Skin, soap, and spaghetti: investigations of co-existing solid and liquid phases in organic materials using solid-state NMR with dynamics-based spectral editing

2.1 Aspects of molecular dynamics: translation, rotation, and conformational isomerization

Classical molecular dynamics simulations yield trajectories of molecular systems containing up to millions of atoms at femtosecond resolution and microsecond duration, thereby providing details not accessible with experimental techniques [28]. Simulation results for a hydrated lipid bilayer are in Fig. 1 shown in several complementary ways to qualitatively illustrate and quantitatively define metrics describing various aspects of dynamics. The series of motion blur images in Fig. 1b visualize the spatial heterogeneity and wide range of dynamical time scales present even in a comparatively simple lipid membrane system: from the picosecond motion of the water molecules and terminal methyl groups of the lipid hydrophobic tails to the orders of magnitude slower motion at the hydrophobic-hydrophilic interface [27].

Fig. 1:

Illustration of the multiple aspects of molecular dynamics using simulations of a hydrated lipid bilayer. (a) Chemical structure of the lipids 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and monosialodihexosylganglioside (GM3). (b) Simulation snapshots as a function of “exposure time” for an all-atom system comprising 112 POPC, 48 GM3, 48 potassium ions, and 10 940 water molecules. Color coding of atoms and bonds emphasizes hydrophilic headgroups (red) and hydrophobic tails (yellow) of the lipids, as well as water (blue). Arrows show the x- and z-directions, the latter defined to be collinear with the normal vector of the bilayer plane. (c) Zoom-in on the carbon 4–7 section of the palmitoyl chain of POPC indicated in panel (a), showing the position r(t) and velocity v(t) of a carbon atom, the orientation n(t) of a C–H bond, and the dihedral angle ϕ(t) for a C–C–C–C fragment. (d) Time-dependent r(t), v(t), n(t), and ϕ(t) and the corresponding correlation functions for the mean-square displacement C _MSD(τ), velocity C _V(τ), C–H bond orientation C _CH,l (τ), and dihedral angle C _D(τ) defined in eqs. (1)–(4). The Cartesian components of the r(t), v(t), and n(t) vectors and the diagonal elements of the C _MSD(τ) and C _V(τ) tensors are shown in red, green, and blue. The trajectories are sampled at 2 fs resolution for an overall duration of 50 ns. Gray dotted lines connect the four exposure times in panel (b) with the corresponding time-lags in panel (d). (e) Polar plots of the distribution functions for C–H bond orientation P _CH(n) (colored surface showing the x-, y-, and z-directions as red, green, and blue) and dihedral angle P _D(ϕ) (data: black, polar grid: gray). The labels in P _D(ϕ) highlight the values of ϕ for the trans (ϕ = 180°), gauche⁺ (ϕ = 60°), and gauche⁻ (ϕ = 300°) conformations. (Simulation results adapted from Ref. [27] with permission from the authors.)

The dynamics is reported quantitatively in Fig. 1d in terms of the time-dependent position r(t) and velocity v(t) of a single carbon atom, the unit vector n(t) describing the direction to one of its covalently bound hydrogen atoms, and the dihedral angle ϕ(t) giving the conformation of the carbon chain. The time-scales of the fluctuations are captured in the correlation functions for the mean-square displacement C _MSD(τ), velocity C _V(τ), C–H bond orientation C _CH,l (τ), and dihedral angle C _D(τ) [29], defined by

and

where 〈…〉_t denotes an average over time t, τ is the time-lag between the two time-points t and t + τ, “·” and “⊗” are inner and outer products, respectively, and P _l (x) is the lth order Legendre polynomial. The case P ₁(x) = x gives the lowest level description of vector reorientation but the functional form for the interaction between two magnetic dipoles makes P ₂(x) = (3x ² − 1)/2 more relevant in NMR. At each value of τ, the functions C _MSD(τ) and C _V(τ) are second-order symmetric tensors while C _CH,l (τ) and C _D(τ) are scalars.

