Cryptorchid with an Enormous Testicle Found on Post-Mortem Examination

ARTICLE IN PRESS Solid State Nuclear Magnetic Resonance 37 (2010) 60–68

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The partial 1H NMR spectra of Al–OH and molecular H2O in hydrous aluminosilicate glasses: Component-Resolved analysis of 27Al–1H cross polarization and 1H spin-echo MAS NMR spectra Wim J. Malfait a,, Xianyu Xue b a b

Institute for Geochemistry and Petrology, ETH Zurich, Sonneggstrasse 5, 8092 Zurich, Switzerland Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193, Japan

a r t i c l e in f o

a b s t r a c t

Article history: Received 5 March 2010 Available online 9 April 2010

The Component-Resolved methodology was applied to 1H spin-echo and 27Al–1H cross polarization (CP) MAS NMR data of aluminosilicate glasses. The method was able to resolve two components with different T2 relaxation rates, hydroxyl groups (OH) and molecular water (H2Omol), from the spin-echo data and to determine partial spectra and the relative abundances of OH and H2Omol. The algorithm resolved two to three components with different 27Al–1H CP dynamics from the 27Al–1H cross polarization data; the obtained partial NMR spectra for Al–OH are in excellent agreement with those obtained previously from the difference spectra between spectra with various contact times and confirm previous quantitative results and models for the Al–OH, Si–OH and H2Omol speciation (Malfait and Xue, 2010). & 2010 Elsevier Inc. All rights reserved.

Keywords: Aluminosilicate glasses Water speciation NMR spectroscopy Cross polarization Spin-echo CORE Quantification Algorithm

1. Introduction As the most abundant volatile component, water has a strong influence on the type, rate and outcome of most magmatic processes. Because of this importance, the speciation of water in aluminosilicate glasses and melts has been the subject of intense spectroscopic study. As a result, it is now generally accepted that water is present in silicate glasses and melts as molecular water (H2Omol) and hydroxyl groups (OH); OH is the more abundant species in samples with a low water content, whilst H2Omol the most abundant species at higher water content [1–4]. However, the nature of the hydroxyl groups in aluminosilicate glasses has long been controversial: dissolution mechanisms in which water depolymerizes the melt through the formation of Si–OH and Al–OH groups, as well as dissolution mechanisms in which water leaves the degree of melt polymerization unchanged, have been proposed [5–11]. Recently, cross polarization (CP) experiments from 27Al and 29Si to 1H have unambiguously demonstrated the presence of Si–OH and Al–OH groups [10,11], confirming the depolymerization mechanism and some (semi-)quantitative data on the relative abundance of the different types of OH groups (e.g. Si–OH, Al–OH, Mg–OH) has become available [9–17].

 Corresponding author. Fax: + 41 44 6321636.

E-mail address: [email protected] (W.J. Malfait). 0926-2040/$ - see front matter & 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.ssnmr.2010.04.002

In a previous study [11], we determined the partial 1H NMR spectrum for H2Omol from spin-echo MAS NMR spectra collected at different echo delays. In addition, we determined the partial 1H NMR spectrum for Al–OH from 27Al–1H CP MAS NMR data and used this partial spectrum to quantify the Al–OH content for a set of hydrous glasses along the SiO2–NaAlSiO4 join from their quantitative 1H MAS NMR spectra. With this approach, we were able to tightly constrain the relative abundances of Si–OH and Al–OH. The shapes of the partial Al–OH spectra were defined as the difference spectra between 27Al–1H CP spectra collected at various contact times. However, this approach has been criticized because, in order to properly scale the CP spectra before taking the difference spectra, we had to a priori impose a spectral region (typically the range 47 ppm) with zero intensity for Al–OH. Recently, Hedin et al. [18] demonstrated the suitability of the Component-Resolved (CORE) method to extract partial NMR spectra from a CP dataset without a priori assumptions about the shape of these partial spectra. The method is based on simultaneously fitting a set of spectra as linear combinations of the partial spectra associated with a limited number of species. Programs based on this principle have been available for over 3 decades [19] and have been applied to a wide range of spectroscopic methods, including spectrophotometry [20,21], pulsed-gradient spin-echo NMR spectroscopy [22–25] and Raman spectroscopy [26–29]. In the present study, we have applied the CORE methodology to our 27Al–1H cross polarization and 1H spin-echo MAS NMR data

ARTICLE IN PRESS W.J. Malfait, X. Xue / Solid State Nuclear Magnetic Resonance 37 (2010) 60–68

in order to determine the partial 1H NMR spectrum of Al–OH groups and H2Omol in aluminosilicate glasses, without any a priori assumptions about its lineshape. The results confirm our previously determined partial spectra for H2Omol and Al–OH and underscore the suitability of combining partial NMR spectra, extracted from cross polarization or spin-echo datasets, with quantitative NMR spectra to determine the relative abundances of species with overlapping partial spectra.

