Daniel M Schneider

Pascal Pagani

Andreas Schwager

MIMO PLC capacity and throughput analysis

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

Introduction

Multiple-input multiple-output (MIMO) systems have been used for many years in the field of wireless communications [1,2]. The huge increases in coverage and capacity offered by MIMO technology are the key benefits of using multiple sensors at the transmitter (Tx) and receiver (Rx). For a single-user transmission, and under the assumption that the channel information is perfectly known at both the Tx and Rx, it has been demonstrated that the capacity increases linearly with the number of antennas. However, in more realistic wireless scenarios, the capacity of a MIMO system depends on a number of practical considerations including channel estimation in a time-varying environment, spatial correlation induced by the sensors and the value of the signal-to-noise ratio (SNR) available at the Rx [3]. Recently, MIMO technology has been applied in the context of power line communications (PLCs), with the aim of offering higher channel capacity and therefore larger system coverage, by including the use of the protective earth (PE) wire in addition to the line (L) and neutral (N) wires [START_REF] Stadelmeier | MIMO for inhome power line communications[END_REF][START_REF] Schneider | Precoded spatial multiplexing MIMO for inhome power line communications[END_REF][START_REF] Hashmat | MIMO communications for inhome PLC networks: Measurements and results up to 100 MHz[END_REF][START_REF] Schwager | Powerline communications: Significant technologies to become ready for integration[END_REF][START_REF] Schneider | Inhome power line communications using multiple input multiple output principles[END_REF] (see Chapter 1). This new application for MIMO technology offers different characteristics as compared to wireless communications, which can in turn effect the capacity gain achieved. On the one hand, the number of input and output ports of a PLC channel is much more constrained than for a radio channel. Due to Kirchhoff's law, only two differential input ports can be used simultaneously, in the three possible combinations (L-N, N-PE and PE-L). At the Rx, three different signals can be monitored, either on a wire-to-wire basis or using differential reception between two wires. In addition, the common-mode (CM) signal generated by asymmetries in the transmission medium can be measured at the Rx, which provides a fourth output of the MIMO system. As a result, a MIMO PLC transmission up to a 2 × 4 configuration is implementable. More details about coupling for MIMO signal injection and reception are given in Chapter 1. SNR values observed in typical PLC scenarios can be much higher than in the case of a classical wireless communication. This high SNR condition is beneficial for MIMO transmission, as it ensures a high capacity gain with respect to single-input single-output (SISO) transmission, even if the channel presents a high degree of spatial correlation.

This chapter is divided into two main sections. First, the PLC channel capacity offered by MIMO technology is analysed in detail (see Section 9.2). The channel capacity provides an upper limit for achievable throughput and does not take system implementation or a particular MIMO scheme into consideration. The achievable throughput for different MIMO schemes in an OFDM system with adaptive modulation is investigated in Section 9.3. The channel capacity analysis in Section 9.2 is elaborated in the following subsections. The mathematical framework used for capacity computation is first presented in Section 9.2.1. The capacity results presented in the literature for different scenarios are discussed in Section 9.2.2. Finally, Section 9.2.3 presents a statistical analysis of the MIMO channel capacity based on the experimental measurement campaign ETSI STF410 presented in Chapter 5. The throughput analysis in Section 9.3 is organised as follows: First, adaptive modulation is applied to the MIMO-OFDM systems introduced in Chapter 8 (Section 9.3.1). As it was shown in Chapter 8, the SNR after MIMO detection/equalisation of the different investigated MIMO schemes is still very frequency-selective. Thus, adaptive modulation specific to the subcarrier is the method of choice for dealing with this frequency selectivity. The bitrate achieved by the different MIMO PLC systems is investigated in Section 9.3.2 for the same set of MIMO PLC channels as used in Section 9.2 for the channel capacity analysis.

MIMO PLC Channel Capacity

Theoretical Background

In the following, a wideband signal transmission is considered, where the transmitted signal s( f ) is defined for a set of frequencies f in the range [f min , f max ]. In general, multi-carrier transmission schemes, such as orthogonal frequency division multiplexing (OFDM), are used to convey wideband signals without suffering from inter-symbol interference (ISI) due to the frequency-selective nature of the channel. More information about MIMO-OFDM systems is detailed in Chapter 8. For transmission over a SISO channel, involving one Tx port and one Rx port, the relation between the received signal r( f) and the transmitted signal s( f) is given by

r f h f s f n f ( ) ( ) ( ) ( ), = + (9.1)
where h(f) represents the SISO channel transfer function (CTF) defined for all frequencies f n(f) denotes the received noise

The concept of channel capacity was developed by Shannon in [START_REF] Shannon | Communication in the presence of noise[END_REF]. According to information theory, data transmission can occur at an arbitrary low error probability, provided that the data rate is lower than the maximum channel capacity. Channel capacity is thus a measure of the maximum transmission rate that can be theoretically obtained over a given channel. For a single-carrier SISO channel, the channel capacity C SISO is given as

C B SISO bit/s = + [ ] •log ( ) , 2 1 Λ (9.2)
where B represents the signal bandwidth in Hz Λ represents the SNR at the receiver For a multi-carrier transmission scheme with L carriers defined at frequencies f 1 to f L with an inter-carrier spacing ∆f, Equation 9.2 translates to

C f f n L n SISO bit/s = + = ∑ ∆ Λ • log ( ( )) [ ]. 2 1 1 (9.3)
For a given signal power spectral density (PSD) P(f) defined in W/Hz at the Tx injection point and denoting N(f) the noise PSD at the Rx in W/Hz, Equation 9.3 can be further detailed as

C f P f h f N f n L n n n SISO bit/s = + ( ) ( ) ( )         = ∑ ∆ • log [ ]. 2 1 2 1 (9.4)
In the case of a MIMO transmission involving N T Tx ports and N R Rx ports, the transmitted signal s(f) is represented as a N T × 1 symbol vector and the received signal r(f) is represented as a N R × 1 symbol vector. Their relation is given by the following equation (see also Section 8.2):

r H s n ( ) ( ) ( ) ( ), f f f f = + (9.5)
where n(f) is the N R × 1 symbol vector representing the noise received at the N R Rx ports

H(f) is the N R × N T MIMO CTF matrix given by H( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) f h f h f h f h f h f h f h f h N N T T R = 11 12 1 21 22 2 1 ⋯ ⋯ ⋮ ⋮ ⋱ ⋮ N NR R R T f h f N N 2 ( ) ( ) , ⋯             (9.6)
where h ml (f) represents the CTF between input port l (l = 1, …, N T ) and receiving port m

(m = 1, …, N R ).
As shown in Section 8.2, the channel matrix H(f) can be decomposed into R = min(N T ,N R ) parallel streams where the attenuation of the streams is described by the singular values

λ p f p R ( ) = , , , ) 1 … of H(f).
The channel capacity formula of Equation 9.4 can be extended to the sum of the channel capacities of the R independent SISO streams as follows [START_REF] Paulraj | Introduction to Space-Time Wireless Communications[END_REF]:

C f P f f R N f p R n L n p n n MIMO bit/s = +       [ ] = = ∑ ∑ ∆ • log ( ) ( ) • . ( ) 2 1 1 1 λ (9.7)
In Equation 9.7, it is assumed that the noise of the N R receive ports is uncorrelated and that the noise power is the same for all receive ports. It can be noted in Equation 9.7 that the signal PSD P(f) is now divided by R = min(N T , N R ) as the available power is shared between the R parallel and independent streams. Note that this assumption may be considered a worst-case assumption. The MIMO PLC signal PSD is not limited by the total power but rather constraint by the EMI properties of the transmission. The discussion on EMI properties of the MIMO PLC transmission can be found in Chapter 7. The analysis in Chapter 7 suggests that the reduction of the transmit power per transmit port may be <3 dB in the case of two transmit ports. The analysis of Chapter 7 is further developed in Chapter 16 in the context of beamforming (BF). The MIMO channel capacity formula according to Equation 9.7 can be further elaborated by taking the correlated noise at the receiver into account. Assuming that the noise is correlated with the noise covariance matrix 2 ( ) can be applied at the receiver. The filtered

N n n c H f E f f ( ) { ( ) ( )} = ( 9
noise ɶ n N n ( ) ( ) ( ) f f f c = - 1 2
is then uncorrelated with

E f f H NR ɶ ɶ n n I ( ) ( ) . { } = (9.9)
The noise whitening filter N c f -1 2 ( ) and the channel matrix H(f) can be combined to form an equivalent channel:

ɶ H N H ( ) ( ) ( ). f f f c = - 1 2
(9.10)

Applying the SVD to the equivalent channel gives the singular values ɶ λ p f ( ) . Using the new equivalent singular values ɶ λ p f ( ) , the channel capacity of Equation 9.7 is extended to

C f P f f R p R n L n p n MIMO bit/s = +         = = ∑ ∑ ∆ • log [ ]. ( ) ( ) 2 1 1 1 ɶ λ (9.11)
Note that the term N(f n ) is removed in Equation 9.11 since the noise power is already considered via the noise whitening filter N c f -1 2 ( ) in ɶ λ p f ( ) and therefore the noise power is equal to 1 according to Equation 9.9. MIMO transmission offers another degree of freedom, namely, the allocation of the total transmit power to the R MIMO streams. This power allocation (PA) can be incorporated in Equation 9 . The optimum PA with respect to the channel capacity is achieved by the water filling (WF) algorithm (see [START_REF] Paulraj | Introduction to Space-Time Wireless Communications[END_REF]). The channel capacity of MIMO PLC using WF was investigated in [START_REF] Schneider | Inhome power line communications using multiple input multiple output principles[END_REF]. It was shown that WF improves the channel capacity for links with very low SNR, while the channel capacity of links with medium to high SNR was only marginally increased when WF was applied. In conclusion, links with low SNR (which are most important to reach coverage goals) may benefit from PA. The application of PA to MIMO PLC systems is discussed in Chapter 8. The simulation results in this chapter do not consider WF.

