty 𝑇 = 25°𝐶 cell and H 2 O were also recorded for both spectrometers. The background sample (D 2 O) signal was subtracted from the experimental data. is defined as where 𝑞 (4𝜋 𝜆)𝑠𝑖𝑛𝜗/2 𝜗 is the scattering angle between the incident and the scattered neutron beams. Data treatment was done with the home-made software package provided at the beamline. Direct determination of the number of neutrons in the incident beam and the detector cell solid angle allowed obtaining absolute values of the scattering intensity. The acquired 2-D raw data were corrected for the scattering of the ambient background and the empty Page 16 of 62 ACS Paragon Plus Environment ACS Applied Bio Materials cell. Further, the data were normalized by the neutron flux on the samples to yield an absolute scale (cross section per unit volume). The data were radially averaged to yield the 1-D intensity distribution . 𝐼(𝑞) Fit of small angle scattering data (SAXS, SANS). All data presented were fitted using a classical core-shell sphere form factor model (assuming a unitary structure factor in the analyzed range of -values), 38 using the SasView 3.1.2 software (CoreShellModel) 𝑞 available free of charge on the developers' website. 39 In the model, we consider the core to be composed of iron oxide and the shell of a homogeneous SL-NDA layer of variable thickness. One should be aware that this is a strong approximation, because SL-NDA could be described by at least three different regions of inequivalent densities: sophorose, oleic acid and NDA. Nonetheless, the goal of the fitting analysis in this work is not to precisely describe the morphology of the of the nanoparticle shell, but to demonstrate that SL-IONP have a shell with a thickness compatible with a monolayer of SL-NDA; the homogeneous core-shell model provides an adequate model with a minimum number of fitting variables to determine the presence and thickness of a reasonably homogeneous shell. All theoretical and technical details of both the model and fitting function can be Page 17 of 62 ACS Paragon Plus Environment ACS Applied Bio Materials

  g.cm -1 . Polydispersity was allowed to vary between 0.1 and 0.15 and the volume fraction was set to 0.4 % for samples 3.1 nm SL-IONP and 4.6 nm SL-IONP and to 0.1 % for sample 14.1 nm SL-IONP, the smaller value coming from the larger amount of SL-NDA in the 14.1 nm SL-IONP sample (please refer to main text for more details). In the final fitting procedure, and are the only structural variable parameters, while the 𝑡 𝜌 𝑠 background level is set as variable mainly to adjust the quality of the final fit. The typical size and composition of SL-NDA also imposes several constraints on the effective and 𝑡 values. One can reasonably consider 2.0 < (nm) < 3.5 for a single SL-NDA layer, 𝜌 𝑠 𝑡

  29 nm. The electron diffraction pattern (inset Figure 1B) shows the high crystallinity of the IONP. The determined ratios of d-spacings show good agreement with the JCPDS database values given for Page 20 of 62 ACS Paragon Plus Environment ACS Applied Bio Materials maghemite or magnetite.[START_REF] Finger | High-Pressure Crystal Chemistry of Spinel (MgAl2O4) and Magnetite (Fe3O4): Comparisons with Silicate Spinels[END_REF] Single-crystalline iron oxide nanoparticles (magnetite and maghemite) in this size-range are known to be superparamagnetic, thereby possessing attractive properties for biomedical imaging and drug delivery.

Figure 1 .

 1 Figure 1. TEM micrographs of three sizes of SL-IONP of sizes A) 3.1 ± 0.3 nm, B) 4.6 ±

Figure 2

 2 Figure 2 ATR-FTIR spectra of as-synthesized IONP (oleic acid capped, green),

Figures

  Figures 3B-C and FiguresS6 and S7show cryo-TEM images of 14.1 and 4.6 nm SL-

Figure 3 .

 3 Figure 3. Cryo-TEM micrographs in H 2 O of A) SL-NDA, B) 14.1 nm SL-IONP and C) 4.6

  and FigureS7), in which many stabilized nanoparticles are observed, but only a limited amount of SL-NDA. With the difficulty to purify nanoparticles from SL-NDA micelles and filaments, one can try to minimize the excess of SL-NDA during grafting to suppress micelle formation. However,

  residual catalyst (COMU), oleic acid or unreacted NDA or SL. The combination of TGA, FTIR and NMR data make this hypothesis unlikely. COMU, which was observed as residue in the SL-NDA batches used for grafting the NPs, has very low affinity for the iron oxide surface. All techniques employed show no evidence of residual OA, while[START_REF] Hong | Synthesis, Characterization and MRI Application of Dextran-Coated Fe3O4 Magnetic Nanoparticles[END_REF] H NMR shows that the SL-NDA does not contain free NDA. A residual amount of unreacted SL (10-20 mol% with respect to SL-NDA) is present. The carboxyl endgroup of SL has high affinity to the IONP, but NDA functionalized ligands possess much higher affinity and outcompete carboxyl anchored ligands on the surface. This is demonstrated by FTIR showing the successful ligand replacement of OA by SL-NDA and previous studies of e.g.