61

the Hartmann-Hahn matching condition and spin-temperature inversion was included in the phase cycle to eliminate the signal from direct polarization. All spectra were collected with a spinning rate of 20 kHz. All spectral and data processing was done in Matlab, using matNMR subroutines for linear prediction, apodization, Fourier transformation and the phasing of the spectra [34] and the lsqnonlin solver from the Matlab Optimization Toolbox for the fitting routines. The algorithms that were written to implement the fitting strategy outlined below are available in the Supplementary Information.

2. Experimental In this study, we are applying a new fitting strategy to previously published 27Al–1H CP and 1H spin-echo MAS NMR data for variable contact or delay times for a set of well characterized hydrous glasses along the SiO2-NaAlSiO4 join [11]; a full description of the sample synthesis and characterization and NMR methodology can be found there and will only be briefly summarized here. Hydrous glasses (0.5–2 wt% water) were prepared by loading the appropriate amount of deionized water and 100 mg of anhydrous glass into Pt capsules (3 mm outer diameter, ca. 2 cm long). The welded capsules were suspended from a Mo wire in the hot zone of an internally heated pressure vessel and held at 1773 K and 200 MPa for 4 h. The samples were isobarically quenched by dropping the capsules to the cold zone (ca. 333 K) of the pressure vessel (estimated quench rate: 200– 500 K/s). The water content of the recovered glasses was determined by quantitative 1H MAS NMR, using adamantane (C10H16) as a standard (measured under identical conditions); the results and synthesis conditions are listed in Table 1, as well as the estimated glass transition temperature and OH/H2Omol ratio [30,31]. For the quantitative 1H MAS NMR spectra, the DEPTH sequence, which contains three back-to-back pulses (p/2–p–p) with a phase cycle of 16, was used to minimize spurious resonances from the probe [32]. The remaining background was removed by subtracting the FID for an empty rotor. For the 1H DEPTH experiments, recycle delays of five times the spin lattice relaxation time (T1) were used to ensure full relaxation of the magnetization (8 soT1o66 s, depending on water content) and 16 to 64 scans were averaged for each sample. The 1H spin-echo data were collected with the rotor-synchronized spin-echo pulse sequence (p/2–t–p–t–acquisition, 50 mso t o12.8 ms). The 27Al–1H CP spectra were collected with a low RF field strength for the contact pulses for 27Al (2.8 kHz, unless otherwise noted), yielding a small value for the adiabatic passage parameter and subsequent high sensitivity [15,33]. The power for the proton channel was ramped (by 5.3 kHz) to improve the stability of

3. Fitting strategy 3.1. General principle The CORE method is based on simultaneously fitting a set of NMR spectra as linear combinations of the partial spectra associated with a limited number of species and depends on the following assumptions:

 Each NMR spectrum is a linear combination of the partial spectra of a limited number of species; in matrix form, this can be written as Aij ¼ Cik  ekj

ð1Þ

where i,j,k are the spectrum index, chemical shift values and species, respectively; Aij is the matrix of CP or spin-echo intensities as a function of chemical shift and contact time or spin-echo delay time Cik is the matrix of the coefficients, related to the spin-echo decay or CP dynamics for each species, and ekj contains the partial NMR spectrum for each species,

Table 2 Principal Component Analysis. Sample

Eigenvalues of the covariance matrix PC1

PC2

PC3

PC4

PC5

PC6

0.072

0.006

0.005

0.002

0.142 0.032 0.022 0.007 0.010 0.031

0.017 0.005 0.007 0.005 0.007 0.025

0.005 0.002 0.005 0.003 0.004 0.015

1

nas033zH2

H spin-echo data 97.878 2.037

27

nas008zH1c nas016zH1 nas025zH1 nas033zH1 nas042zH1 nas050zH1b

1

Al- H cross polarization data 96.232 3.068 0.535 96.332 3.552 0.078 93.168 6.745 0.053 96.389 3.549 0.048 97.955 1.995 0.030 99.508 0.380 0.042