Review of MIMO Channel Capacity Computations from the Literature

The MIMO PLC channel capacity was investigated for the first time in [START_REF] Stadelmeier | MIMO for inhome power line communications[END_REF] based on in-home PLC measurements in German houses and flats. These investigations were further elaborated in [START_REF] Schneider | Inhome power line communications using multiple input multiple output principles[END_REF]. The authors found that the MIMO channel capacity is on average double that of SISO. These results were confirmed and extended to a frequency range of up to 100 MHz in [START_REF] Hashmat | MIMO communications for inhome PLC networks: Measurements and results up to 100 MHz[END_REF][START_REF] Hashmat | MIMO capacity of inhome PLC links up to 100 MHz[END_REF] for measurements in France. In [START_REF] Canova | Receivers for MIMO-PLC channels: Throughput comparison[END_REF], the throughput of different MIMO PLC schemes is compared on the basis of a theoretical MIMO channel model and additive white Gaussian noise (AWGN). Rende et al. [START_REF] Rende | Noise correlation and its effect on capacity of inhome MIMO power line channels[END_REF] investigated the MIMO PLC channel and channel capacity based on measurements in North America, focusing on the influence of the noise correlation on the channel capacity. Versolatto and Tonello [START_REF] Versolatto | A MIMO PLC random channel generator and capacity analysis[END_REF] derived a bottom-up MIMO PLC channel model and compared, among other features, the MIMO PLC channel capacity of the proposed model to the MIMO channel capacity based on the earlier mentioned measurements. Schneider et al. [START_REF] Schneider | European MIMO PLC field measurements: Channel analysis[END_REF] analysed the MIMO PLC channel and computed MIMO channel capacity based on the ETSI MIMO channel measurement campaign of STF410 (see Chapter 5,[START_REF][END_REF][START_REF][END_REF][START_REF][END_REF]). However, the noise was assumed to be white and uncorrelated in this analysis.

Statistical Analysis of the MIMO Channel Capacity from European Field Measurements

The statistical analysis of the channel capacity is based on the MIMO PLC channels obtained in the European (EU) field measurement campaign of ETSI STF410. This measurement campaign recorded the complex S 21 scattering parameter (among other channel and EMI features) between hundreds of outlets for different MIMO feeding and receiving options. Additionally, the noise at the outlets was recorded for all MIMO ports simultaneously. This allows the derivation of the noise correlation among the receive ports. The noise correlation is considered in the analysis of the channel capacity below. The frequency range of the measurement campaign goes up to 100 MHz. The measurements were performed in Germany, Italy, Spain, France, Belgium and in the United Kingdom. Details about the measurement campaign may be found in Chapter 5. In total, 285 channels are used in the statistical analysis later. Note that reciprocal channel measurements were removed from the data set. The transmit power is considered as a parameter in the following analysis to reflect different regulatory constraints in different parts of the world. The transmit PSD masks introduced in Chapter 6 are used. In particular, the EU, US and JP transmit masks according to Figure 6.3 are assumed.

The channel capacity was calculated for each link according to the channel capacity of Equation 9.11. Figures 9.1 through 9.3 show the complementary cumulative distribution function (C-CDF) of the channel capacity for different transmit power masks, namely, the ones in Europe, the United States and JP, respectively. The C-CDF figures may be read to obtain different coverage values, that is, with which probability a certain bitrate is exceeded. The channel capacity is derived for different MIMO configurations. The MIMO configurations from left to right in Figures 9.1 through 9.3 are summarised in Table 9.1. The first configuration is SISO, where the D1 port of the delta-style coupler (differential feeding between L and N) was used at the transmitter and the S1 port (L) of the star-style coupler was used as the receive port. Note that the SISO configuration with feeding on D1 and reception on S2 (N) yields the same performance as the SISO configuration with reception on D1 (L). Therefore, this second SISO configuration is not shown in Figures 9.1 through 9.3. Following are three SIMO configurations, each with feeding on D1 port (L-N) and with an increasing number of receive ports. The 1 × 2 configuration might be used in homes where the third wire is not present; 1 × 4 might be used if the transmitter is a legacy (non MIMO) modem and the receiver has full MIMO capabilities. The three MIMO configurations use the same receive ports as the SIMO configurations and use feeding on D1 (L-N) and D3 (L-PE). Details about the couplers and port definitions may be found in Chapter 1. The 2 × 2 configuration might be the most advantageous as coupler resources are used symmetrically when transmitting or receiving. 2 × 4 is today's maximum configuration on a three-wire network. • The SIMO configurations with only one transmit port already offer a gain compared to SISO. The channel capacity of the best SIMO scheme, 1 × 4, is increased by 37% (EU mask), 39% (US mask) and 56% (JP mask) compared to SISO. The increasing relative gain starting with the EU mask, followed by the US mask, and ending with the JP mask, is explained considering absolute bitrates. The higher the absolute bitrate, the lower the relative SIMO gain. And vice versa, channels supporting only lower absolute bitrates offer the highest gain relative to SISO. The same tendency is observed for MIMO in the high coverage area. The overall lower bitrates of the US and JP masks compared to the EU mask are derived from the transmit masks: the US mask is 5 dB below the EU mask, while the JP mask does not even allow any transmission above 30 MHz.

• Using the second transmit port results in full MIMO configurations and provides a significant increase in bitrate compared to SISO, reflected by 71% (EU and US masks) and 72% (JP mask) for the 2 × 2 scheme and 116% (EU and US masks) and 146% (JP mask) for the 2 × 4 MIMO configuration. (The bitrate increase when applying the JP power transmit mask is hypothetical, because the third wire only rarely exists in JP outlets.)

MIMO Configurations

MIMO Configuration Tx Ports

Rx Ports In conclusion, the MIMO channel capacity of the full (2 × 4) MIMO configuration is on average more than double the SISO capacity.

1 × 1 D1 (L-N) S1 (L) 1 × 2 D1 (L-N) S1 (
Next, consider the high coverage area (98% point):

• At the high coverage area, the SIMO configurations already offer a significant gain compared to SISO: factors of 2.12 (EU mask), 2.03 (US mask) and even 5.37 (JP mask) are observed for the 1 × 4 configuration.

• In contrast to 1 × 4 MIMO, the 2 × 2 configuration provides less gain: 1.87, 1.94 and 3.52 for the EU, US and JP masks, respectively. The second, weaker stream (eigenmode) does not contribute much for low SNR channels. It is more important to collect all the available signal energy at the receiver. This is reflected by the number of receive ports.

• Combining the use of the maximum number of receive ports and the use of two streams for the 2 × 4 configuration shows the highest gain compared to SISO: 2.88, 3.05 and 6.35 for the EU, US and JP masks, respectively.

The MIMO gain in the high coverage area is even higher compared to the median values. Thus, MIMO especially improves the difficult links with high attenuation and therefore low SNR at the receiver, making MIMO a promising method for meeting ambitious coverage requirements. Note that the presented results are the theoretical channel capacity.

The choice of the implemented MIMO scheme and the system parameters for modulation, coding and implementation aspects and limitations influence the achievable throughput in real modem implementations (e.g. a 10 bit analogue-to-digital converter (ADC) might not utilise the full SNR available at the channel).

MIMO PLC Throughput Analysis

The aim of this section is to verify the MIMO channel capacity gains of the previous section for different MIMO PLC systems. In particular, the OFDM-based MIMO PLC schemes introduced in Chapter 8 are investigated with respect to the achieved bitrate. Adaptive modulation is applied to the SNR after detection (see Section 9.3.1). As for SISO, the SNR after MIMO processing is still very frequency-selective. This makes subcarrier-specific adaptive modulation a good choice for maximising the PLC throughput. The achieved bitrate is analysed in Section 9.3.2 for a large set of MIMO PLC channels.

Adaptive Modulation

The frequency-selective PLC channel leads to high SNR variations for different OFDM subcarriers. To overcome this problem, adaptive modulation is applied. Each subcarrier is bit loaded and modulated according to the corresponding SNR. The higher the SNR, the higher the quadrature amplitude modulation (QAM) constellation. , (

QPSK -QAM -QAM ≤ ( ) < ≤ ( ) < Λ Λ n n ) ). , ( )
θ θ θ θ ≤ ( ) < ≤ ( ) < Λ Λ n n -QAM --QAM -QAM
).

, (

). 4096 4096

4096 θ ≤ ( )              Λ n (9.12)
In Equation 9.12, the modulation order M = 1 indicates that no information is assigned to the subcarrier, that is, log 2 (1) = 0 bit is assigned. The choice of the SNR thresholds θ M influences both the achieved bitrate and the bit error ratio (BER). The bitrate D is the sum of the bits assigned to each subcarrier divided by the OFDM symbol length T u : The BER depends on the SNR Λ and the modulation order M. For an AWGN channel, the BER is given by the tight approximation [START_REF] Chung | Degrees of freedom in adaptive modulation: A unified view[END_REF][START_REF] Proakis | Digital Communications[END_REF]:

D M n T n L u = ( ) ( ) = ∑ log
P M M M M M b ( , ) , , log ( ) ( ) Λ Λ Λ = ⋅ ( ) = ⋅ -       ⋅ -    1 2 2 2 1 1 3 2 1 2 erfc erfc              , log ( ) 2 M even (9.14)
with erfc( ) exp( )

x t dt x = - ∞ ∫ 2 2 π
being the complementary error function. Binary reflected Gray bit labelling is assumed for the even constellations (log 2 (M) even) in Equation 9.14.

With M(n) the modulation order and Λ(n) the SNR of subcarrier n (1 ≤ n ≤ N), the BER of each subcarrier P b (M(n),Λ(n)) can be calculated according to Equation 9.14. The overall average BER P b is given as the average number of bits in error divided by the total number of transmitted bits [START_REF] Proakis | Digital Communications[END_REF] and can be calculated as

P P M n n b b n N = = ⋅ = ∑ Number of errors Number of bits 1 2 ( ( ), ( )) log ( Λ M M n M n n N ( )) log ( ( ))
. Recall that the SNR thresholds θ M determine the modulation order M(n) of each subcarrier according to Equation 9.12 and thus influence both the bitrate according to Equation 9.13 and the average BER according to Equation 9 ≤ ′ uses fixed SNR thresholds. For a given target BER P b ′ and modulation order M, Equation 9.14 can be solved for Λ which is then used as SNR threshold θ M . Figure 9.5 shows the BER depending on the SNR for different modulation orders. The figure also provides the SNR thresholds for a target BER of P b ′ = - 10 3 . The BER value of 10 -3 may be sufficient for the raw physical layer since additional forward error correction (FEC) will improve the BER. This algorithm guarantees that the average BER P b does not exceed the target BER ′ P b in every case. Usually, the average BER P b will be lower than the target BER ′ P b since many subcarriers have higher SNR than the SNR thresholds. Schneider et al. [START_REF] Schneider | Precoded spatial multiplexing MIMO for inhome power line communications[END_REF][START_REF] Schneider | Inhome power line communications using multiple input multiple output principles[END_REF] propose an algorithm which maximises the bitrate D, for a desired target BER ′ P b . The algorithm takes the SNR distribution of the given channel into account, that is, the algorithm adapts the SNR thresholds to the current channel conditions.

