Site-resolved 2H relaxation experiments in solid materials by global line-shape analysis of MAS NMR spectra

Site-resolved

2

H relaxation experiments in solid materials by global

line-shape analysis of MAS NMR spectra

E.L. Lindh

a,b,c

_{, P. Stilbs}

a

_{, I. Furó}

a,⇑ a

Division of Applied Physical Chemistry, Department of Chemistry, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden

b

Wallenberg Wood Science Center, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden

c

Innventia AB, Box 5604, SE-114 86 Stockholm, Sweden

a r t i c l e i n f o

Article history:

Received 16 February 2016 Revised 20 April 2016 Accepted 25 April 2016 Available online 26 April 2016 Keywords:

Solid state NMR Magic angle spinning Spectral resolution Chemical shift Longitudinal relaxation

a b s t r a c t

We investigate a way one can achieve good spectral resolution in2_{H MAS NMR experiments. The goal is}

to be able to distinguish between and study sites in various deuterated materials with small chemical shift dispersion. We show that the2_{H MAS NMR spectra recorded during a spin-relaxation experiment}

are amenable to spectral decomposition because of the different evolution of spectral components during the relaxation delay. We verify that the results are robust by global least-square fitting of the spectral series both under the assumption of specific line shapes and without such assumptions (COmponent-REsolved spectroscopy, CORE). In addition, we investigate the reliability of the developed protocol by analyzing spectra simulated with different combinations of spectral parameters. The performance is demonstrated in a model material of deuterated poly(methacrylic acid) that contains two2_{H spin}

popu-lations with similar chemical shifts but different quadrupole splittings. In2_{H-exchanged cellulose}

con-taining two 2_{H spin populations with very similar chemical shifts and quadrupole splittings, the}

method provides new site-selective information about the molecular dynamics.

Ó 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Deuterium (2_{H) has several advantageous features that}

facili-tate its use when investigating the molecular structure and

dynamics of solid materials[1]. First, its dominant spin coupling

is quadrupolar and therefore2_{H relaxation reports about the}

rela-tively simple re-orientational (as opposed to coupled translational/

re-orientational dynamics relevant for1_H–1_{H dipole–dipole}

cou-pling) dynamics of the spin-bearing species. Hence, quadrupolar relaxation lends itself well to molecular dynamics (MD)

simula-tions. Secondly,2_{H has a relatively weak quadrupole moment that}

presents no excessive methodological demands (such as

radiofre-quency power). Thirdly,2_{H has a low natural abundance yet}

suit-able isotope-enriched compounds are readily availsuit-able. Hence,2_H

NMR permits the user to assess site selectivity via, for example, exchange processes. This last feature has been extensively

exploited in structural biochemistry[2].

A large number of studies have been performed using2_{H as the}

probe of molecular properties; examples are dynamics of silanol

groups in silica gels and nanoparticles [3,4], methylene group

dynamics[5], conformations of membrane lipids[6], dynamics of

different segments of polymer chains[7], distinguishing among

and characterizing polymorphs[8] and hydrogen-bond

arrange-ments in various materials [9,10]. Typically, such studies

con-cerned2

H populations at respective single sites in which case the whole spectrum reported on the same phenomenon. In solid or

semisolid materials with non-zero static quadrupole coupling[1],

the spectral intensities at particular frequencies correspond to molecules/regions with particular orientation; hence, anisotropy

of spin relaxation may lead to a more complex behavior[11], even

with single sites.

In systems with more than one2_{H spin populations, the large}

static quadrupolar broadening of the signal components typically masks features arising from small chemical shift differences between the involved sites. Therefore, except cases where the sites exhibit large differences among their quadruple coupling constants

[12], information may not be obtained on a site-resolved manner.

For such systems, magic angle spinning (MAS) can yield beneficial line narrowing. Indeed, it has been demonstrated recently that on this way one may gain access to site-specific information to

molec-ular dynamics in deuterated solids[13–15]. In addition, MAS also

suppresses the effect of relaxation anisotropy on the obtained line

shapes[16]. One should note that 2D quadrupole echo with

suit-able phase cycling is also capsuit-able to resolve sites with different

chemical shifts[17,18].

http://dx.doi.org/10.1016/j.jmr.2016.04.014

1090-7807/Ó 2016 The Authors. Published by Elsevier Inc.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑Corresponding author.

E-mail address:furo@kth.se(I. Furó).

Contents lists available atScienceDirect

Journal of Magnetic Resonance

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j m r

In previous work, spectral information for different sites was easily resolved since the involved chemical-shift differences were

at least 2–3 ppm[15]. In many interesting systems, the available

chemical shift range is much smaller; as one example, the total hydrogen chemical shift range for various carbohydrates like

cellu-lose or starch or chitin but also simple sugars[19–22]is in the

order of one ppm. In this paper we extend the2_{H MAS}

methodol-ogy to systems with small chemical-shift differences. With application to cellulose and related materials in mind, we show

that 2_{H MAS NMR in combination with relaxation experiments,}

here specifically inversion recovery, can resolve sites with small or insignificant chemical shift differences. The relaxation module in the experiment has a dual purpose: (i) for sites with different relaxation rates, it aids the separation of their respective signals and (ii) provides access to site-specific information about molecu-lar dynamics. Here, we are going to emphasize the first of those features and demonstrate the performance of the methodology in both a model material and in deuterium-exchanged microcrys-talline cellulose (MCC). In addition, we also show that the methodology is robust by comparing the results obtained by different spectral deconvolution techniques such as direct spectral

fitting and COmponent-REsolved (CORE) analysis[23].

2. Experimental section 2.1. Materials

Deuterated poly(methacrylic acid)-d5from Polymer Source Inc.

(PMAA-d5, see molecular structure inFig. 1), 2_H

2O (99.9 atom%

2

H), microcrystalline cellulose (MCC, S5504) cotton linter powder, and tetramethylsilane (TMS, 99.95%) all from Sigma–Aldrich, were used as obtained. The MCC was placed for a couple of days in a ves-sel with a heavy-water atmosphere of relative humidity of roughly

91%, established by saturated solution of KNO3in2H2O placed in

the vessel. Under such conditions at room temperature, the acces-sible hydroxyl groups, such as the ones on the surface of cellulose

fibrils[24], become deuterated. Finally, after having been

deuter-ated the sample was dried in a vacuum oven operating at 50°C;

this treatment removed the water adsorbed on the MCC and left

–O2_{H groups of cellulose as the dominant source of the}2_{H NMR}

signal.

2.2. NMR experiments

The 2_{H NMR spectra were recorded on a Bruker Avance HD}

500 MHz spectrometer operating at a resonance frequency of 76.1 MHz and equipped with a 4 mm MAS probe. The sample

spin-ning speed was set to 10 kHz and the 90° pulse length to 3

l

s. The

spectra presented were recorded at 25°C with 256 scans (PMAA)

respectively 4096 scans (MCC) and recycle times of 1 s (PMAA) respectively 5 s (MCC). The relaxation delays for inversion recovery (IR) were roughly logarithmically arranged between 0.6 ms and 4.8 s. All spectra were phase-corrected according to the spectrum recorded with the longest relaxation delay; the results obtained

in the PMAA sample are shown in Fig. 2 (see MCC spectra in

Supplementary Material). The TMS signal, used for chemical-shift referencing, was recorded separately for TMS filled in a rotor and with a spinning speed of 10 kHz.

2.3. Spectral analysis

The MAS-peak manifold contains a central peak and numerous spinning sidebands (SSB) that flank the central peak at set frequen-cies. Within all peaks, the relative position of signal from different sites is governed by the respective isotropic chemical shift. In our case, the central peak in the cellulose sample (see Supplementary Material) has clearly a contribution from a component that was absent in the cellulose sideband spectra. The corresponding total signal was negligible (we tentatively assign this mobile peak to remaining heavy water molecules), but because of this feature we excluded the cellulose central peak from the data-treatment procedure outlined below.