Table 1 Hydrous glasses: composition, synthesis conditions, glass transition temperature (Tg) and water speciation. Sample

nas008zH1c nas016zH1 nas025zH1 nas033zH1 nas033zH2 nas042zH1 nas050zH1b a

Anhydrous compositiona

1

H NMR

Literature estimates

Na2O (wt%)

Al2O3 (wt%)

SiO2 (wt%)

Al/(Al+ Si) (molar ratio)

H2Otot (wt%)

P (MPa)

Tmelt (K)

tmelt (h)

Tgb (K)

OH/H2Ototc

4.2 8.1 11.8 15.3 15.3 18.7 21.8

6.9 13.3 19.4 25.2 25.2 30.7 35.9

89.0 78.6 68.7 59.5 59.5 50.7 42.3

0.083 0.167 0.250 0.333 0.333 0.417 0.500

0.93 0.79 0.93 0.62 1.97 0.84 0.54

200 200 200 200 200 200 200

1773 1773 1773 1773 1773 1773 1773

4.5d 4.0 4.0 4.0 4.0 4.5d 4.0

822 838 822 861 749 832 874

0.82 0.84 0.81 0.88 0.61 0.82 0.89

Composition as prepared, confirmed by electron microprobe (Malfait and Xue [11]). Estimated from Morizet et al. [30] for Tg corresponding to the Cp maxima. c Estimated from Ohlhorst et al. [31] for a Tg derived from Morizet et al. [30] and H2Otot from NMR. d Capsules did not drop on first run (4 h), but did drop after a second run of 30 min. b

Synthesis conditions

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25. 6 ms

T2=0.58 ms; 30% T2=9.4 ms; 70%

Intensity (arb. units)

12. 8 ms

6. 4 ms

3. 2 ms

Echo intensity (arb. units)

1. 6 ms

12

0. 8 ms

10

8

6

4

2

0

-2

Chemical shift (ppm) Fig. 2. Partial spectra obtained from the 1H spin-echo spectra with the core methodology for nas033zH2 glass (Al/(Al+ Si) ¼ 0.33, 1.97 wt% water). The relatively narrow component with the shortest T2 relaxation time (dotted line) can be assigned to H2Omol. The other component contains the signal from hydroxyl groups (Si–OH and Al–OH). The integrated intensity of the OH component, extrapolated to a delay of zero, contains 70% of the signal, in reasonable agreement with the OH/H2Omol ratio determined by infrared spectroscopy (66%) [11,37].

0. 4 ms

0. 2 ms

  0. 1 ms

8

6 4 2 Chemical shift (ppm)

Echo intensity (arb. units)

10

0

-2

T2=0.58 ms T2=9.4 ms

thus only non-negative values. During the fitting, the shapes of these partial spectra are treated as unknowns, i.e. no a priori assumptions about the peak shapes are needed. The shapes of the partial NMR spectra are independent of contact time or spin-echo delay time. The spin-echo decay or CP dynamics of each species can be described by an analytical expression with a small number of fitting parameters.

The goal of the optimization is to solve simultaneously for the partial NMR spectra, ekj, and the parameters for the spin-echo decay or CP dynamics by minimizing the squared deviation between the measured and calculated spin-echo or CP intensity, summed over all spin-echo delays/contact times and all chemical shift values. The objective function for the minimization is then: #) ( " X X ð2Þ ðAij Cik  ekj Þ2 F¼ i

j

3.2. Number of species

0

5

10

15

20

25

Time (ms ) Fig. 1. 1H spin-echo NMR spectra and two-component fits for nas033zH2 glass (Al/(Al+ Si)¼ 0.33, 1.97 wt% water); the intensities are normalized to the same number of acquisitions per spin-echo delay. The measured spectra are indicated by the black dots (only one out of 3 shown for clarity); the fitting envelope by the black line; the fitted components by the blue lines and the residual by the red line. The bottom figures show the echo decay (summed over the entire chemical shift range) as a function of the delay time; dots are measured data; black line fitting envelope and blue lines indicate the intensities of the fitted components. The spectra were collected with a spinning rate of 20 kHz, a recycle delay of 12 s (1.25 times T1) and 16–32 acquisitions per spin-echo delay. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

We have used Principal Component Analysis (PCA) to determine the number of independent contributions to the set of spectra Aij, and thus, for the number of species that need to be considered in the treatment (k). PCA transforms a number of possibly correlated values into a smaller number of uncorrelated values (PC), where the first PC accounts for as much of the variability as possible and each succeeding component accounts for as much of the remaining variability as possible. For the spin-echo data, the third component accounts for just 0.07% of the variance in the spin-echo spectra, indicating that two components are sufficient to fit the spin-echo data. For the 27Al–1H CP data, the third principal component accounts for less than 0.1% of the variance in the CP spectra of the more Al-rich samples (Al/(Al+Si)40.1) (Table 2). For the most Al-poor sample, the third principal component accounts for 40.5% of the variance, indicating that a third component may be needed to fit the CP spectra (see below).