The SNR thresholds shown in Figure 9.4 are obtained according to the algorithm described earlier for a target BER of 10 -3 . Note that the SNR thresholds are lower compared to the fixed SNR thresholds shown in Figure 9.5. Thus, the bitrate of the proposed algorithm is higher compared to the algorithm with fixed thresholds.

The MIMO scheme and detection algorithm determine the SNR of the MIMO streams as shown in Chapter 8. Adaptive modulation is applied for each MIMO stream separately. Figure 9.6a shows the block diagram of the adaptive modulation algorithm for MIMO.

The SNR thresholds θ M are calculated according to the SNR of the subcarriers after MIMO detection. These thresholds are used to assign the QAM constellation to each subcarrier. Note that the blocks adaptive QAM pattern and adaptive thresholds in Figure 9.6 require knowledge of the SNR for all subcarriers; thus, these blocks operate in parallel. The calculation of the PA coefficients is based on the SNR and the QAM constellations (see Section 8.3). This results in a dependency between the PA and the adaptive modulation as highlighted in Figure 9.6b. The combination of adaptive modulation and PA has to be calculated iteratively in this case.

Simulation Results

The MIMO-OFDM system described in Chapter 8 forms the basis of the system simulations. 1296 subcarriers are used in the frequency range from 4 to 30 MHz. Each subcarrier is adaptively modulated, according to the adaptive modulation algorithm described in Section 9.3.1. The target average BER of the uncoded system is adjusted to 10 -3 . An additional FEC might easily reduce this BER. The bitrate is obtained as the sum of the number of bits assigned to all subcarriers divided by the OFDM symbol length. This bitrate describes the raw physical layer bitrate without considering the guard interval length, training data or FEC overhead. The basic system parameters are summarised in Table 9.3.

The noise is modelled by AWGN with zero mean, and it is assumed that the noise is uncorrelated and that the noise power is the same for all receive ports. The transmit power to noise power level is assumed to be ρ = 65 dB. This value corresponds to a transmit PSD of -55 dBm/Hz (see Chapter 6) and an average noise PSD of -120 dBm/Hz (this corresponds to the 90% point of CDF of the noise according to Chapter 5). Impulsive noise is not considered. The focus is on the comparison between MIMO and SISO schemes. It is expected that impulsive noise will influence all receive ports in a similar way. Thus, mitigation techniques known from SISO systems can be applied [START_REF] Biglieri | Coding and modulation for a horrible channel[END_REF][START_REF] Fertonani | On reliable communications over channels impaired by bursty impulse noise[END_REF]. The measured MIMO PLC channels obtained during the European measurement campaign (ETSI STF410, see Chapter 5) are used in the system simulations. In the case of MIMO, the two feeding ports D1 and D3 (i.e. L-N and L-PE, see Chapter 1) and all four receive ports (S1, S2, S3 and S4) are used; in the case of SISO, the D1 (L-N) port is used at the transmitter and the S1 port (L) at the receiver. It was observed that using the S2 (N) at the receiver yields the same performance as using the S1 port. The corresponding SNR is calculated based on the channel matrix of each subcarrier (channel estimation is assumed to be perfect), depending on the MIMO scheme as shown in Chapter 8. Then, the derived SNR is used with the adaptive modulation algorithm to determine the subcarrier's constellations. Adaptive modulation is applied to each of the MIMO schemes in this section. Figure 9.7 compares the C-CDF of the bitrate at ρ = 44 dB for different MIMO schemes, namely, SISO, the Alamouti scheme and spatial multiplexing (SMX) with different detection algorithms (see Chapter 8) and BF. The measured MIMO PLC channels form the basis of the comparison. No PA is applied here. SISO is expected to offer the lowest bitrate. However, SMX with zero-forcing (ZF) detection performs about the same or even worse, compared to SISO for most channels and bitrates up to about 40 Mbit/s. The high correlation of the power line channels results in high values of the detection matrix entries, leading to an amplification of the noise (refer also to Section 8.6). This effect is mitigated using more advanced detection algorithms. The bitrate is increased, as seen in Figure 9.7 for minimum mean squared error (MMSE), successive interference cancellation (SIC)-ZF and SIC-MMSE. Ordered SIC (OSIC) receivers are not shown in Figure 9.7, because their performance improvement compared to SIC is only marginal. Eigenbeamforming (EBF) achieves the highest bitrate. The Alamouti scheme performs almost as well as EBF, especially for low bitrates or the high coverage point. The bitrate gain of MIMO compared to SISO is highest for the low bitrate region in Figure 9.7, that is, for channels with high attenuation. The gain of MMSE versus ZF becomes smaller compared to the lower transmit to noise power level in Figure 9.7. The SIC receivers reach the performance of EBF. However, it has to be kept in mind that no PA and no error propagation of the SIC receiver are considered here. The Alamouti scheme performs well for high values of the C-CDF, that is, for channels with low bitrate due to high attenuation and correlation. However, due to the transmission of replicas, no multiplexing gain is achieved for channels with high bitrate (as can be seen by the low values of the C-CDF in Figure 9.8 where the line of the Alamouti scheme reaches the SISO's line).

Figure 9.9 compares the PA for SMX and EBF for ρ = 44 dB and ρ = 65 dB. There is only a marginal performance improvement of mercury water filling (MWF) compared to the simplified PA (as introduced in Chapter 8). The gain of PA is most visible for low ρ. As explained also by the SNR results in Chapter 8 (see Figure 8.14), EBF benefits most from PA. The PA's gain of SMX (SMX-ZF) is relatively small. This is observed for all different receivers for SMX.

Figure 9.10 is similar to Figure 9.7. However, it includes PA. Additionally, one-stream BF is shown where the total power is assigned to the first stream. Figure 9.10a shows the complete coverage range, Figure 9.10b shows the median coverage point and Figure 9.10c shows the high coverage point. Most carriers of the EBF's second stream turn out to carry no information for highly attenuated channels. The shift of the second stream's power to the first stream of EBF results in 3 dB higher SNR of the first stream if none of the carriers of the second stream are carrying any information. Obviously, the performance of onestream BF is close to two-stream BF because as only a few carriers of the second stream contribute to the bitrate. The superior performance of BF over the Alamouti scheme is more visible compared to no PA in Figure 9.7. Please note that PA cannot be used for the Alamouti scheme since each symbol is transmitted via each transmit port. Table 9.4 summarises the mean values of the bitrates for the different MIMO schemes. The two transmit to noise power levels of ρ = 44 dB and 65 dB are considered. The gain of a MIMO scheme is defined as the ratio of the MIMO bitrate to the SISO bitrate.

Conclusions

This chapter analysed the theoretical MIMO channel capacity based on an extensive measurement set of MIMO PLC channels obtained during the ETSI measurement campaign of STF410. The channel capacity was computed under different regulatory constraints, that is, different transmit power masks. Not only were the measured MIMO CTF taken into account but also the measured noise statistics, which incorporate the spatial correlation of the noise. The MIMO channel capacity is, on average, doubled compared to SISO. In particular, highly attenuated channels benefit most from the application of MIMO which makes MIMO a promising method for improving PLC coverage.

In a next step, the gain of throughput was verified for different MIMO PLC systems. Adaptive modulation was applied to the SNR after MIMO detection of the MIMO PLC schemes introduced in Chapter 8, and the achieved bitrate was analysed. Similar conclusions as for the SNR analysis in Chapter 8 can be drawn for the throughput analysis. Generally, there is a significant increase of bitrate for all MIMO schemes compared to SISO transmission. This confirms the channel capacity gain found in the first part of this chapter. The Alamouti scheme improves the bitrate compared to SISO and showed good performance for highly attenuated channels. However, no multiplexing gain is achieved because of the transmission of replicas of each symbol. Adaptive modulation already adapts to the frequency-selective channel, making the property of the Alamouti scheme to combat fading counterproductive. SMX increases the bitrate compared to the Alamouti scheme for low attenuated channels. Care has to be taken with respect to which MIMO detection algorithm is used. ZF detection fails for a high correlation of the channel, and more complex detection algorithms (like MMSE and SIC) are suggested to increase the performance. The earlier MIMO schemes are open-loop MIMO schemes which require no channel state information at the transmitter. An additional performance gain is achieved by closed-loop MIMO schemes like BF which use channel state information at the transmitter. BF offers the highest bitrate in all scenarios and comes closest to the channel capacity by adapting the transmission to the eigenmodes of the channel. The full spatial diversity gain is achieved for highly attenuated channels and maximum bitrate gain is achieved for channels with low attenuation. BF requires knowledge about the channel state information at the transmitter. Usually, only the receiver has channel state information. Thus, information about the precoding matrix has to be fed back from the receiver to the transmitter. The application of adaptive modulation already requires feedback about the constellation maps from the receiver. This feedback path might also be used to return the BF information to the transmitter. The feedback rate can be kept low because the in-home PLC channel is less time varying compared to, for example, a mobile channel. Schneider et al. [START_REF] Schneider | Precoded spatial multiplexing MIMO for inhome power line communications[END_REF][START_REF] Schneider | Inhome power line communications using multiple input multiple output principles[END_REF] investigated the amount of feedback overhead needed to feed back the information about the precoding matrices and showed that the required feedback for the precoding matrices lies in the same order of magnitude as the feedback required for adaptive modulation. For these reasons, a BF-based MIMO-OFDM system with adaptive modulation is a well-suited MIMO system for PLC. The adoption of MIMO and precoded SMX or BF to the latest PLC specifications is discussed in detail in Chapter 12 for G.hn/G.9963 and in Chapter 14 for HomePlug AV2. A study of a MIMO PLC hardware implementation with BF can be found in Chapter 24.