In the procedure termed ‘‘component fitting”, we least-square fitted both to the central line and all SSBs (for PMAA-d5) or to the SSBs only (for MCC) a theoretical expression representing the sum of Lorentzian peaks as

Sð

s

;

m

; nÞ ¼X i I1i;n 1 Ene s T1;i   _T2 ;i 1þ 2

p

T2_;ið

m



m

i n

m

rotÞ  2 ð1Þ

where

s

is the IR delay time,

m

the spectral frequency, and n the SSB

index while Enis the inversion efficiency (<2, because of limited

radiofrequency power) at frequencies n

_m

rot relative to the central

frequency. In addition, I1_i;nis the thermal equilibrium intensity of a

spectral component i in a given SSB[25]that is also characterized

by a chemical shift defined as di¼ ð

m

i

m

0Þ=

m

0, where

m

i and

m

0

the is the resonance frequencies of the spectral component i and

TMS, respectively. Finally, T1,i(strictly speaking, T1zthat

character-izes the relaxation of Zeeman order) and T2,iare the

component-specific longitudinal and transverse spin relaxation times, respec-tively. The relaxation parameters are global because all SSBs are

sig-nal averages over the whole sample[26]. For both samples, the fits

performed with the Levenberg–Marquardt algorithm with two spin populations (an assumption for the cellulose sample); the results

obtained are presented inTable 1.

In contrast to the procedure above with set Lorentzian line shapes, the other procedure used for analyzing the spectral

mani-fold exploits the CORE[23]analysis (software available athttps://

www.kth.se/en/che/divisions/tfk/staff/emeriti/stilbs/core-data-processing-downloads-1.193738). The CORE processing is also a global least-square fitting of the spectral data, but without an assumed line shape. Instead, the CORE analysis assumes that the spectrum consists a set number of components and each compo-nent exhibits a variation by a specific mathematical function along an extra experimental variable, in our case the evolution time in the inversion recovery experiment. This translates into having fit-ted the variation of the spectral intensity with the evolution time at each frequency point by a two-exponential function (that is, one assumes two components) where the time constants were glo-bal as Sð

s

;

m

; nÞ ¼X i I1i;n;m 1 Ee s T1;i   ð2Þ In other words, for each frequency point it is the relative contribu-tion of the two involved relaxacontribu-tion procedures that is allowed to vary. In CORE, we simply approximate the same inversion efficiency for the whole spectral range.

The band shapes resulting from the CORE analysis are illus-trated in Supplementary Material. Because the CORE analysis does not assume any particular band shape, the chemical shift is n

C

D

2

C

D

3

O

HO

estimated from the an intensity-weighted average resonance frequency of each component

m

i¼ P

n;mIi;n;m_Pð

m



m

0 n

m

rotÞ

n;mIi;n;m ; ð3Þ

where Ii;n;mdenotes the intensity of component i in the nth SSB at

frequency

_m

(see Supplementary Material for details, such as setting

the frequency range for the summation in Eq.(3)). I1_i;nfrom CORE is

obtained as the sum of the fitted final intensities I1_i;n¼PmI1i;n;mwithin

the two components. To be able to quantitatively compare the

component-specific SSB band shapes, the second moment M2 of

the spectral components were calculated as M2;i¼

P

n

m

2i;nI1i;n

P

nI1i;n ð4Þ

where

_m

i;nis the position of peak i in the nth SSB, relative to the

cen-tral transition.

3. Results and discussions

InFig. 2, peaks in the spectral center exhibit faster relaxation than those at the edge that indicates clearly that in PMAA-d5 there

are two spin populations with different T1values: one population

with long T1and large quadrupole coupling and another one with

short T1and small quadrupole coupling. Since in PMAA-d5 we have

full information about the sites and their coupling constants[27],

we identify the former and latter populations as those correspond-ing to the methylene and methyl deuterons, respectively. Illustra-tive examples for SSB line shapes in PMAA-d5 are shown in detail inFig. 3. For the inner SSBs (Fig. 3a –c) it is clear that the peak has more than one components with different relaxation times while

the outer SSBs (Fig. 3d) seem to exhibit only one relaxing

compo-nent. The results from the global (that is, simultaneous for all SSB line shapes) fit of the spectral manifold of PMAA-d5 are

sum-marized inTable 1.

An important question that arises is whether the procedure out-lined above is accurate or not. Systematic error can, for example, be introduced if the actual line shapes are not Lorentzian (but instead Gaussian or a Gaussian–Lorentzian mixture). In addition, any solid material may contain defects that can lead to a distribution of chemical shift. To investigate the effect of that, we re-analyzed

the data using the CORE procedure[23,28]that makes use of no

particular line shapes but merely assumes that there are two decaying spectral components in the series of spectra. The results

of that re-analysis are also presented inTable 1(see also the band

shapes obtained by CORE analysis in Supplementary Material); clearly, the parameters extracted by the component-fitting and CORE procedures are consistent.