ARTICLE IN PRESS W.J. Malfait, X. Xue / Solid State Nuclear Magnetic Resonance 37 (2010) 60–68

nas008zh1c

nas016zh1

nas025zh1

8 ms

4 ms

2 ms

8 ms

CP intensity (arb. units)

CP intensity (arb. units)

CP intensity (arb. units)

8 ms

63

4 ms

2 ms

4 ms

2 ms 1 ms 1 ms

1 ms

0.5 ms 0.5 ms

0.5 ms

0.25 ms

0.25 ms

0.25 ms

8

6

4

2

0

-2

10

0

2

4

6

8

8

10

0

2

Contact time (ms)

4

2

0

-2

10

4

6

8

10

0

2

0

-2

4

6

8

10

nas050zh1

8 ms

CP intensity (arb. units)

CP intensity (arb. units)

2 ms

4

Contact time (ms)

8 ms

4 ms

6

2

nas042zh1

8 ms

8

Chemical shift (ppm)

Contact time (ms)

nas033zh1

CP intensity (arb. units)

6

Chemical shift (ppm) CP intensity (arb. units)

CP intensity(arb. units)

Chemical shift (ppm)

CP intensity (arb. units)

10

4 ms

4 ms

2 ms

2 ms 1 ms

1 ms 1 ms

0. 5 ms

0. 5 ms

0. 5 ms 0. 25 ms

0. 25 ms 10

8

0. 25 ms 6

4

2

0

-2

10

Chemical shift (ppm)

8

6

4

2

0

2 4 6 8 Contact time (ms)

10

8

6

4

2

0

-2

Chemical shift (ppm) CP intensity (arb. units)

CP intensity (arb. units)

CP intensity (arb. units)

0

10

-2

Chemical shift (ppm)

0

2 4 6 8 Contact time (ms)

10

0

2 4 6 8 Contact time (ms)

10

Fig. 3. 27Al–1H CP NMR spectra and two-component fits for 6 glasses along the SiO2–NaAlSiO4 join (RF power of 2.8 kHz for 27Al); the intensities are normalized to the same number of acquisitions per contact time. The measured spectra are indicated by the black dots (only one out of 3 shown for clarity); the fitting envelope by the black line; the fitted components by the blue lines and the residual by the red line. The smaller figures below show the CP intensities (summed over the entire chemical shift range) as a function of the CP contact time; dots are measured data; black line fitting envelope and blue lines indicate the intensities of the fitted components. The spectra were collected with a spinning rate of 20 kHz, a recycle delay of 0.5 s and 4000 to 256,000 acquisitions per contact time. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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CP intensity (arb. units)

nas008zh1c

nas016zh1

CORE CORE, 3 comp.

nas025zh1

CORE DIFF

CORE DIFF

DIFF

12

10

8

6

4

2

0

-2

12

10

8

CP intensity (arb. units)

nas033zh1

10

8

6

4

2

0

-2

12

10

2

0

-2

12

Chemical shift (ppm)

10

6

4

2

0

-2

2

0

-2

nas050zh1b

CORE DIFF

4

8

nas042zh1

CORE CORE - high RF DIFF

12

6

CORE DIFF

8

6

4

2

0

-2

12

10

Chemical shift (ppm)

8

6

4

Chemical shift (ppm)

Fig. 4. Normalized partial 1H NMR spectra for Al–OH (RF power of 2.8 kHz for 27Al, unless stated otherwise). The partial spectra obtained with the two-component CORE method (black lines) (this study), are in excellent agreement with those obtained from the difference spectra (red lines) [11]. For the nas008zH1 sample, the partial spectra for the two- and three-component fits (blue dots) agree well over the 0–3 ppm range. For the jadeite glass (nas033zH1), the partial spectra obtained with CORE from 27 Al–1H CP spectra collected with different RF power (6–7 kHz vs. 2.8 kHz) are nearly identical. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.3. Spin-echo decay