. 8 )

 8 (see alsoChapters 4 and 5), where N c (f) is of dimensions N R × N R . As shown in Section 8.5.4, a noise whitening filter N c f -1

  .11 by a factor a p for each transmit stream with

FIGURE 9 . 1 FIGURE 9 . 2 FIGURE 9 . 3

 919293 FIGURE 9.1Channel capacity for the EU transmit power mask.

  -N) and D3 (L-PE) S1 (L), S2 (N) and S3 (PE) 2 × 4 D1 (L-N) and D3 (L-PE) S1 (L), S2 (N), S3 (PE) and S4 (CM)

Figure 9 .

 9 [START_REF] Stadelmeier | MIMO for inhome power line communications[END_REF] shows an example of a typical SISO PLC channel. The SNR, depending on the frequency from 4 to 30 MHz, illustrates the frequency-selective channel. The QAM constellations with modulation order M used here are binary phase-shift keying (BPSK) (M = 2) and the even or square QAM constellations from quadrature phase-shift keying (QPSK) to 4096-QAM (M = 4, 16, 64, 256, 1024, 4096). The number of bits per QAM symbol is log 2 (M). The SNR thresholds θ M for each modulation order M are illustrated by the horizontal lines in Figure9.4 for each modulation scheme. These thresholds define the assignment of the QAM constellation depending on the SNR of each subcarrier. A subcarrier can also be omitted (notched) if the SNR is too low to carry any information.If Λ(n) is the SNR of subcarrier n (1 ≤ n ≤ N), the assignment to modulation order M(n) of subcarrier n depends on the thresholds θ M of each modulation order M:

.

FIGURE 9 . 4

 94 FIGURE 9.4Adaptive modulation: available SNR depending on the frequency, and application of QAM constellations depending on the available SNR, SISO, transmit power to noise power level ρ = 65 dB.

. 14 .

 14 The design of the SNR thresholds θ M can be optimised with respect to two different criteria: • Minimising the BER for a fixed bitrate • Maximising the bitrate for a fixed BER The second criterion is considered here. A simple algorithm that guarantees a certain target BER P b ′ with P P b b

FIGURE 9 . 5

 95 FIGURE 9.5 BER depending on SNR for different QAM orders and SNR values required for a target BER of 10 -3 .

FIGURE 9 . 6

 96 FIGURE 9.6 Block diagram of the adaptive modulation algorithm, without PA (a) and with PA (b).

Figure 9 .

 9 8 is similar to Figure 9.7 with a higher transmit signal to noise power level of ρ = 65 dB. Here, SMX with ZF detection overrides SISO in contrast to Figure 9.7. SMX-SIC-ZF SMX-SIC-MMSE BF Bitrate D [Mbit/s]

FIGURE 9 . 7 C

 97 FIGURE 9.7 C-CDF of the bitrate for different MIMO schemes, ρ = 44 dB, no PA, N T = 2, N R = 4.

FIGURE 9 . 8 CFIGURE 9

 989 FIGURE 9.8 C-CDF of the bitrate for different MIMO schemes, ρ = 65 dB, no PA, N T = 2, N R = 4.

FIGURE 9 .

 9 FIGURE 9.10 (continued) (b,c) C-CDF of the bitrate for different MIMO schemes with PA, ρ = 44 dB, N T = 2, N R = 4.

Table 9 .

 9 2 summarises the median value (50% point) and the 98% point (high coverage point) of the C-CDF shown in the Figures 9.1 through 9.3. The following observations may be drawn from the figures and the table. First, consider the median values:

TABLE 9 . 1

 91

TABLE 9 . 2

 92 Channel Capacity and Gain Compared to SISO for Different Transmit Power Masks: Median Values and 98% Coverage Point

	MIMO		EU Mask			US Mask			JP Mask
	Config-	Median	98%		Median	98%		Median	98%
	uration	Mbit/s Gain Mbit/s Gain Mbit/s Gain Mbit/s Gain Mbit/s Gain Mbit/s Gain
	1 × 1	568		82		499		62		149		6
	1 × 2	651	1.15	126	1.55	571	1.14	103	1.65	184	1.24	23	3.63
	1 × 3	751	1.32	154	1.88	670	1.34	127	2.04	226	1.51	31	4.81
	1 × 4	777	1.37	173	2.12	694	1.39	143	2.30	233	1.56	34	5.37
	2 × 2	971	1.71	153	1.87	851	1.71	121	1.94	257	1.72	23	3.52
	2 × 3	1126	1.98	201	2.46	984	1.97	160	2.57	323	2.17	35	5.48
	2 × 4	1227	2.16	235	2.88	1077	2.16	190	3.05	367	2.46	41	6.35

TABLE 9 .3

 9

	Basic System Parameters
	FFT points	2048
	Nyquist frequency (MHz)	40
	Frequency band (MHz)	4-30
	Number of active subcarriers (4-30 MHz)	1296
	Carrier spacing (kHz)	19.53
	Symbol length (μs)	51.2
	Modulation (per subcarrier)	BPSK, QPSK, 16-, 64-, 256-, 1024-, 4096-QAM
	Uncoded target BER	10 -3

TABLE 9 . 4

 94 Mean Values of the Bitrates for Different MIMO and Power Allocation Schemes, 2 × 4 MIMO Configuration

				ρ = 44 dB					ρ = 65 dB
				Simplified					Simplified
	MIMO	No PA	PA		MWF		No PA		PA		MWF
	Scheme	Mbit/s Gain Mbit/s Gain Mbit/s Gain Mbit/s Gain Mbit/s Gain Mbit/s Gain
	SISO	55	1	PA cannot be used		147	1	PA cannot be used
	Alamouti	79	1.4	PA cannot be used		201	1.4	PA cannot be used
	One-	93	1.7	PA cannot be used		217	1.5	PA cannot be used
	stream BF
	SMX-ZF	85	1.6	88	1.6	91	1.7	264	1.8	266	1.8	269	1.8
	SMX-	92	1.7	98	1.8	101	1.8	270	1.8	273	1.9	276	1.9
	MMSE
	SMX-	105	1.9	110	2.0	113	2.1	306	2.1	309	2.1	313	2.1
	SIC-ZF
	SMX-SIC-	109	2.0	114	2.1	117	2.1	310	2.1	313	2.1	316	2.1
	MMSE
	Two-	110	2.0	119	2.2	120	2.2	311	2.1	315	2.1	317	2.2
	stream BF


est destinée au dépôt

  In patients with anorexia nervosa, myokine levels are altered but are not associated with bone mineral density loss and bone turnover alteration Laurent Maïmoun, Denis Mariano-Goulart, Helena Huguet, Eric Renard, Patrick Lefebvre, Marie-Christine Picot, Anne-Marie Dupuy, Jean-Paul Cristol, Philippe Courtet, Vincent Boudousq, et al. To cite this version: Laurent Maïmoun, Denis Mariano-Goulart, Helena Huguet, Eric Renard, Patrick Lefebvre, et al.. In patients with anorexia nervosa, myokine levels are altered but are not associated with bone mineral density loss and bone turnover alteration. Endocrine Connections, 2022, 11 (5), pp.e210488. 10.1530/EC-21-0488. hal-03669685


C Chamignon

N Haroune

C Forano

A.-M Delort

P Besse-Hoggan

& B Combourieu
email: bruno.combourieu@univ-bpclermont.fr

Mobility of organic pollutants in soil components. What role can magic angle spinning NMR play?

The adsorption-desorption mechanisms at the interface between organic and inorganic soil colloids influence the movement of pesticides and hence their bioavailability and biotransformation processes. Direct analyses of soils have been reported in the literature with the use of solid-state nuclear magnetic resonance (NMR) spectroscopy on dry samples. We recently demonstrated the potential of the 1 H high resolution magic angle spinning (MAS) NMR technique to study such mechanisms in situ on highly hydrated samples. By using a well-characterized soil model, it was possible to distinguish the mobile and immobile pesticide unambiguously. In the present communication, a short review of MAS NMR techniques that allow covalent and non-covalent bond analysis is provided. The results obtained in our group on the adsorption of some pollutants such as phosphonomethylglycine (glyphosate), MCPA and 2benzothiazole sulphonate are also presented. Specifically, we focus on the potential of MAS NMR spectroscopy for probing the behaviour (mobility) of these organic pollutants loaded onto the surface of different clays. The influence of clay hydration on NMR spectra has also been evaluated.