Fig. 2. The evolution of the2

H MAS spectra with the delay time in the inversion-recovery experiment in PMAA-d5. Every second spectra are red in for better visibility.

Table 1

The average results of the fitting procedure in PMAA. The error estimates, as obtained from three repeated experiments, represent one standard deviation.

Component Data analysis Chemical shift (ppm)

T1(ms) Population

fraction (%) Methylene Component fitting 2.1 ± 0.1 94 ± 5 39.5 ± 0.5

Methylene CORE 2.1 ± 0.05 88 ± 1 35.1 ± 0.2

Methyl Component fitting 1.0 ± 0.1 7.7 ± 0.1 60.5 ± 0.5

The method assigns the chemical shifts in the expected order: dmethylene> dmethyl, with a calculated chemical shift difference of ca

1.1 ppm. In liquids, the corresponding shifts in PMAA are typically

given as 0.9–1.0 ppm (for CH3) and 1.7 ppm (for CH2) [29,30].

Hence, the methylene–methyl shift difference is about 0.7 ppm, smaller than that measured here; this variance between liquid and solid states can be easily explained by the different inter-molecular environments for the involved groups in neat PMAA

solid and in a solvent[31–33].

As an additional test of consistency, we display inFig. 4for both

procedures the spectral intensities I1_i;n. Those spectral intensities,

that are expected to roughly follow the2_{H powder-pattern}

envel-opes, coincide well for the component fitting and the CORE

proce-dures (Fig. 4). Another question is whether or not the same result

could have been achieved without performing the inversion recov-ery (or perhaps some other relaxation or magnetization transfer) experiment. To investigate this issue, we performed a global fit to the longest-delay spectral manifold in terms of two spin popula-tions contributing to the different SSBs. The results were unambigu-ous; it was impossible to separate the different spin populations without using time-dependent spin-relaxation-weighted data.

Regarding microcrystalline cellulose prepared under the mild conditions used here, in heavy-water atmosphere there is an exchange of hydrogens of surface hydroxyl groups to deuterons. FT-IR spectroscopy provided indication that two of the possible three (on C2, C3, and C6 carbons) exchangeable hydroxyl groups [34,35]that may get exchanged. In liquid state, the chemical shift

difference[19–22]between those peaks is small and its variation

with, for example, solvent is comparable to its value. As concerning

the magnitudes of their quadrupole coupling, there is no prior data available; the only related (though, not directly comparable) data are the C–H bond order parameters obtained from residual

13_C–1_{H dipole–dipole couplings which show a rather small or}

neg-ligible (depending on the source of cellulose) difference between

C6 residues on one hand and C-2,3 residues on the other hand[36].

Just like in PMAA, the two procedures (component fitting, see

illustrative SSB spectra in Fig. 5, and CORE) provide consistent

results in microcrystalline cellulose (see more details in

Supple-mentary Material). This is shown both byTable 2(similar

relax-ation features) and Fig. 4b (similar spectral envelopes). Hence,

we conclude that the method explored here captures the spectral

features of2_{H nuclei even in case of strong spectral overlap. The}

two concluded sites seem to possess similar residual quadrupole

couplings (Fig. 4b) yet strongly different longitudinal relaxation

times that may set strong constraints when comparing results of molecular dynamics simulations. The residual quadrupole cou-plings can be compared in more detail via the second moment

cal-culated as given by Eq. (4), yielding similar values for the two

assume MCC sites: M2(2HO(a)) = 3.5 109s2 and M2(2HO(b))

= 2.8_{ 10}9_s2_{(for PMAA, the methylene and methyl groups}

val-ues were 2.2 109_s2_{and 2.9 10}8_s2_{, respectively, a much}

lar-ger difference).

Comparison to13C spin relaxation data obtained in (hydrated)

cellulose[34,37,38]suggests that the site (b) is positioned at C6.

This is also verified by the obtained order of the chemical shifts of the two components, O(6)H has a lower chemical shift in

dis-solved b-cellobiose [20] and cyclodextrins and maltoheptoses

[19]by roughly 0.3–0.6 ppm. Furthermore, the obtained absolute

30000 31000 -0,1 0,0 0,1 0,2

(a)

In

te

nsi

ty

[a.

u.