Figure 4 .

 4 Figure 4. A) SANS (blue) and SAXS (green) profiles for 4.6 nm SL-IONP in D 2 O. The red

Figure 5 .

 5 Figure 5. SANS data recorded for 14.1 nm SL-IONP in D 2 O (blue filled circles) and MeOD-

  This is attributed to the novel synthesis protocol with improved ligand and anchor chemistry for grafting to monodisperse iron oxide core particles. Volume weighted size distributions of 10 % FCS in Milli-Q without 𝐷 𝐻 nanoparticles measured at 20 °C and 70 °C are shown in Figure S8B. The size of serum proteins was measured to be 5 nm at 20 °C. A size shift to 8 nm was observed at elevated temperatures.

Figure 6 .

 6 Figure 6. Volume weighted hydrodynamic diameters of 4.6 nm SL-IONP dispersed in 𝐷 𝐻

Figure 7

 7 presents the typical SANS spectra for the 3.1 nm and 4.6 nm SL-IONP in 1 M NaCl D 2 O in comparison with SL-IONP in pure D 2 O.

Figure 7 .

 7 Figure 7. SANS data recorded for 3.1 nm and 4.6 nm SL-IONP in D 2 O (red and grey

grafted 4 .

 4 6 nm IONP do not affect the viability of the two tested cell lines. The results suggest an excellent biocompatibility of the SL-IONP.

Figure 8 .

 8 Figure 8. A) Cellular uptake of 4.6 nm SL-IONP for human monocytes (U937) and human

SL-IONP uptake by cells and iron quantification. For

	Page 11 of 62		ACS Applied Bio Materials
			𝑿 𝑿 𝑪 * 𝟏𝟎𝟎 %
	with	𝑋	the average value determined for cells incubated with SL-IONP and	𝑋 𝑐	the
	average value measured for control cells.
			uptake experiments, 2x10 6 cells
	(monocytes) and 1x10 6 cells (MCF-7) were seeded in a total volume of 5 ml in 6-well
	plates and incubated for 12 h. 50 µL of a 1 mg/mL Fe dispersion of SL-IONP were added
			ACS Paragon Plus Environment

Transmission electron microscopy (TEM) and analysis. TEM

	images were recorded on
	a FEI Tecnai G2 20 transmission electron microscope at 160 kV for low resolution and
	200 kV for high resolution imaging. Samples were drop-casted from toluene dispersions
	(IONP capped by oleic acid) or aqueous dispersions (SL-IONP) onto a 300-mesh carbon-
	coated copper. The Pebbles 37 software package was used to determine the size
	distributions from the micrographs. Approximately 900 IONP were used for size
	determination by Pebbles for each sample of nanoparticles.

Transmission Electron Microscopy experiments under cryogenic conditions (cryo- TEM). Cyro

	individual measurements were performed with 13 runs of 10 s each. All samples of SL-
	-TEM images were recorded on a FEI Tecnai 120 twin microscope at 120 kV IONP were measured at a concentration of 0.5 mg Fe /mL. The nanoparticles were
	with a Gatan Orius CCD numeric camera and a Gatan Cryoholder (Gatan 626DH, Gatan). dispersed in water (2 mg/mL) and 10 % fetal calf serum for experiments in which the
	DigitalMicrograph™ software was used for image acquisition. A custom-built device was temperature was varied from 20 °C to 70 °C and back with 5 °C steps and an equilibration
	used for cryo-fixation. SL-IONP aqueous dispersions and SL-NDA solutions were time of 2 minutes. At each temperature, 3 individual measurements with 13 runs of 10 s
	deposited on glow-discharged holey carbon copper grids (Quantifoil R2/2, Germany). The were recorded.
	grids were immediately plunge-freezed by dipping into liquid ethane at -180 °C and
	transfered into liquid nitrogen. All grids were stored in liquid nitrogen.
	Thermogravimetric Analysis (TGA). TGA data were measured using a Mettler-Toledo
	TGA/DSC 1 STAR System in a temperature range of 25-650 °C with 10 K/min. A stream
	of 80 mL/s of synthetic air was used to ensure complete combustion of the SL-NDA
	ligands since NDA is known to polymerize by pyrolysis under N 2 . 0.5 -1.5 mg sample
	were measured, The total organic content (TOC) was calculated as the fraction of mass
	loss up to 650 °C.
	Dynamic Light Scattering (DLS). DLS was measured on a Malvern Zetasizer Nano-ZS
	at 20 °C. Instrument settings: Fe 3 O 4 , Milli-Q as dispersant (0.89 mPa•s, RI=1.33), 3

1 H

Nuclear magnetic resonance (NMR) measurements. 1

	H NMR data were acquired on
	a Bruker Avance III 300 spectrometer using a 5 mm 1 H-X BBFO probe, 16 transients with
	1 s recycling delay. The value chemical shifts (δ) are reported in ppm at 298 K using
	tetramethylsilane (TMS) as reference. MeOD-d4 was used as solvent. COSY spectra
	were acquired using a standard pulse program form the Avance III library, with 1 s
	recycling delay, 8 transients per scan and 256 spectra acquired in the F1 dimension.