Bond libration on time scales faster than ∼1 ps gives rise to oscillatory behavior in mainly C _V(τ), the rapid increase in C _MSD(τ), and the initial small decay of C _CH,l (τ) and C _D(τ). The time-lag where C _V(τ) reaches zero corresponds to the transition from the ballistic to the diffusive regime where the elements of C _MSD(τ) increase linearly with τ. The motion blur in Fig. 1b is most directly related to the time where the square-root of C _MSD(τ) approaches the ∼0.1 nm distance between neighboring atoms, which because of the coupling between rotational and translational motion happens to coincide with the time scale for the main decay of C _CH,l (τ) and C _D(τ).

At values of τ above ∼1 ns, both C _CH,2(τ) and C _D(τ) reach non-zero plateaus given by the bond [30, 31] and dihedral [29] order parameters S _CH and S _D determined by the anisotropy of the corresponding probability distribution functions P _CH(n) and P _D(ϕ) displayed in Fig. 1e. Visual inspection of the simulation snapshot in Fig. 1b reveals that the lipid hydrophobic chains are partially aligned with the bilayer normal and mainly assume trans conformations. The chain alignment results in C–H bonds preferentially oriented within the bilayer plane and the corresponding “donut” shape of P _CH(n), having low probability along the z-axis and equal probability in all directions of the xy-plane. Analogously, the preference for trans conformations gives P _D(ϕ) with a global maximum at ϕ = 180° which is far larger than the local maxima at ϕ = 60° and 300° for the gauche conformations. While the decay of C _D(τ) originates from libration and conformational isomerization, the decay of C _CH,2(τ) also results from whole-lipid wobble and rotation. For a collection of lipid bilayers with an isotropic distribution of orientations, which is beyond the reach of current atomistic simulations, C _CH,2(τ) would eventually reach zero on account of whole-lipid rotation caused by translational diffusion between bilayer sections with different orientations.

The general concept of “dynamics” is often thought of as translational motion, which is quantified by the functions C _MSD(τ) and C _V(τ) and may be investigated with NMR techniques using magnetic field gradients [32], [33], [34]. In the context of ¹³C spectroscopy, however, “dynamics” refers mainly to C–H bond reorientation and conformational isomerization described by the functions C _CH,2(τ) and C _D(τ) which are directly related to fluctuations of ¹H–¹³C dipolar interactions and ¹³C chemical shifts.

2.2 DP-CP-INEPT signal intensities and dynamics

To rationalize the effects of dynamics, the DP, CP, and INEPT signal intensities I _DP, I _CP, and I _INEPT can be written as a function of the recycle delay τ _R, CP contact time τ _CP, and in-phase/anti-phase coherence conversion delays τ ₁ and τ ₂ as [9, 38, 39]

and

where I _DP ^eq is the DP signal intensity at infinite τ _R. Additionally, γ _H and γ _C are the ¹H and ¹³C gyromagnetic ratios, n the number of covalently bound hydrogens, and J _CH the ¹H–¹³C scalar coupling constant. The connection between signal intensities and molecular dynamics lies in the ¹H–¹³C CP buildup rate R _CH, the ¹H and ¹³C longitudinal relaxation rates R ₁ ^H and R ₁ ^C, the ¹H longitudinal relaxation rate in the rotating frame R _1ρ ^H, and the ¹H and ¹³C transverse relaxation rates R ₂ ^H and R ₂ ^C, which are determined by the C–H bond reorientation as quantified by the function C _CH,2(τ), and, more specifically, its Fourier transform j(ω) at a few selected frequencies ω as indicated in Fig. 2b for the model for relaxation by random fields [40]. It should be noted that in particular eq. (6) is a rather crude approximation and the theoretical framework for analysis of CP in the presence of multiple ¹H spins and molecular dynamics is still being further developed [41]. In practice, the measurements are often performed using τ _R >> 1/R ₁ ^H where the [1 − exp(−R ₁ ^H τ _R)] factor in eqs. (6) and (7) approaches unity.