IðtÞ ¼ I0  expðt=T2Þ

ð3Þ

3.4. Cross polarization dynamics To a first approximation, and in the case of cross polarization from a spin-1/2 (S) to a spin-1/2 nucleus (I), the variation of CP intensities as a function of contact time can be described by the following two-parameter equation: IðtÞ ¼ I0 

½expðt  R1rS Þexpðt  RSI Þ ð1R1rS =RSI Þ

ð4Þ

where t equals the contact time and the relaxation rates R1rS and RSI describe the dynamics of the spin lock and cross polarization, respectively. This relation has been applied successfully to a set of 1 H–29Si CP spectra by Hedin et al. [18]. For our data, with cross polarization from a quadrupolar nucleus, high spinning rates and RAMP-CP, the spin lock conditions and CP dynamics are expected to be more complex [35,36]. An expression derived to describe cross polarization from the central transition of a quadrupolar, half-integer nucleus (S) to a spin-1/2 nucleus (I) [35] includes additional parameters, including R1rI, the rotating frame relaxation rate for spin I: IðtÞ ¼

W¼

I0 xRSI ½expððR1rS þR1rI þ RSI  ð1þ lÞ þWÞ  t=2Þ W ðexpððR1rS þ R1rI þ RSI  ð1 þ lÞWÞ  t=2Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðR1rS R1rI RSI  ð1lÞÞ2 þ 4RSI 2  l

ð5Þ

ð6Þ

nas008zH1c nas016zH1 nas025zH1 nas033zH1 nas042zH1 nas050zH1b

Normalized intensity (arb. units)

The spin-echo decay of a given component is governed by its spin-spin relaxation (T2). Assuming exponential T2 relaxation, the intensities can be expressed as a function of the echo delay (t=2t) with the equation:

12

10

8

6

4

2

0

-2

Chemical shift (ppm) Fig. 5. Normalized partial spectra for Al–OH groups for glasses with different Al contents obtained with the two-component CORE methodology. The asymmetry of the main band increases and its position shifts to higher ppm values with increasing Al content. The smaller additional peak around 7 ppm is an artifact from fitting a three-component system with just two components (see text).

where l is a scaling factor describing the different spin environments (l ¼3 for H with one Al next-nearest neighbor, l ¼3/2 for H with two Al next-nearest neighbors) and x is a correction factor related to the intensities of the spinning sidebands, assumed to be equal to 1 for our relatively high spinning rates (20 kHz). We have applied both Eq. (4) and Eqs. (5) and (6) to fit our data: both fits reproduce the data well and result in similar partial NMR spectra for the various species. For both equations, some of the fitting parameters for the CP dynamics, and in the case of Eqs. (5) and (6) also the partial NMR spectra, depend on the initial guesses

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used for the fits. This indicates that the fits are not always well constrained and occurs much more often for the fits with Eqs. (5) and (6), most likely due to the inclusion of additional fitting parameters, i.e. degrees of freedom. On this empirical basis, we have opted to use Eq. (4) to fit our data. However, even with this equation, the obtained values for R1rS and RSI are not robust. Because of the peculiarities of Eq. (4), e.g. both the numerator and denominator approach zero when R1rS approaches RSI, strongly different pairs of values for R1rS and RSI sometimes describe nearly identical curves. Thus, it is important to note that the fitted values for the parameters

65

for the CP dynamics have restricted physical meaning, given the fundamental limitations of Eq. (4) in describing the CP dynamics for quadrupolar nuclei and the fitting problems outlined above. However, the fitted shapes of the partial NMR spectra are more robust, i.e. they do not significantly depend on the initial guesses. This is because the fitted partial NMR spectra (ekj) depend on the calculated CP dynamics curve (the values of Cik) rather than the parameters that describe it (R1rS and RSI). Because the CP spectra are partially resolved, the shape of the CP dynamics curves for both species are well enough constrained, even if the parameters of the analytical expression describing them not always are.