Attenuated total reflection -Fourier transform infra-red (ATR-FTIR) measurements. IR

	spectrometer with diamond single-reflection ATR equipment and a resolution of 4 cm -1 ,
	averaging 32 scans.
	spectra of the lyophilized samples were recorded on a Perkin Elmer 400 FTIR

Small Angle X-ray Scattering (SAXS

). SAXS patterns were measured using a Dectris-Pilatus 1M detector with a resolution of 981 × 1043 pixels and a pixel size of 172 × 172 μm at the Dutch-Belgian Beamline (DUBBLE) station BM26B of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The sample to SAXS detector distance was set to ca. 3100 mm using a wavelength of 1.033 Å. SAXS patterns were integrated azimuthally to obtain a typical spectrum. A quartz capillary, used as 𝐼(𝑞)

Table 1 .

 1 Structural parameters used in the core-shell sphere model to fit both the SANS and SAXS data recorded for the SL-IONP.

	Parameter	Description

The fixed parameters of the fitting function vary according to the type of technique used to study the samples. The fixed values which we have used in this work are reported

Table 2 .

 2 TGA results for SL-IONP of three different core sizes. Total organic contents (TOC) was converted into average number of ligands/nm 2 (n ligands /nm 2 ) using the known SL-NDA Mw (902 g/mol).

	Page 25 of 62	ACS Applied Bio Materials
	SL-IONP type	𝑛 𝑙𝑖𝑔𝑎𝑛𝑑𝑠 nm 2	[dispersant/nm 2 ]	TOC [%w/w]
	3.1 ± 0.3 nm dialyzed		8.0 a	82.3 a
	3.1 ± 0.3 nm Amicon		7.1 a	80.5 a
	4.6 ± 0.3 nm dialyzed		4.3	60.8
	4.6 ± 0.3 nm Amicon		3.3	55.6
	14.1 ± 0.9 nm dialyzed		37.4 a	82.1 a
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a Samples contained large amounts of excess ligand.

Table 3 ,

 3 𝑡

	Page 35 of 62

Table 3 .

 3 Structural parameters for the 3.1 nm and 4.6 nm SL-IONP obtained by combining TEM, SAXS and SANS analyses.

	Sample	Technique	Core diameter (nm) 𝑑	Shell Thickness (nm) 𝑡	𝜌 𝑠𝑜𝑙𝑣 -𝜌 𝑐 (x 10 -6 Å -2 )	𝜌 𝑠𝑜𝑙𝑣 -𝜌 𝑠 (x 10 -6 Å -2 )
		TEM	3.1 ± 0.2	-	-	-
	3.1 SL-IONP nm	SAXS	3.0 ± 0.4	-	-30.60	< -1.00
		SANS	3.0 ± 0.4	2.5 ± 0.2	-0.57	2.63
		TEM	4.6 ± 0.2	-	-	-
	4.6 SL-IONP nm	SAXS	4.8 ± 0.4	-	-30.60	< -1.00
		SANS	4.8 ± 0.4	2.2 ± 0.2	-0.57	3.00

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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Funding Sources

This work received financial support by the Institut Laue-Langevin (ILL), Grenoble, France, under the experiment number 9-12-481 (D33, D16 beamlines), and by the European Synchrotron Radiation Facility (ESRF), Grenoble, France, under the experiment number SC-4419. The research presented in that paper was funded by the Austrian Science Fund (FWF) project I 3064 and by the European Research Council under the European Union's Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement No. 310034. ACKNOWLEDGMENT This work benefited from the use of the SasView application, originally developed under NSF award DMR-0520547. SasView contains code developed with funding from the European Union's Horizon 2020 research and innovation programme under the SINE2020 project, grant agreement No 654000. We thank the Lawrence Berkeley Page 54 of 62 ACS Paragon Plus Environment ACS Applied Bio Materials

nanoparticles can display unique targeting ability towards lectin-rich biological membranes, including tumor cells and pathogenic bacteria. ASSOCIATED CONTENT Supporting Information. Additional information on Materials. Control over iron oxide core size by the precursor to surfactant ratio. Detailed synthetic protocols. NMR, IR, TGA, TEM, cryo-TEM and DLS data for SL-NDA and SL-IONP. Photos of colloidal suspensions.

Additional SAXS and SANS data with fits.

AUTHOR INFORMATION

Corresponding Authors

*Erik Reimhult: erik.reimhult@boku.ac.at; Niki Baccile: niki.baccile@upmc.fr.

Author