Introduction

The fate of organic pollutants in the environment is strongly dependent on the interactions they can make with organic (humic and fulvic acids) and inorganic (clays, metal (hydr)oxides) soil constituents (Cornejo & Jamet, 2000). The strength of these interactions controls not only the potential of the pollutant to reach groundwater but also its bioavailability towards microorganisms or plants. Numerous studies have documented the key role of organic matter in the sorption of non-polar compounds [START_REF] Spark | Effect of soil composition and dissolved organic matter on pesticide sorption[END_REF], and references cited therein). However, clay particles, due to their small size (< 2 µm), large surface area (100-800 m 2 g -1 ), ion exchange properties and open layered structure, can also make a considerable contribution to the pollutant sorption process (surface and inter-crystallite adsorption, intercalation or irreversible grafting), especially when the pollutant is polar (even weakly so) [START_REF] Gilchrist | Atrazine interactions with clay minerals: kinetics and equilibria of sorption[END_REF][START_REF] Laird | Reactions of pesticides with soil minerals[END_REF]. Indeed, adsorption properties of soils are mainly due to phyllosilicates, hydrated oxides and hydroxides either in their natural state or associated with humic substances [START_REF] Matthes | Sorption of organic compounds by Al-and Zr-hydroxy-intercalated and pillared bentonite[END_REF][START_REF] Laird | Reactions of organic molecules with smectite surfaces in aqueous systems[END_REF][START_REF] Vereecken | Mobility and leaching of glyphosate: a review[END_REF][START_REF] Gimsing | Adsorption of glucosinolates to metal oxides, clay minerals and humic acid[END_REF]. When covalent bonds are created, the pollutant forms bound residues with soil that are no longer extractable or bioavailable. It can participate in the humification process or induce some eco-toxicological problems. The pollutant can also interact with weak bonds; in that case it is likely to be more bioavailable for microbes or plants or be transported to ground water. Studying these interactions at a molecular level or, more macroscopically, studying the mobility of the pollutant is not an easy task. Nuclear magnetic resonance (NMR) spectroscopy is a useful method to assess molecular mechanisms. Most of the studies published are focused on organic matter (OM) composition in terms of its geographical origin and/or the treatment to which it has been submitted by using the classical 13 C crosspolarization magic angle spinning (MAS) solid state NMR sequence. Comparatively, the behaviour of organic pollutants in soils or soil fractions has been less studied. Nevertheless, various NMR approaches have been developed to study covalent and non-covalent interactions between pollutants and soil [START_REF] Nanny | Nuclear Magnetic Resonance in Environmental Chemistry[END_REF][START_REF] Combourieu | Pesticides mobility studied by nuclear magnetic resonance[END_REF]. It should be noted that, due to the relatively low sensitivity of NMR techniques, reported studies were carried out exclusively under laboratory and not under field conditions, usually with 13 C or 15 N-labelled compounds to allow specific detection of residues resulting from covalent bonding (the concentration of the organic pollutant compared with the amount of soil organic matter is very small). This limitation explains why only a few types of compound have been studied to date. 1D and 2D 15 N-13 C DCP-MAS (double cross polarization magic angle spinning) NMR techniques, which allow specific identification of 13 C-NMR signals of 13 C atoms directly bound to 15 N atoms, have been used successfully to give evidence of covalent bonds between 15 N-TNT (trinitrotoluene) and carboxylic and methyl groups of humic acids [START_REF] Knicker | Incorporation of 15 N-TNT transformation products into humifying plant organic matter as revealed by oneand two-dimensional solid state NMR spectroscopy[END_REF]. This technique is extremely powerful and novel but remains limited by its poor sensitivity. Non-covalent interactions imply a rather high degree of mobility of the molecules, which are usually in a hydrated environment. Consequently, the various strategies to study these interactions are aimed at assessing this mobility. First, an indirect approach consists of establishing correlations between organic carbon normalized sorption coefficients (Koc values) of organic pollutants with soil matrices and structural elements of soil organic matter (OM). These correlations should, in principle, allow extrapolation to possible interactions between a pollutant and soil OM. NMR only plays a role in determining the structural groups of OM. The techniques used are mainly CPMAS 13 C NMR at natural abundance, but also liquid state 13 C NMR for model compounds [START_REF] Golding | Investigation of the role of structural domains identified in sedimentary organic matter in the sorption of hydrophobic organic compounds[END_REF][START_REF] Oren | Sorption-desorption behavior of polycyclic aromatic hydrocarbons in upstream and downstream river sediments[END_REF][START_REF] Ahmad | The molecular composition of soil organic matter as determined by 13 C NMR and elemental analyses and correlation with pesticide sorption[END_REF][START_REF] Smernik | NMR characterization of 13 C-benzene sorbed to natural and prepared charcoals[END_REF][START_REF] Bonin | Variation in phenanthrene sorption coefficients with soil organic matter fractionation: the result of structure or conformation[END_REF]. However, many of these correlations are unsatisfactory when the pollutant bears polar functions and depend on the percentage or the nature of the OM present. A second approach takes advantage of NMR properties connected to the orientation or movement of the molecules. For instance, because of the specific properties of the 2 H nucleus, 2 H MAS-NMR spectra can be used as 'fingerprints' of orientation and movement of 2 H-labelled pollutants within a solid matrix. This approach is based on the comparison of experimental and simulated spectra [START_REF] Emery | Solid-state 2 H MAS NMR studies of TNT absorption in soil and clays[END_REF] and this technique requires labelled compounds. The T 1 relaxation time is basically an NMR parameter that reflects the intrinsic mobility of each atom, as T 1 is inversely proportional to the correlation time, τ c . In other words, the greater T 1 , the more mobile the atom. Decrease in T 1 reflects a stronger interaction between the pollutant and the matrix [START_REF] Nanny | Noncovalent interactions between monoaromatic compounds and dissolved humic acids: a deuterium NMR T 1 relaxation study[END_REF]. A last class of NMR experiment carried out on hydrated solid matrices (peat, soil, clay), which can be considered as more relevant to real environmental conditions, allows study of molecular species at the liquid/solid interface. Basically, the NMR signals detected reflect the degree of mobility of these species: highly mobile molecules give narrow signals, similar to liquid state NMR spectra; in contrast, when the strength of the interaction increases, the signals become progressively broader. Reported studies in this field have been performed at natural abundance on certain pollutants, without labelling them, using 19 F or 31 P (efficient but restricted to those containing at least one such atom) [START_REF] Kohl | Solid-state 19 F NMR investigation of hexafluorobenzene sorption to soil organic matter[END_REF][START_REF] Seger | NMR investigation of the behavior of an organothiophosphate pesticide, chlorpyrifos, sorbed on montmorillonite clays[END_REF] or 1 H NMR. The 1 H is present in almost all organic pollutants and has the greatest sensitivity. Therefore, 1 H NMR is the most promising for general application. In the past, its use was very restricted because of the narrow range of chemical shifts, the interference with other protons of the matrix and the strong dipolar coupling constants, which gave very broad lines when 1 H solid-state NMR was used. The very recent development of the 1 H HR-MAS (high resolution magic angle spinning) technique combined with specific HR-MAS probes that allow the use of gradients and shimming coils, opens a new field in environmental studies. Basically, this technique allows the characterization by NMR of inhomogeneous compounds with liquid-like dynamics [START_REF] Piotto | Destruction of magnetization during TOCSY experiments performed under magic angle spinning: effect of radial B 1 inhomogeneities[END_REF][START_REF] Simpson | The application of 1 H high-resolution magic-angle spinning NMR for the study of clay-organic associations in natural and synthetic complexes[END_REF]. It has also been applied to study the interactions of pesticides with soil [START_REF] Simpson | The application of 1 H HR-MAS NMR spectroscopy for the study of structures and associations of organic components at the solid-aqueous interface of a whole soil[END_REF] or clay [START_REF] Combourieu | Differentiation of mobile and immobile pesticides on anionic clays by 1 H HR MAS NMR spectroscopy[END_REF]. Interactions between pesticides and the surrounding soil matrix, swollen in water, could be observed despite the massive presence of water in the samples. The purpose of the present communication is to evaluate the potential of MAS NMR spectroscopy for probing the behaviour (mobility) of organic pollutants loaded onto the surface of different clays: cationic (montmorillonite) and anionic (hydrotalcite-like materials, named layered double hydroxides or LDHs). The influence of clay hydration on NMR spectra has also been evaluated. Our NMR results are compared with those obtained with Fourier transform infrared (FTIR) spectroscopy and X-ray diffractometry. Three ionic organic pollutants have been chosen: two well-known and widely used herbicides (4-chloro-2methylphenoxyacetic acid (MCPA) and N-phosphonomethylglycine (glyphosate)) and an industrial pollutant of the widely used benzothiazole family: 2-benzothiazolesulphonate (BTSO 3 ) (Figure 1). Benzothiazoles (BTs) have many applications: fungicides in lumber and leather production, antialgal agents, slimicides in the paper and pulp industry, chemotherapeutic agents, and vulcanisation catalysts (see De Wever et al., 2001). BTSO 3 is a by-product of an industrial process but is also released from manufactured compounds that contain BTs. Therefore, BTSO 3 has been detected not only in industrial wastewaters but also in various environmental compartments [START_REF] Reemtsma | Polar pollutants entry into the water cycle by municipal wastewater: a European perspective[END_REF]. In the case of BTSO 3 , the potential of MAS NMR to monitor its biotransformation in situ by the bacterial strain Rhodococcus erythropolis in the presence of anionic clays is presented.

Figure 1

Chemical structures of 4-chloro-2-methylphenoxyacetic acid (MCPA), N-phosphonomethylglycine (glyphosate, PMG) and 2-benzothiazolesulphonate (BTSO 3 ).

Materials and methods

Chemicals

BTSO 3 was donated by Bayer (Antwerp, Belgium); N-phosphonomethylglycine (95%) was purchased from Aldrich (Saint-Quentin Fallavier, France); MCPA (sodium salt) was purchased from Fluka (L'Isle d'Abeau, France); and tetradeuterated sodium trimethylsilylpropionate (TSPd 4 ), hexadeuterated sodium 3trimethylsilyl-1-propanesulphonate (DSS) and D 2 O (99%) were purchased from Eurisotop (Saint Aubin, France).

Preparation and characterization of clay samples

Montmorillonite KSF was purchased from Aldrich (batch no. 28,153-0), and the LDHs were prepared in the laboratory as described by [START_REF] Inacio | Adsorption of MCPA pesticide by MgAl-layered double hydroxides[END_REF]. The mineralogical composition of clays was determined by X-ray diffractometry (CuKα radiation; Philips X'Pert automated X-ray diffractometer). The samples were step-scanned in increments of 0.08° 2θ and 4s per step counting time. Powder XRD patterns were recorded in order to determine whether pollutants were intercalated in the layers or adsorbed on the surface. The choice of an acid activated montmorillonite (KSF) was guided by some recent results concerning glyphosate adsorption: decreasing pH and increasing ionic strength lead to an increase of surface coverage and thus glyphosate adsorption [START_REF] Damonte | Some aspects of the glyphosate adsorption on montmorillonite and its calcined form[END_REF]. These relatively large adsorption capacities may be suitable to evaluate the potential of MAS NMR to study the behaviour of glyphosate as sensitivity of NMR is rather low.