4. Results 4.1. Spin-echo spectra The spin-echo data for the nas033zH2 sample (hydrous jadeite glass with 1.97 wt% H2O) can be well reproduced by a linear combination of two components (Fig. 1). The partial spectrum for the component with the shorter T2 relaxation time (0.61 ms) consists of a relatively narrow band around 4.5 ppm (Fig. 2) with small tales towards higher and lower wavenumbers. This component strongly resembles the difference spectra for different spinning rates, different echo delays or from samples with different water contents (hence different OH/H2Omol ratios) [11]. We assign this component to H2Omol: the stronger dipolar coupling between the protons of the water molecule causes an incomplete refocusing of the signal during the spin-echo experiments, resulting in a shorter T2 relaxation time and causing the relative contribution of H2Omol to the spin-echo spectra to decrease with increasing echo delay OH/H2Otot ¼ 61% according to Table 1. The other component has a longer T2 relaxation time (9.5 ms) and contains the signal from hydroxyl groups. The integrated intensity of the OH component, extrapolated to an echo delay of zero, contains 70% of the total signal, in reasonable agreement with the OH/H2Otot ratio determined by infrared spectroscopy (66%) [11,37] or calculated from the literature (61%) [31]. This agreement demonstrates that

4 ms

2 ms

1 ms

0.5 ms

0.25 ms

8

6 4 2 Chemical shift (ppm)

0

-2

CP intensity (arb. units)

10

0

2

4

6

8

10

CP intensity (arb. units)

CP intensity (arb. units)

8 ms

Contact time (ms) Fig. 6. Three-component fit to the 27Al–1H CP spectra of nas008zH1 (Al/ (Al+ Si)¼ 0.083, 0.93 wt% water, RF power of 2.8 kHz for 27Al); the intensities are normalized to the same number of acquisitions per contact time. The measured spectra are indicated by the black dots (only one out of 3 shown for clarity); the fitting envelope by the black line; the fitted components by the blue lines and the residual by the red line. The bottom figure shows the CP intensities (summed over the entire chemical shift range) as a function of the CP contact time; dots are measured data; black line fitting envelope and blue lines indicate the intensities of the fitted components. The spectra were collected with a spinning rate of 20 kHz, a recycle delay of 0.5 s and 23300 to 256,000 acquisitions per spin-echo delay. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

1 ppm band 4.5 ppm band 7 ppm band

0

1

2

3

4

5

6

7

8

9

10

Contact time (ms) Fig. 7. Normalized 27Al–1H CP buildup curves for the three-component fit for nas008zH1 (Fig. 6). Intensities were normalized to the intensity at 10 ms for ease of comparison. The buildup rate for the component near 7 ppm is intermediate between that of the 1 and 4 ppm components, but closer to that of the 4 ppm component.

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1 H spin-echo MAS NMR data, combined with the CORE algorithm, can provide a quantitative estimate of the OH/H2Omol speciation. However, the uncertainties of this approach are most likely much

larger than those associated with infrared [1,3,4] or static, low temperature 1H NMR spectroscopy [2]. The fits of the spin-echo data for the nas033zH1 sample (hydrous jadeite glass with 0.62 wt% H2O) did not provide any meaningful results: the CORE method was not able to resolve the small contribution of H2Omol for this sample (OH/H2Omol ¼0.90, related to its low total water content) [11,37].

8 ms 4.2.

CP intensity (arb. units)

4 ms

2 ms

1 ms

0.5 ms

0.25 ms

10

CP intensity (arb. units)

4

8 6 4 2 Chemical shift (ppm)

0

-2

x 104

3 2 1 0 0

2

4

6

8

10

Contact time (ms) Fig. 8. 27Al–1H CP NMR spectra and two-component fits for a hydrous jadeite glass (Al/(Al+ Si)¼ 0.33, 0.7 wt% water, RF power of 6–7 kHz for 27Al). The measured spectra are indicated by the black dots (only one out of 3 shown for clarity); the fitting envelope by the black line; the fitted components by the blue lines and the residual by the red line. The bottom figures show the CP intensities (summed over the entire chemical shift range) as a function of the CP contact time; dots are measured data; black line fitting envelopes and blue lines indicate the intensities of the fitted components. Notice the different CP dynamics compared to those for nas033zH1 (a nearly identical glass), collected with an RF power for 27Al of 2.8 kHz (Fig. 3). The spectra were collected with a spinning rate of 20 kHz, a recycle delay of 0.5 s and 40,000 to 60,000 acquisitions per contact time (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