Fig. 2:

Principles of ¹H–¹³C polarization transfer for dynamics-based editing of ¹³C magic-angle spinning (MAS) NMR spectra. (a) Schematics of the direct polarization (DP), ramped cross polarization (CP) [7, 35] and refocused insensitive nuclei enhanced by polarization transfer (INEPT) [8, 36] sequences with double arrows indicating the time durations for CP contact τ _CP, in-phase to anti-phase ¹H coherence conversion τ ₁, and anti-phase to in-phase ¹³C coherence conversion τ ₂. Narrow and broad vertical bars show, respectively, 90° and 180° radiofrequency pulses, and the decaying sinusoid illustrates detection of ¹³C signal while applying ¹H decoupling. The recycle delay τ _R (not shown) is the time between the end of ¹³C detection and the 90° pulse of the following repetition of the sequence. (b) C–H bond orientation correlation function C _CH,2(τ) and corresponding spectral density j(ω) for the two-step model, see eq. (8), with time constants τ _c and τ _s, intermediate plateau S _CH ², and modulation by MAS at the frequency ω _MAS. The ¹³C signal intensities are mainly determined by j(ω) at the ¹³C Larmor frequency ω _0C for DP, the ¹H nutation frequency ω _1H and ¹H–¹³C nutation frequency mismatch ω _1H–ω _1C for CP, and the ω = 0 component for INEPT. (c) Theoretical CP (blue) and INEPT (red) signal enhancement as a function of τ _c and |S _CH| at constant τ _s = 1 ms for a methylene segment using the acquisition parameters ω _0C/2π = 125 MHz, ω _MAS/2π = 5 kHz, τ _CP = 1 ms, ω _1H/2π = 100 kHz, (ω _1H–ω _1C)/ω _MAS ramped from 2.5 to 0.5, τ ₁ = 1.8 ms, τ ₂ = 1.2 ms, and τ _R = 5 s. Details of the calculation are given in Ref. [37].

Although the rate constants can be calculated from C _CH,2(τ) obtained by molecular dynamics simulations [37], insights into the most important properties are obtained by invoking the two-step bond reorientation model developed for analyzing ¹³C relaxation in surfactant micelles [42], proteins [31], and lipid bilayers [43]. In this model, the function C _CH,2(τ) is written as

where the effects of the “internal” molecular-scale types of motion, such as libration, trans-gauche isomerization, and whole-lipid wobble and rotation, are lumped into a single correlation time τ _c and the C–H bond order parameter S _CH, while the isotropic global motion resulting from, for instance, rotational diffusion of micelles or vesicles as well as translational diffusion of molecules between bilayers with different orientations, is captured by the correlation time for “slow” motion τ _s. In the absence of molecular motion, the slow decay originates from flip-flop transitions in the ¹H dipolar network [44]. The last factor in eq. (8) results from MAS at the frequency ω _MAS, giving rise to oscillations of C _CH,2(τ) at the frequencies ω _MAS and 2ω _MAS [45] as shown in Fig. 2b. Fourier transformation of the expression in eq. (8) gives a spectral density j(ω) comprising a sum of Lorentzians with center frequencies determined by ω _MAS, widths by τ _c and τ _s, and relative areas by S _CH.