Adsorption isotherms

The adsorption isotherms were determined according to the OECD Guideline 106 (OECD, 2000) with a batch equilibrium method at 25°C. Each experiment was repeated twice. The samples were dispersed in decarbonated deionized water (10 or 50 ml) in order to obtain a homogeneous dispersion and stirred for 24 hours before the pollutant was added. In the case of LDHs, the pH was adjusted to 7.5 by HCl (0.1 mol litre -1 ) or NaOH (0.1 mol litre -1 ). Montmorillonite KSF buffered the medium to pH 4 (no change during sorption process): thus no pH adjustment was necessary. After a contact time of 24 hours, the suspensions were centrifuged (10 minutes, 12 500 g). In the case of MCPA, some adsorption isotherms were carried out in fully (99%) deuterated water to minimize contributions of clay protons during 1 H MAS NMR experiments. Solid-liquid ratios were: 100 mg in 10 ml (1/100) and 50 mg in 10 ml (1/200) for glyphosate; 50 mg in 50 ml (1/1000) for MCPA; 50 mg in 50 ml (1/1000) and 500 mg in 10 ml (1/20) for BTSO 3 . In the case of BTSO 3 , the adsorption isotherms were recorded at pH 8.0 in a concentration range between 0.10 and 2.0 mmol litre -1 for the two solid-liquid ratios. It should be noted that at this pH, BTSO 3 may be principally present in its sulphonate form. The amount of pollutant adsorbed by clays (Cs) was determined from the difference between the initial (Ci) and final (or equilibrium) concentrations (Ce) of the pollutant per gram of clay adsorbent: Cs = (Ci-Ce) × V/m (Equation 1), where V (litre) is the volume of the mixture and m (gram) is the mass of clay. The adsorption isotherms were obtained by plotting the amount of pollutant adsorbed (Cs) versus the adsorbate concentration in the equilibrium solution (Ce).

Measurements of pollutant concentrations

MCPA concentrations were determined by UV spectrophotometry by measuring the absorbance at 279 nm with a Perkin-Elmer Lambda 2S UV-Visible spectrometer (Courtaboeuf, France). Concentrations of BTSO 3 were measured by reversed-phase HPLC with a Perkin Elmer Series 200 chromatograph (Column SPHERI-5 RP-18; 5 µm, 250 × 4.6 mm) equipped with a DAD UV detector set at 298 nm. The mobile phase was acetonitrile/water (20/80 V/V); flow rate: 0.7 ml minute -1 . Glyphosate was detected after derivatization [START_REF] Miles | Extraction of glyphosate herbicide from soil and clay minerals and determination of residues in soils[END_REF]) by reversed-phase HPLC (Column Nucleodur C18, 5 µM, 150 × 4.6 mm) on an Agilent 1100 chromatograph (Massy, France) equipped with a fluorescent detector (270 nm for excitation and 317 nm for emission). The mobile phase was a mixture of phosphate buffer (50 mmol litre -1 KH 2 PO 4 ; pH adjusted to 6.0 with 2 mol litre -1 KOH) and acetonitrile, 70/30 V/V; flow rate: 1 ml minute -1 . FTIR measurements. FTIR spectra of the adsorbed pollutant-clay samples were recorded with a Perkin Elmer 16 PC FT-IR spectrophotometer on pellets by pressing, under vacuum, uniformly prepared mixtures of 2 mg of the solid investigated and 198 mg of spectrometry grade KBr. Pellets were measured immediately after pressing.

1 H liquid state NMR measurements. 1 H liquid state NMR was performed at 25°C at 500 MHz on an Avance 500 Bruker spectrometer (Bruker Biospin, Wissembourg, France) equipped with a tripleresonance ( 1 H, 13 C, 15 N) inverse probe with 5-mm diameter tubes containing 600 µl of sample, with water being suppressed by a classical two phase-shifted pulse saturation sequence. Approximately 256 scans were collected (90° pulse, 7.3 µs; saturation pulse, 3 s; relaxation delay, 3 s; acquisition time, 4.679 s; 65 536 data points). A 1-Hz exponential line-broadening filter was applied before Fourier transformation, and a baseline correction was performed on spectra before integration using Bruker software. Under these conditions, the limit of detection and quantification were within the range of 1-10 µmol litre -1 , respectively.

MAS NMR measurements.

NMR spectra were performed on a Bruker Avance DSX-300 spectrometer or a Bruker Avance 500 spectrometer, both equipped with a double-bearing magic angle spinning (MAS) probehead. The samples were packed in 4-mm zirconia rotors fitted with Kel-F caps. For hydrated sample analysis (HR MAS), the volume was restricted to approximately 12 µl in the centre of the rotor by means of a Teflon insert. The high-resolution 13 C solid state spectra were performed at 75.46 MHz at the magic angle with a spinning rate of 10 kHz at ambient temperature. A ramped cross-polarization (RACP) sequence was used to enhance 13 C magnetization. Hartmann-Hahn cross-polarization from protons to carbon was carried out at a proton nutation frequency of 70 kHz over a contact time of 1.5 ms, chosen according to variable contact time experiments. A TPPM decoupling with 1 H nutation frequency of 70 kHz, pulse length of 6.0 µs and phase shift of 15° was used. A recycle delay of 4 s was used. Free induction decays (FID) were digitized into 6K data points and Fourier-transformed after applying 5 Hz exponential line-broadening. The number of transients was fitted to reach optimal signal to noise ratios . The 13 C chemical shifts were referenced to an external reference taken from the carbonyl group of glycine (176.03 p.p.m.).

H MAS and H MAS Hahn echo experiments.

These were carried out at 300.13 MHz. The high resolution component of a 1 H MAS spectrum can be well isolated from the broadline one by the Hahn echo sequence with a long echo time. Compared with the CRAMPS experiment [START_REF] Duer | Dipolar coupling: its measurements and uses[END_REF], which measures the proton system as a whole, the high resolution echo-MAS method measures only a fraction of the solid, which is usually small at room temperature and quite different from the majority of the solid in both molecular motion and chemical environment. However, when several resonances with different chemical shifts exist, a long delay time will cause severe first-order phase distortion. The phase distortion usually becomes increasingly severe with increase in the delay time and the magnetic field. The Hahn echo pulse sequence (π/2-τ/2-π-τ/2-AQ) is found to be very useful for obtaining a pure absorption mode high resolution spectrum at both high field and longer delay times. In addition, a greater sensitivity is obtained by the echo sequence because the main field inhomogeneity is refocused. We have chosen to use a rotor synchronized version of this classical Hahn echo experiment in order to improve the efficiency of the refocalization. When τ is larger than 1 ms, a perfectly phased high resolution spectrum is obtained. As for all spin echo experiments, the high resolution spectrum obtained by the echo-MAS experiment at an arbitrary τ value is generally not quantitative. Thus the choice of the echo value is a crucial issue. The spinning rate was 12 kHz for these experiments. A π/2 pulse of 3.9 µs was used. A variety of echo times was evaluated (100 µs-1.6 ms). A 3 Hz exponential line-broadening was applied before Fourier transformation. The same phase and baseline corrections were applied to all spectra. The chemical shifts were referenced to TSPd 4 taken as an external reference.

H HR-MAS experiments.

To assess the mobility of adsorbed pollutants on clays, samples (15 mg) were swollen with 30 µl of deionised water. The sample volume was restricted to approximately 12 µl in the centre of the rotor by means of a Teflon insert. The spectra were recorded with a rotor-synchronized single pulse experiment (t90° = 6.2 µs) with pre-saturation during the relaxation delay (3 s) for water resonance suppression. Its robustness was greater than that of the classical Watergate experiment in such heterogeneous samples. The samples were spun (v r ) at 3 kHz. Chemical shifts are reported in p.p.m. relative to TSPd 4 as external standard. TSPd 4 was also used for quantification. The number of transients was typically 128 or 256 to achieve a good signal-to-noise ratio. 1 H T 1 measurements of BTSO 3 were carried out using the inversion-recovery sequence that included two water saturation periods during recycle and recovery delays. The measurements were repeated twice both on a pure BTSO 3 solution and on LDH-BTSO 3 complexes. BTSO 3 biodegradation in the presence of clays. Rhodococcus erythropolis was grown and prepared as previously described [START_REF] Besse | Long-range 1 H-15 N heteronuclear shift correlation at natural abundance: a tool to study benzothiazole biodegradation by two Rhodococcus strains[END_REF]. Different quantities of LDHs (Mg 3 AlCO 3 : 10 mg, 250 mg, 500 mg, 1 g) were added to 8 ml of a 2 mmol litre -1 BTSO 3 solution in deionised water containing or not an internal standard (DSS at 0.5 mmol litre -1 ). The suspension was incubated in 50 ml Erlenmeyer flasks at 27°C, with shaking at 200 r.p.m. After 24 hours, a cell suspension (0.2 g wet weight biomass prepared as previously described [START_REF] Haroune | Métabolisme de benzothiazoles par des souches de Rhodococcus: étude par RMN in situ[END_REF]) in 2 ml Volvic ® (Danone, Volvic, France) water was added. This mineral water was chosen for its low and constant ion content (especially carbonates that can drastically affect adsorption properties). Incubation conditions were the same as those described previously (27°C, with shaking at 200 r.p.m). Samples (500 µl) were taken regularly to be analysed by HPLC and 1 H liquid state NMR after centrifugation (12 500 g, 10 minutes). Concomitantly, 12 µl samples of the suspension (without centrifugation) were taken and introduced into a 4-mm zirconia rotor to be directly analysed by 1 H HR-MAS NMR (without any treatment). Controls without cells were prepared under the same conditions. Controls were also prepared to evaluate the impact of DSS on BTSO 3 metabolism.

Results and discussion

Adsorption and properties of glyphosate adsorbed on montmorillonite KSF Two solid-liquid ratios were used (1/100 and 1/200) and gave similar results. Isotherms of glyphosate (PMG) adsorption on this montmorillonite are all non-linear, have two steps and indicate that ligand exchange is the main adsorption mechanism (Figure 2).