27

Al–1H cross polarization data

Because we are investigating the spectral signature for the different types of hydroxyl groups, we will focus on samples for which the spectral contribution of H2Omol will be small, i.e. with low total water contents ( r1 wt% H2O), hence high OH/H2Omol ratios (Table 1). In general, the measured 27Al–1H intensities are well reproduced by linear combinations of the partial NMR spectra for two components (Fig. 3). For all samples but one, the fits reproduce both the CP spectra and the CP buildup curves well. For the nas025zH1 sample, the fit is not as satisfactory as for the other samples, due to the relatively high intensity for the CP spectra collected with a contact time of 4 ms. Excluding this spectrum from the dataset results in a goodness of fit similar to that for the other samples and partial spectra that are similar to those of the current fit (not shown). The partial spectra for both components consist of a main asymmetric band, around 1 and 4 ppm, respectively. The partial spectra for the component with the faster cross polarization rate are nearly identical to the ‘‘close-to-Al’’ component from a previous study, obtained by taking the difference spectra for a short minus a long contact time (Fig. 4) [11]. The fast 27Al–1H CP buildup rate and its increase in intensity with increasing Al content, confirms its previous assignment to Al–OH groups [9–11,38,39]. The asymmetry of the main band around 1 ppm increases and its position shifts to higher ppm values with increasing Al content (Fig. 5). For the samples with the lowest Al content (nas008zH1c and nas016zH1), and additional band, centered around 7 ppm, is present in the partial spectra. The PCA analysis shows a relatively high intensity for PC3 for these two samples (Table 2). In fact, the intensity of the 7 ppm band seems to correlate with the intensity of the third component from the PCA analysis. This could be indicative for the presence of an additional component with a specific CP buildup curve. In order to verify this hypothesis, we have fitted the 27Al–1H CP data for these samples with three components (k ¼3). For the nas008zH1 data, the CORE method is able to resolve the three components (Fig. 6). For the nas016zH1 sample, the three-component fit was not well constrained (not shown), consistent with the smaller intensity of PC3 (Table 2). The component around 7 ppm has a CP buildup rate that is intermediate between that of the 1 and 4 ppm component, but closer to that of the 4 ppm component (Fig. 7). As a result of this intermediate buildup rate, the signal from this species is divided between both components, when the CP spectra are fitted with just two components (Fig. 3). The component around 7 ppm cannot be unambiguously assigned to a particular species. The intermediate CP buildup rate of the component would be consistent with, albeit not proof of, the tentative assignment we made to Si–OH groups that are hydrogen-bonded to Al (Si–OH?O–Al) [11]. The absence of this component from the partial spectra for glasses that are more rich in Al, could then be explained by the fact that all Si–OH groups, not just Al–OH and Si–OH?O–Al, have some Al close by, which would remove the distinction in CP dynamics between hydrogen-bonded and nonhydrogen-bonded Si–OH. Alternatively, the spectra for high-silica content samples may contain signal near 3–4 ppm related to

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nas008zH1c

Intensity (arb. units)

nas025zH1

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nas016zH1

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Fig. 9. Fits of the Al–OH partial spectra (dashed lines) to the quantitative DEPTH spectra (full lines, normalized to the same maximum intensity). The relative abundance of Al–OH is directly proportional to the area of the fitted Al–OH profile. The remaining signal originates from Si–OH and H2Omol.

dynamics are different when a higher RF field is applied; as a result, the peak shape for the CP spectra depends on the RF power, with less prominent intensity for Al–OH for a given contact time. Nevertheless, the Al–OH partial spectrum obtained with the CORE methodology is nearly identical to the one obtained at the lower RF power (Fig. 4).

1 Malfait and Xue (2010) − model Malfait and Xue (2010) − data This study − data This study − model

0.9 0.8

Al−OH/OHtot

0.7 0.6 0.5

5. Discussion

0.4

In this study, we have determined the partial 1H NMR spectra for Al–OH in hydrous aluminosilicate glasses as a function of Al content with the CORE methodology, i.e. without a priori assumptions about the shape of these partial spectra, but with the explicit assumption of the functional form of the CP dynamics (Eq. (3)). The results are in excellent agreement (Fig. 4) with those of a previous study [11], where we have defined the partial 1H NMR spectra for Al–OH as the difference spectra between CP spectra with a short and long contact time, which needed the assumption that some region of the partial spectra had zero intensities, but without any a priori assumptions on the functional form of the CP dynamics. The agreement between both studies demonstrates that the partial Al–OH spectra are valid, independent of any a priori assumptions about their shape or the functional form of the CP dynamics. The only remaining assumption is that the shape of the Al–OH partial spectrum does not change as a function of the contact time, i.e. that all Al–OH have the same CP dynamics; a reasonable assumption given the narrow range of expected Al–H distances for Al–OH groups and supported by the results of the PCA analysis, i.e. the negligible intensity of PC3. The lack of intensity for Al–OH at ppm values higher than 6 ppm provides evidence that Al–OH groups do not act as hydrogen donors in strong hydrogen bonds, confirming earlier predictions from ab initio calculations [13]. Previously, we have used the Al–OH partial spectra to fit the 1 H spectra and quantify the Al–OH abundances as a function of Al content of the glasses. We then derived a set of equilibrium