]

[Hz] 40000 41000 -0,05 0,00 0,05 0,10 0,15

(b)

In

te

nsi

ty

[a.

u.

]

[Hz] 50000 51000 -0,05 0,00 0,05 0,10

(c)

In

tensi

ty

[a

.u

.]

[Hz] 70000 71000 -0,01 0,00 0,01 0,02

(d)

In

tensi

ty

[a

.u

.]

[Hz]

Fig. 3. Illustrative examples of SSB line shapes and the corresponding results of the global spectral fit of the whole manifold for PMAA-d5. To aid visibility, only spectra with the following delays are plotted: (a, b) 0.006, 0.0016, 0.0042, 0.0067, 0.0107, 0.0172, 0.0275, 0.0704 and 4.8357 s; (c, d) 0.006, 0.0107, 0.0172, 0.0275, 0.0440, 0.0704, 0.1126, 0.1801, 0.4612 and 4.8357 s.

chemical shifts are also in rough agreement with the chemical

shifts of dissolved maltoheptose (O(2)H: 6.4 ppm, O(6)H:

5.9 ppm) andb-cyclodextrin (O(2)H: 6.4 ppm, O(6)H: 6.1 ppm). It

is suggestive that chemical modifications of cellulose fibrils that exploit reactions with hydroxyl groups were found to act mainly

on the O(2)H and O(6)H moieties[39,40].

CORE (2_{HO(a)) CF (}2_HO(a)) CORE (2HO(b)) CF (2HO(b))

-100000 -50000 0 50000 100000 0,0 0,2 0,4 0,6 0,8 1,0

(b)

P

eak

area

[a

.u

.]

[Hz]

-100000 -50000 0 50000 100000 0,0 0,2 0,4 0,6 0,8 1,0

(a)

Pe

a

k

a

re

a

[a

.u

.]

[Hz]

CORE (Methyl) CF (Methyl) CORE (Methylene) CF (Methylene)

Fig. 4. Thermal equilibrium intensities I1i;nfor the different spectral components (marked by either triangles or circles, normalized to respective maximum intensities) at

different SSBs as extracted by component fitting (red) and CORE (black) procedures in PMAA (a) and cellulose (b).

30000 31000 -0,2 0,0 0,2 0,4

(a)

In

te

nsi

ty

[a.

u.

]

[Hz] 40000 41000 -0,2 0,0 0,2 0,4 0,6

(b)

In

te

nsi

ty

[a.

u.

]

[Hz] 50000 51000 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8

(c)

In

tensi

ty

[a.

u.

]

[Hz] 70000 71000 -0,2 0,0 0,2 0,4 0,6 0,8

(d)

In

tensi

ty

[a.

u.

]

[Hz]

Fig. 5. Illustrative examples of SSB line shapes and the corresponding results of the global spectral fit of the whole manifold for deuterium exchanged cellulose. To aid visibility, only spectral with the following delays are plotted: 0.006, 0.0107, 0.0172, 0.0275, 0.0440, 0.0704, 0.1126, 0.1801, 0.4612 and 4.8357 s.

To investigate the limitations of the presented method for extracting reliably spectral parameters such as small chemical shift differences, we have performed some additional simulations. First,

2_{H MAS powder spectra were generated in Matlab by integrating}

the suitable analytical form[41]for two sites with identical line

widths (FWHH = 400 Hz), and slightly different quadrupole

split-tings of 60 kHz and 70 kHz. Series of composite spectra with equal weight of these two sites were created for simulated IR

experi-ments with two parameters, the chemical shift differenceDd and

the ratio of the two involved longitudinal relaxation times

Tslow1 =T

fast

1 , varied independently. To the spectra, white noise was

added to yield a set signal-to-noise ratio for the topmost peak intensity at the longest IR delay value. The different spectral series were then analyzed using the CF protocol. To determine if the pro-tocol successfully extracted the individual spectral parameters we used compounded criteria – less than a given difference between

the input and fitted spectral parameters and a reduced

v

2

(least-square deviation between the simulated and fitted SSB intensities

normalized but the simulated intensities[42], seeFig. 6b) less than

given threshold. Illustrative results are presented inFig. 6a, for less

than 5% difference between the input and fitted line widths and T1

values, less than 0.05 ppm difference between the input and fitted

values the chemical shift differenceDd and a reduced

v

2_{less than}

0.1. As a general feature, small chemical shift differences could be resolved if the ratio of the involved relaxation times was suffi-ciently large. There exists a region of inaccessible combination of