Figure 2 Isotherm of glyphosate adsorption on montmorillonite KSF for a 1/200 solid-liquid ratio. X-ray diffractograms were made for material representing each point of the isotherm and indicated an increase in the basal spacing from 11.8 to 13.2 Å. This increase in the interlamellar distance appears insufficient for guest PMG between the sheets. It is clear that glyphosate may interact with a positively charged surface through its ammonium moiety. However, to be intercalated into the sheets, PMG must be oriented parallel to the layers and the minimum distance for this was calculated to be 4 Å. No other significant structural changes were observed after adsorption. The FTIR spectra of pure and exchanged montmorillonites were similar (data not shown). The content of physisorbed water was greater after adsorption of PMG. Vibrational bands of PMG were systematically masked by those of the clays. Consequently, FTIR spectroscopy is not an appropriate method in this case. Thus, we recorded 1 H MAS Hahn echo spectra with a 1 ms echo time (data not shown). However, mobile water resonance dominated the spectra, avoiding unambiguous data analysis. The same samples were subsequently hydrated (200% w/w) and analysed by 1 H 1D HR-MAS NMR. The primary aim was to mimic environmental conditions more reasonably, in which water content usually plays an important role in the fate of pollutants. Moreover, it thus may be possible to increase the mobility of the adsorbed PMG. By this means, we expected sharper signals. The 1 H HR-MAS spectra of hydrated samples are presented in Figure 3(b-d). Resonances in the range 2.1-2.3 p.p.m. belong to 'impurities' of montmorillonite 'salted out' during adsorption of PMG. These resonances were not present in the PMG solution and they were not observed when montmorillonite was analysed just after swelling (Figure 3a). The major features of these spectra were as follows. (i) The high resolution of the spectra containing PMG, with its resonances clearly observed at 3.24 and 3.82 p.p.m., the coupling constant (11.5 Hz) being observed on some spectra. (ii) PMG signal intensities increased with the amount of PMG loaded onto the surface. It indicates that NMR preserves its quantitative properties despite the heterogeneous state of the samples. (iii) Signals were rather sharp, suggesting a relatively weak interaction between PMG and the negatively charged surface. This hypothesis is reasonable bearing in mind that PMG must interact with the montmorillonite surface by its ammonium moiety, contrary to previously published studies on goethite in which PMG entered the coordination sphere of iron via one of its phosphonate oxygens [START_REF] Sheals | Adsorption of glyphosate on goethite: molecular characterization of surface complexes[END_REF]. Further experiments are in progress in our group to confirm the nature of the interaction of PMG with the surface of this montmorillonite.

Figure 3 1 H HR-MAS spectra of hydrated (200% w/w) PMG-montmorillonite phases obtained after PMG adsorption for a 1/200 solid-liquid ratio (spinning rate: 3 kHz). From bottom to top: Cs = 0, 0.12, 0.16 and 0.29 mmol g -1 . Note that (a) corresponds to the spectrum of the hydrated montmorillonite.

Thus, to increase our knowledge of the mechanisms involved at the solid-liquid interface, we decided to simplify the solid model.

MCPA adsorption

To evaluate the potential of MAS NMR to study interactions between MCPA and fully characterized hydrotalcite-like materials (LDHs), adsorption isotherms were determined in water or deuterated water. The shape of the isotherms makes it difficult to classify them. The isotherms resemble S-type isotherms but tend to L-type for Ce 1.5 mmol litre -1 . The changes from S to L types within the same isotherm are likely to be due to changes from external to interlayer adsorption. Indeed, at a Ce value of 1.3 mmol litre -1 , intercalation proceeds via an increase of the basal spacing from 7.94 Å for [Mg 3 AlCl] to 22.1 Å for [Mg 3 AlMCPA] as shown by powder X-ray diffraction. We have previously shown that 13 C CP MAS spectra recorded on dry samples clearly showed the presence of adsorbed and intercalated MCPA in the clay samples [START_REF] Combourieu | Differentiation of mobile and immobile pesticides on anionic clays by 1 H HR MAS NMR spectroscopy[END_REF]. The various carbons of the MCPA molecule did not shift compared with free MCPA. A slight difference of relative CO 3 2-and C 1 signal intensities for the two populations (adsorbed and intercalated) was due to the poorer efficiency of the polarization transfer between 1 H and 13 C nuclei located at the surface. Improved resolution of the intercalated MCPA spectrum can be explained by greater structural order of this solid phase. Solid state 1 H MAS experiments made on both adsorbed and intercalated clays showed very broad signals and did not allow differentiation of both populations of MCPA. This is easily explained by the presence of a large number of protons in LDHs, mainly from hydroxides, structural and physisorbed water. To solve this problem, adsorption isotherms were obtained in deuterated water. The 1 H MAS spectrum corresponding to Ce (1 mmol litre -1 ) is shown in Figure 4(d) and was compared with that of intercalated MCPA (Figure 4c). Greater resolution of the spectra was possible but adsorbed and intercalated samples could not be differentiated by this means. The next step was to hydrate the samples strongly and to record the 1 H HR-MAS NMR spectrum at a slow spinning rate (< 6 kHz). As mentioned above, in HR-MAS NMR, the signals detected basically reflect the degree of mobility of the species loaded onto the surface of a solid matrix: very mobile molecules give narrow signals, close to those of liquid-state NMR spectra. In contrast, when the strength of the interaction increases, the signals are broader. In this way, despite the massive presence of water in the samples, we were able to differentiate adsorbed versus intercalated MCPA [START_REF] Combourieu | Differentiation of mobile and immobile pesticides on anionic clays by 1 H HR MAS NMR spectroscopy[END_REF].

The adsorbed species gave sharp signals, close to those of liquid state 1 H NMR ( coupling constants are visible), indicating great mobility at the solid-aqueous interface. In contrast, the intercalated species gave very wide, unresolved resonances due to their strong interactions with the clay. Thus, it appears that HR-MAS NMR performed on greatly hydrated samples was suitable to discriminate different species (mobile and immobile) of a pesticide loaded onto the surface of anionic clays. In order to generalize this simple approach to other pollutants and materials, we have investigated the behaviour of another organic pollutant on LDHs.

Behaviour of 2-benzothiazole sulphonate loaded on anionic clays

BTSO 3 adsorption. The adsorption on the chloride phase was stronger for the 1/1000 solid-liquid ratio (Figure 5). It may be due to a more favourable dispersion effect. The BTSO 3 adsorption on the carbonate phase (1/1000 ratio) was less strong than for the chloride one (Figure 5a). This result, enhanced for Ce < 1 mmol litre -1 , is explained by the strong affinity of carbonate ions for the positively charged LDH surface. Indeed, for Ce < 1 mmol litre -1 competition by carbonate affected BTSO 3 adsorption at the surface. With a 1/20 solid-liquid ratio, no significant BTSO 3 adsorption was observed for this carbonatecontaining phase (data not shown) while little adsorption occurs for the chloride phase (Figure 5b), with Cs values roughly 100 times less than for the 1/1000 solid-liquid ratio. For the various phases, the different solid-liquid ratios and for each point of the isotherms, dry samples were analysed by X-ray diffraction, FTIR and MAS NMR spectroscopy. However, to simplify the following discussion, only results concerning the chloride phase are presented because conclusions are similar for all phases. For a 1/20 solid-liquid ratio, the XRD patterns did not reveal any modification of mineral structures compared with the precursor phase, whatever the initial concentration of BTSO 3 . However, for a 1/1000 solid-liquid ratio, new diffraction peaks appeared at 2c/3 (c = 2 mmol litre -1 ) (Figure 6). Intercalation of BTSO 3 anions in the lamellar host structure was clearly demonstrated by the increase in the basal spacing, from 7.68 Å for the chloride precursor to 18.2 Å for the organic intercalate (Figure 6). This distance suggests that the sulphonate moiety interacts directly with the positively charged mineral surface, the benzene ring being perpendicular to the layers. No intermediate distance was observed on spectra below concentrations of 2c/3, indicating that the adsorption -intercalation process was an anion exchange mechanism.

Figure 6 (a) X-ray diffraction patterns recorded after adsorption of BTSO 3 on Mg 3 AlCl material for a 1/1000 solid- liquid ratio. From top to bottom: c (2 mmol litre -1 ), 3c/4, 2c/3, c/2, c/3, c/4, c/5, c/10, c/20, blank. (b) Expanded region.

FTIR spectra of the Mg 3 -Al-Cl precursor and the BTSO 3 exchanged samples in a solid-liquid ratio of 1/20 were identical. No vibrational band of BTSO 3 was visible, although the adsorption isotherm clearly indicated an adsorption process (Figure 7). For a 1/1000 solid-liquid ratio, vibration modes of BTSO 3 were visible from concentrations of c to c/4 but not below. The S=O band was shifted from 1250 to 1222 cm -1 after exchange, suggesting greater covalent character. The C=N band (1260 cm -1 ) was unaffected by adsorption and/or intercalation during exchange. This result confirmed that BTSO 3 interacts with the surface by its sulphonate moiety. However, the spectra did not show any change between adsorbed and intercalated samples. This result indicates a similar interaction between the pollutant and clays during adsorption and intercalation, with BTSO 3 being perpendicular to the sheets.

MAS NMR

To compare FTIR spectra recorded on dry samples with NMR data, CPMAS 13 C experiments were performed on dry samples (Figure 8). Resonances between 119 and 130 p.p.m. correspond to carbons C4, C5, C6 and C7 (see Figure 8 for carbon numbering). The apparent loss of a resonance in Figure 8(b) is due to a small variation in chemical shift consequent on a π-π stacking effect between two BTSO 3 aromatic rings. Moreover, the poorer resolution -probably due to a greater disorder at the surface after adsorption of BTSO 3 -does not allow observation of all resonances. Small variations in carbons C3a and C7a 13 C chemical shifts and in the shape of signals were observed between pure and adsorbed and/or intercalated BTSO 3 samples. The C2 resonance was also shifted by 3 p.p.m., which suggests the involvement of the sulphonate group in the interaction with clays. However, these slight changes do not allow us to determine a particular geometry for the pollutant. The same effect as that described for MCPA was observed for intensities. Quantities of BTSO 3 loaded in intercalated samples were about 10 times greater than those present in adsorbed samples. Consequently, the source of protons was bigger and the polarization transfer more efficient for intercalated samples. Therefore, CPMAS 13 C NMR did not provide new information on the kind of interactions involved. Nevertheless, it should be noted that both 1/20 and 1/1000 solid-liquid ratios gave identical results for intercalated versus adsorbed samples. To obtain more information from NMR data, 1 H Hahn echo experiments were carried out on dry samples (Figure 9). Hahn echo experiments were carried out for the two solid-liquid ratios and each point of the isotherms was analysed by this sequence. Varying echo times provided useful results. At an echo time of 410 µs, the residual of the broadline component was still visible (data not shown). For an echo time of 825 µs, the spectrum was dominated by the high-resolution component and the intensity of the broadline component was greatly reduced. Quantification was then possible. Above 900 µs, most of the high-resolution component was lost. For the 1/20 solid-liquid ratio, 1 H Hahn echo spectra showed that signal intensities increased with the quantity of BTSO 3 adsorbed onto the surface. Conversely, the 1 H NMR signals decreased for the 1/1000 solid-liquid ratio while the amount of BTSO 3 loaded onto the material increased. These results were complementary to the FTIR and X-ray diffraction pattern data. They may be explained thoroughly because a complete mathematical development exists for the Hahn echo experiment [START_REF] Bilski | Solid echo in the slow-motion region. Effects of the finite pulse widths[END_REF]. It has been established for the two types of solid echo experiments (π/2-τ/2-π-τ/2-AQ and π/2τ/2-π/2-τ/2-AQ) that time position and amplitude of the solid-echo maximum depend on the correlation time, τ c , of molecular motion, and on the width of the RF pulses. When the pollutant is constrained near the surface or intercalated into the lamellar host, a slow-motion region may be reached. Consequently, the amplitude of the echo signal is reduced and its maximum is shifted to the end of the second pulse. It thus appears that the signal intensity in a Hahn echo experiment can be used to appreciate the global 'molecular dynamic process' or more generally the 'macroscopic mobility' of an organic pollutant loaded onto the surface of a solid matrix. Thus, the use of such a NMR experiment may be appropriate only when there is little adsorption, which is the dominant situation in the environment.