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1

Al/(Al+Si) Fig. 10. The Al–OH/OHtotal ratio as a function of the Al content, determined by fitting the Al–OH partial NMR spectra obtained in the present study (Figs. 3–5) to the quantitative 1H DEPTH spectra from Malfait and Xue [11] (Fig. 9), and the modeled speciation derived from this data according to Eqs. (7)–(9). The results by fitting the Al–OH partial NMR spectra obtained by the difference method and the modeled speciation derived from those fits [11] are plotted for comparison.

Si–OH without any Al next-nearest neighbors (hence slow 27 Al–1H CP buildup rate), in addition to a broad component encompassing the entire frequency range Z2 ppm, related to Si–OH with a range of Al next-nearest neighbors (hence the intermediate 27Al–1H CP buildup rate). It is difficult to distinguish the two cases mathematically. In order to test if the partial spectrum for Al–OH depends on the RF conditions, we have applied the CORE method to 27Al–1H CP data collected on a jadeite glass with ca. 0.7 wt% water at higher 27Al RF power (6–7 kHz) during CP (Fig. 8). The CP

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reactions and constants to predict the Si–OH, Al–OH and H2Omol speciation as a function of Al and water content [11]. The confirmed validity of the Al–OH partial spectra strengthens these results. Fig. 9 shows a fit of the partial NMR spectra of Al–OH, determined by the CORE method, to the quantitative 1H DEPTH spectra [11]. The relative abundances of Al–OH are equal to the relative areas of the fitted Al–OH partial spectrum, the rest of the signal results from Si–OH and H2Omol. Fig. 10 shows the Al–OH/ OHtotal ratios as a function of the Al content, determined in Fig. 9. As expected from the good agreement between both sets of partial NMR spectra (Fig. 4), also the speciation obtained with both sets of partial spectra is in good agreement. The variation of the Al–OH/OHtotal ratio as a function of the Al content can be described by the Al-avoidance reaction (7) and a set of hydroxyl exchange reactions (8) and (9): Si–O–Si +Al–O–Al¼2 Si–O–Al with K7 ¼[Si–O–Al]2/[Si–O–Si].[Al–O–Al]

(7)

Si–O–Si +Al–OH¼Si–O–Al + Si–OH with K8 ¼[Si–O–Al].[Si–OH]/[Si–O–Si].[Al–OH]

(8)

Si–O–Al+ Al–OH¼Al–O–Al +Si–OH with K9 ¼[Al–O–Al].[Si–OH]/[Si–O–Al].[Al–OH]

(9)

Because reaction (9) is a linear combination of reactions (7) and (8), with K9 ¼K8/K7, The Al–OH/OHtotal ratio can be fitted by optimizing for 2 unknowns (K7 and K8). Fitting the speciation results from the CORE method returns values of 64 and 4.8 for K7 and K8, respectively (Fig. 10), within the 95% confidence interval (25–91 and 4.6–6.1, respectively) for the difference spectrum method [11].

6. Conclusions The Component-Resolved method resolves two components with different 1H T2 relaxation rates (OH and H2Omol) and two to three components with different 27Al–1H CP dynamics for hydrous aluminosilicate glasses, and the partial NMR spectra for these species are determined without any a priori assumptions about their lineshape. The partial NMR spectra for H2Omol and Al–OH groups are in excellent agreement with those obtained previously from the difference spectra and quantitatively support our previous results and models for the Al–OH, Si–OH and H2Omol speciation [11]. The demonstrated approach, i.e. fitting quantitative NMR spectra with partial spectra obtained with the CORE algorithm from cross polarization or spin-echo spectra, provides a new method to extract robust quantitative data from highly overlapping NMR spectra. Its main advantage is the fact that one does not require any a priori knowledge or assumptions about the shape of the partial spectra for each species. The method is directly applicable to other classes of materials and other (pairs of) nuclei.

Acknowledgments This project was supported by grant PBEZ2-118889 from the Swiss National Science Foundation to WJM and Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan to XX.

Appendix A. Supplementary materials The online version of this article contains additional supplementary data. Please visit doi:10.1016/j.ssnmr.2010.04.002.

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