spectral parameters in the lower left corned inFig. 6a. This region

increases with decreasing signal-to-noise ratio and the stricter suc-cess criteria (see also Supplementary Material). Yet, two robust features emerge. At signal-to-noise ratios being above 10 (the signal-to-nose ratio in our cellulose spectra was ca 50), (i) any

chemical shift difference can be reliably extracted if the Tslow1 =T

fast 1

is larger than 3 and (ii) at chemical shift differences larger than half

the line width any Tslow

1 =T fast

1 ratio can be reliably extracted. We

note here that instrumental imperfections (whose effect was not investigated here) may lower reliability. Yet, the presented simula-tions provide a rather conservative and positive assessment of the reliability of our results in cellulose.

4. Conclusions

We have shown that2_{H MAS NMR relaxation experiments can}

resolve spectral lines that are separated by a few tenth of ppm.

To be able to resolve 2

H peaks in solid-state spectra is rather important in a number of biomolecular materials where the hydro-gen spectral dispersion is small. Primary examples are cellulose

and its derivatives. At the same time,2H is a very useful tool when

studying surface access and or molecular dynamics; particularly, water and hydroxyl group behavior in cellulosic materials that is essential for the macroscopic material properties is amenable on this manner. Other potentially interesting applications are in the field of lipids and inorganic materials (such as silica) with essential surface hydroxyl groups.

While access to molecular dynamics can be the actual aim in a particular investigation, the other role of the relaxation pulse sequence (here, inversion recovery – one could also use saturation recovery) is to color the signal from the different sites by their respective relaxation time. It is this feature that permits the sepa-ration of the signals at nearby chemical shift values. Other pulse sequences that permit a spin-property-dependent modulation of

the line shapes may also be feasible; in particular for 2_{H MAS,}

one could exploit the contact time dependence of the1_H–2_{H cross}

polarization[43–45]. This latter procedure is less time consuming

than IR but may be less distinctive in our current cellulose sample. We have shown that the separation is a rather robust feature as witnessed by the very similar results provided by two fundamen-tally distinct least-square fitting procedures, one with and one without any assumed line shapes. Besides providing site-resolved relaxation data, the procedure was also shown to provide a reliable representation of the individual quadrupole-broadened line shapes. In microcrystalline cellulose, the obtained spectral and

Table 2

The results of the different fitting procedures of cellulose. Component Data analysis Chemical

shift (ppm)

T1(ms) Population

fraction (%)

2

HO(a) Component fitting 5.8 360 59

2_{HO(a) CORE 6.0 330 57}

2

HO(b) Component fitting 5.6 32 41

2 HO(b) CORE 5.6 25 43 1 2 3 4 5 0 5 10 15 20 25 30 35 40

(a)

Tslow 1 /T fast 1 Δδ /F W H H [% ] -100000 -50000 0 50000 100000 0,0 0,2 0,4 0,6 0,8 1,0

(b)

Peak area [a.u.]

[Hz]

Fig. 6. Illustrative examples of the result of CF fits to simulated2

H MAS line shapes for two-site composite spectra, see text. In (a), the green area indicates those combinations of two parameters, chemical shift difference relative to line width and the ratio of the T1values for the two sites, where the fitted parameters and spectral

shapes were deemed to be sufficiently close to the input values. The applied criteria were less then 5% difference between the input and fitted values T1and line width,

less than 0.05 ppm difference between the input and fitted values the chemical shift differenceDd and less than 0.1 for the reduced v2

representing the deviation between input and fitted MAS line shapes. To illustrate the latter feature, SSB manifolds with reduced v2

slightly below 0.1 are compared in (b, symbols correspond to fitted values while lines without symbols illustrate the input SSB intensities without noise). In all simulations represented here, the signal-to-noise ratio for the topmost peak intensity at the longest IR delay value was set to 10.

relaxation features permitted us to assign the detected signals to particular exchanged hydroxyl groups. Further studies of various other biomaterials by this method are under way.

Acknowledgment

The Knut and Alice Wallenberg Foundation and the Swedish Research Council (VR) are gratefully acknowledged for the financial support.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in

the online version, athttp://dx.doi.org/10.1016/j.jmr.2016.04.014.

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