Insertion of j(ω) from the two-step model into the expressions for the rate constants in the random fields model and, subsequently, into eqs. (6) and (7) yields CP and INEPT intensities as shown in Fig. 2c for a CH₂ segment as a function of τ _c and |S _CH| with τ _s = 1 ms and typical experimental parameters including ω _MAS/2π = 5 kHz, τ _CP = 1 ms, τ ₁ = 1.8 ms, and τ ₂ = 1.2 ms. For explicit equations and explanations of the approximations involved, we refer the interested reader to Ref. [37]. The theoretical results in Fig. 2c are consistent with the well-established notion of CP and INEPT as complementary dynamics-based filters, with INEPT occupying the τ _c < 10 ns and |S _CH| < 0.2 corner of the dynamics space, but also add details crucial for correct interpretation of experimental data. Importantly, there are dynamical regimes in which either both (τ _c < 10 ns and |S _CH| ≈ 0.1) or none (τ _c ≈ 1 µs) of CP and INEPT are efficient. The former case contradicts the common oversimplified explanation of CP and INEPT as being selective for solids and liquids, respectively. For anisotropic liquids the selectivity is in fact rather poor, and the same molecules can be observed equally well with CP and INEPT [46]. Within each anisotropic domain, the molecules in effect become equivalent by exploring all available conformations and orientations (see Fig. 1) on time-scales that are many orders of magnitude smaller than the millisecond durations of the polarization transfer. Comparison of the CP and INEPT intensities yields crude and ambiguous estimates of τ _c and |S _CH| which can be determined with greater precision using dedicated relaxation [31, 42, 43] and dipolar coupling measurements [47] at the cost of orders of magnitude longer experimental times.

As illustrated in Fig. 3, the value of ω _MAS can be used to tune the borders between the dynamical regimes dominated by CP or INEPT. In the regime of fast dynamics (τ _c < 10 ns), the border moves to higher values of |S _CH| with increasing ω _MAS: from approximately |S _CH| = 10⁻² at ω _MAS/2π = 0 kHz, to |S _CH| = 10⁻¹ at ω _MAS/2π = 10 kHz, and |S _CH| = 1 at ω _MAS/2π = 100 kHz. The latter experimental condition also allows detection of INEPT signal in the regime of slow dynamics (τ _c > 0.1 ms) [48]. Notably, for every value of ω _MAS there is a range of τ _c where neither CP nor INEPT give signal.

Fig. 3:

Theoretical polarization transfer efficiency for a series of MAS frequencies ω _MAS using the same two-step model and acquisition parameters as in Fig. 2c with the exception of ω _1H/2π = 250 kHz during CP for the highest value of ω _MAS. Note that the |S _CH| axes cover two orders of magnitude more than in Fig. 2c.

The two-step model in eq. (8) also accommodates cases where the isotropic global reorientation with correlation time τ _s takes place on the same time-scale, or even faster than, the molecular-scale one, for instance vesicles with gel-state lipids or solid organic nanoparticles suspended in solution. Application of the Stokes–Einstein–Debye relation for the reorientation of spherical particles in water at 25 °C yields the approximate values τ _s = 1 ns, 1 µs, and 1 ms for the radii of 1, 10, and 100 nm, respectively, roughly corresponding to the typical dimensions of surfactant micelles, small unilamellar vesicles, and large unilamellar vesicles. Figure 4 shows CP and INEPT signal enhancement vs. τ _s and |S _CH| for the cases of fast (τ _c = 1 ns), intermediate (τ _c = 1 µs), and slow (τ _c = 1 ms) molecular-scale dynamics. As the global motion in eq. (8) is by definition isotropic, INEPT dominates at τ _s < 10 ns irrespective of the details of the molecular-scale anisotropic dynamics as quantified with the parameters τ _c and |S _CH|. For small unilamellar vesicles with τ _s ≈ 1 µs, CP is generally inefficient while INEPT yields signal if the internal motion is sufficiently fast and isotropic (τ _c < 10 ns and |S _CH| < 0.2).

Fig. 4:

Predicted polarization transfer efficiency with emphasis on the effects of global isotropic reorientation with correlation time τ _s in addition to the “internal” molecular-scale anisotropic reorientation quantified with τ _c and |S _CH|. The CP and INEPT signal enhancements are plotted as a function of τ _s and |S _CH| for a series of values of τ _c using acquisition parameters identical to the ones in Fig. 2c.