H HR-MAS 1D experiments

Further experiments were carried out on greatly hydrated (200% w/w) samples in order to appreciate the various degrees of mobility of the pollutant. The BTSO 3 signals were well resolved. For the 1/1000 solidliquid ratio, BTSO 3 concentrations found in heterogeneous media by HR-MAS and in solution by liquidstate NMR were similar. This indicates that under these conditions HR-MAS only reflects the fraction of the pollutant with a great mobility; that is, interacting weakly with the surface. Thus, the small fraction of BTSO 3 strongly adsorbed onto clays (as shown by adsorption isotherms) cannot be observed by HR-MAS, contrary to 1 H MAS NMR performed on dry samples with high-power amplifiers. This result is consistent with that found for MCPA. For the ratio 1/20, the same results were observed. The sole limitation is the relatively high detection threshold of HR-MAS (measured at 30 µM in our conditions) because adsorbed quantities are less in this case (Figure 5). Then, we estimated the strength of the interaction in the case of weak adsorption via longitudinal relaxation times (T 1 ) of both BTSO 3 and the internal standard (TSPd 4 ).

Longitudinal relaxation time (T 1 ) measurements by 1 H HR-MAS

An inversion-recovery sequence including water saturation during recycle and recovery delays was used. In the presence of clays, a decrease of T 1 was observed for all signals (Table 1), thus indicating a priori less mobility of organic compounds. This may be due to weak interaction with the surface and is consistent with results previously described. [START_REF] Haroune | Métabolisme de benzothiazoles par des souches de Rhodococcus: étude par RMN in situ[END_REF]. In the presence of clays, the degradation rate of BTSO 3 decreased substantially due to the poorer bioavailability of the pollutant. The potential of 1 H HR-MAS NMR spectroscopy to study this biodegradation in the presence of clay was tested. Our aim was to check whether the fraction of the pollutant interacting with clays (as suggested by the T 1 data) was less bioavailable than that 'free' in the medium. The kinetics of degradation obtained by 1 H HR-MAS (without centrifugation) were compared with those analysed by HPLC and liquid state 1 H NMR after centrifugation. In this case, DSS was chosen as the internal standard. Indeed, it is not transformed either chemically or biochemically in the presence of clays, contrary to TSPd 4 . Moreover, it is not significantly adsorbed onto LDHs. Finally, DSS does not affect the bacterial metabolism of BTSO 3 .

The 1 H HR-MAS spectra of these complex and heterogeneous mixtures are presented in Figure 10. Note that despite the presence of cells and clay particles, spectra were of good quality, with BTSO 3 signals sharp and well resolved. This sharpness suggests a great mobility of the pollutant. The analyses of supernatants after centrifugation (12 500 g, 10 minutes) showed that with 10 mg of LDHs, no difference was observed compared with controls without clays (data not shown). From 250 mg to 1 g of LDHs, the degradation rate decreased slightly but not significantly. The pH, increasing from 8.3 to 8.9 with the amount of hydrotalcite (from 10 mg to 1 g), was not responsible for this slight decrease. Controls without clay particles but with various ions introduced in the medium (as HCl, MgCl 2 or MgCO 3 , NaCl or NaOH) revealed that they were responsible for this decrease (inhibition of some metabolic pathways). Nevertheless, no metabolites of BTSO 3 were observed in either case, BTSO 3 being partially mineralized.

Figure 10

In situ 1 H HR-MAS NMR spectra of samples taken at 5 minutes, 2, 4, 6 and 8 hours of incubation of 2 mmol litre -1 BTSO 3 with resting cells of Rhodococcus erythropolis in the presence of 10 mg anionic clays (Mg 3 AlCO 3 ).

The analysis of the medium performed directly by 1 H HR-MAS without centrifugation showed a similar degradation curve even if only small differences were observed in the degradation compared with results obtained from HPLC or 1 H liquid-state NMR of supernatants (Figure 11). The most important change concerned the initial BTSO 3 concentration, which is greater in the case of HR-MAS by 15%. Several hypotheses could explain this. (i) A small fraction of the pollutant interacting with the surface was not present after centrifugation and thus neither observed by HPLC nor 1 H liquid state NMR. (ii) The interaction affecting BTSO 3 and DSS relaxation properties may interfere in quantification. However, T 1 of both BTSO 3 and DSS decreased by about 10%. Consequently, the relative concentration may not be different. (iii) The spinning rate increased molecular diffusion and the LDH adsorption capacities of one compound compared with batch equilibrium experiments made as described in the OECD Guideline 106 (OECD, 2000) (i.e. not in a HR-MAS NMR rotor). This hypothesis was not consistent with the T 1 data and quantification experiments carried out under the same conditions (solid-liquid ratio, spinning rate, temperature). Thus, one of the most probable reasons was the influence of cells. Indeed, the adsorption of BTSO 3 or DSS on cells was highly likely as such phenomena have often been described in liquid media.

A similar hypothesis would be that cells generate macromolecules that affect adsorption properties of BTSO 3 or DSS. In contrast, the 1 H HR-MAS NMR showed that the organic compounds interact with the solid at the solid-liquid interface, although adsorption isotherms did not suggest it. This requires further investigation.

Conclusions

We found that although NMR application is limited to laboratory experiments, it is a unique tool to assess these mechanisms at a molecular level. It appears that (HR) MAS NMR spectroscopy allows direct -'in situ'observation of the adsorption mechanism at the surface of a colloid. Although observed chemical shifts correspond to an average of several molecules on the NMR time-scale, it clearly appears in this work that the intensity of the detected signals can be analysed in terms of intensity of the interaction involved. The mobility of a pollutant at the surface of solid matrix can thus be assessed; in particular, HR-MAS is very promising in differentiating molecular species according to their degree of mobility in hydrated matrices. In the present communication, we have illustrated the potential of various MAS NMR approaches with the case studies of the interactions of three organic pollutants, glyphosate, MCPA and BTSO 3 , with clay materials. It was shown that CPMAS 13 C NMR did not give any conclusive information; in contrast 1 H (HR) MAS NMR gave complementary information including T 1 values, mobility and quantification of this pollutant loaded at the surface of a solid matrix. Although the NMR technique remains quite insensitive, 1 H can be detected relatively easily at natural abundance (vide supra). We have shown that these techniques could be applied both on synthetic anionic clays close to hydrotalcites but also on natural cationic clays such as montmorillonites. This methodology was also successfully applied to monitor the biodegradation of xenobiotics by microorganisms in model soil, directly in situ; in the future it may be interesting to correlate the level of a pollutant loaded at the surface of a soil component -and the interactions involved -to its bioavailability. Dynamic properties of the pollutants, obtained by various relaxation measurement experiments performed on hydrated samples, will be reasonably key points to reach this objective.

Figure 4

 4 Figure 4 1 H MAS spectra of hydrated samples obtained during the adsorption (a), the intercalation (b) of MCPA on the Mg 3 AlCl phase. The exchanges were carried out in D 2 O. 1 H MAS spectra of dry samples: (c) intercalated, (d) adsorbed and (e) precursor material.

Figure 5

 5 Figure 5 Isotherms of BTSO 3 adsorption (a) on Mg 3 AlCO 3 (×) and on Mg 3 AlCl for a 1/1000 solid-liquid ratio (▪) and (b) on Mg 3 AlCl for 1/20 solid-liquid ratio (▴).

Figure 7

 7 Figure7FTIR spectra of Mg 3 AlCl after adsorption of BTSO 3 ; (a) 1/1000 and (b) 1/20 solid-liquid ratios.

Figure 8

 8 Figure 8 CPMAS 13 C NMR spectra of (a) pure, (b) adsorbed and (c) intercalated (co-precipitated) BTSO 3 on the Mg 3 AlCl phase. Spinning rate: 12 kHz.

Figure 9

 9 Figure 9 1 H MAS Hahn echo spectra of the BTSO 3 -Mg 3 AlCl phase obtained (a) for 1/20 and (b) 1/1000 solid-liquid ratios. The percentages correspond to signal area normalized to the greatest concentration used in the adsorption isotherms. Blank: spectra of precursor, without BTSO 3 .

Figure 11

 11 Figure 11 Time course of BTSO 3 concentration in the presence of 10 mg of Mg 3 AlCO 3 LDH phase determined by 1 H liquid state NMR after centrifugation (○) and by 1 H HR-MAS NMR performed directly on the raw medium (□).

Table 1 1

 1 H Longitudinal relaxation of BTSO 3 signals and TSPd 4 measured directly by HR-MAS in the presence or the absence of clays

		TSPd 4		BTSO 3
		0 p.p.m.	7.64 p.p.m.	7.70 p.p.m.	8.14 p.p.m.
	Without clays	3.511	4.409	4.278	5.660
	With clays	2.948	3.695	3.171	4.646
	BTSO 3 metabolism in the presence of clays
	We have recently established the full metabolic pathway of BTs, including BTSO 3 , by Rhodococcus
	erythropolis in homogenous suspension (without clays) on a laboratory scale

Acknowledgements

N. Haroune was a recipient of a grant from the Ministère de l'Education Nationale et de la Recherche. We greatly acknowledge Martine Sancelme for her precious help in biodegradation experiments.