Since the CP and INEPT intensities depend on dynamics, they cannot directly be used to determine the relative amounts of different molecular sites along the lines of conventional quantitative NMR [49]. For molecules yielding CP signal, the sensitivity to dynamics can be reduced by application of multiple short CP blocks interleaved with periods of z-storage to replenish the ¹H magnetization, thereby enabling internal quantification within the more rigid subset of molecules [50]. Correspondingly, internal comparison among the mobile ones can be achieved using INEPT with systematic variation of the τ ₁ and τ ₂ delays and fitting of eq. (7) to the data to take the effects of relaxation into account [51]. However, simultaneous quantification of both mobile and rigid molecules may require time-consuming DP measurements using values of τ _R on the order of minutes to allow for complete longitudinal relaxation of all investigated ¹³C sites [52].

2.3 Chemical shifts and dynamics

For the simple case of a hydrocarbon chain, there is a ¹³C shift difference of approximately 5 ppm between trans and gauche conformations [5, 53]. In the absence of conformational isomerization, the distribution of dihedral angles P _D(ϕ) as observed in the simulation data in Fig. 1e would lead to a distribution of ¹³C shifts covering about 5 ppm for each of the carbon atoms, resulting in spectra with poor atomic resolution that could not be improved by MAS or ¹H decoupling. Observation of peaks from the individual conformations requires that their lifetimes exceed the inverse of the difference in resonance frequencies [54], which for typical ¹³C Larmor frequencies corresponds to ∼1 ms. The dihedral correlation function C _D(τ) in Fig. 1d shows conformational exchange on time-scales smaller than 1 ns, which would give rise to a single narrow peak at an intermediate shift equal to the P _D(ϕ)-weighted average of the contributions from the individual conformations. The linewidth thus provides additional but ambiguous information about dynamics: narrow peaks are expected for both liquids with rapid exchange between conformations and crystalline solids where all molecules have identical conformation. This ambiguity is of course easily resolved by the CP and INEPT intensities.

2.4 Example data from simple model systems

Experimental verification of the theoretical predictions in Fig. 2c can be found in Fig. 5, showing data for the surfactant n-octyl-β-d-maltoside (C₈G₂) at variable water content and temperature. Surfactants comprise hydrophilic and hydrophobic moieties that in aqueous systems promote self-association of the molecules into, for instance, micelles and bilayers, as well as the formation of various liquid crystals and crystalline hydrates [2]. As opposed to the rich phase behavior of most conventional surfactants, C₈G₂ remains in a lamellar liquid crystalline state (Fig. 5b) over a wide range of conditions but undergoes a glass transition [55] wherein the molecular dynamics changes by orders of magnitude over a narrow temperature interval, thereby offering a convenient model system for investigating the effects of dynamics on experimental observables such as the ¹³C NMR signal intensities of interest here. At the highest water content and temperature, many of the carbon atoms of C₈G₂ give rise to individual ¹³C peaks with CP and INEPT intensities determined by the values of |S _CH| rather than τ _c. Similar to the behavior of other surfactants and lipids in a lamellar liquid crystalline state [56], [57], [58], there is a trend of decreasing values of |S _CH| from the beginning (carbon 1) to the end (carbon 8) of the hydrophobic tail (Fig. 5c), resulting in a corresponding trend of CP and INEPT intensities according to the τ _c < 10 ns region of Fig. 2c. At the lowest water content and temperature, the spectrum is overwhelmingly dominated by broad CP signals as expected for an amorphous solid with molecules kinetically trapped in many different conformations. Assuming Arrhenius-like changes of τ _c as a function of temperature, analysis of the data (see Ref. [37] for details) indicates that the CP and INEPT intensities follow the predictions in Fig. 2c with a transition from INEPT to CP at τ _c ≈ 10 ns and a narrow region with neither CP nor INEPT at τ _c ≈ 1 µs. In the latter regime the peaks are also broadened by interference between molecular dynamics and ¹H decoupling [59] or MAS [60] but remain visible in DP, thus illustrating the importance of including all measurements in the DP-CP-INEPT combination to minimize the risk of accidentally finding experimental conditions where some carbons are undetectable.

Fig. 5:

Structures, molecular dynamics simulations, and NMR data for the glass-forming surfactant n-octyl-β-d-maltoside (C₈G₂) with transition temperature depending on hydration level. (a) Chemical structure with numbering of carbon atoms. (b) Snapshot from a molecular dynamics simulation of a united-atom model of C₈G₂ at the water content n _w/n _C8G2 = 3 and temperature T = 310 K. The lamellar structure is shown by color-coding of the water (blue) as well as the C₈G₂ hydrophilic headgroups (red) and hydrophobic tails (yellow). (c) C–H bond order parameter |S _CH| and reorientational correlation time τ _c vs. carbon index for the hydrophobic tail as obtained from the molecular dynamics simulations in panel b. (d) 2D array of ¹³C MAS NMR spectra of C₈G₂ as a function of n _w/n _C8G2 and T acquired at ω _0C/2π = 125 MHz, ω _MAS/2π = 5 kHz, 48 kHz TPPM ¹H decoupling, and τ _R = 5 s using DP (gray); CP (blue) with τ _CP = 1 ms, ω _1C/2π = 80 kHz, and ω _1H/2π ramped from 72 to 88 kHz; and INEPT (red) with τ ₁ = 1.8 ms and τ ₂ = 1.2 ms. The chemical shift scale is shown in the bottom left spectra and peak assignments in the top right. Rough estimates of τ _c are shown for carbon 8 and the cluster of peaks from carbons 1, 2′–5′, and 2″–5″. (Adapted from Ref. [37] with permission from Elsevier Inc.)

Additional examples of liquid crystalline and solid phases are illustrated in Fig. 6 for the cationic surfactant cetyltrimethylammonium CTA⁺ with different counterions and co-surfactants. Even without a more detailed analysis, simple visual inspection of the DP, CP, and INEPT spectra in Fig. 6 allows separation between several important cases:

1. solid (high CP, no INEPT) and liquid (high INEPT) phases

2. isotropic (no CP, high INEPT) and anisotropic (CP and INEPT peaks with identical shifts and linewidths and similar amplitudes) liquid crystalline phases

3. amorphous (broad CP) and crystalline (narrow CP) solid phases

4. all-trans (∼33 ppm) and conformationally disordered (29–31 ppm) hydrocarbon chains.

Fig. 6:

Structures and NMR data for liquid and solid crystalline phases comprising hydrated cetyltrimethylammonium ions (CTA⁺) with various counterions and additives. (a) Chemical structure of CTA⁺ with numbering of selected carbon atoms. (b) Molecular packing of CTA⁺ into spherical/cylindrical (top) or planar (middle, bottom) aggregates with cationic headgroups (blue) facing the surrounding water (not shown) and hydrocarbon chains (yellow) undergoing trans/gauche isomerization (top, middle) or in all-trans conformation (bottom). (c) Nanometer-scale structures of hydrated CTA⁺ with succinate (suc) or DNA as counterions and decanol (dec) as cosurfactant. The water content is reported in terms of the water-hydrocarbon chain molar ratios n _w/n _CTA or n _w/(n _CTA + n _dec). (d) ¹³C MAS NMR spectra of the phases in panel (c) using the same acquisition parameters as in Fig. 5. Peak assignments refer to the carbon atom numbering in panel (a) while asterisks indicate peaks originating from succinate or decanol. Vertical dashed lines point out the typical chemical shifts of hydrocarbon chains adopting an all-trans conformation or transitioning between trans and gauche conformational isomers (Adapted from Ref. [9] with permission from the American Chemical Society).

On the other hand, there are relevant cases that cannot be distinguished from the CP and INEPT intensities alone:

1. isotropic liquids and isotropic liquid crystals (no CP, high INEPT)

2. hexagonal and lamellar liquid crystalline phases (similar amplitude CP and INEPT)

3. viscous liquids with τ _c ≈ 100 ns or τ _c > 10 μs and solids with τ _c >> 1 s (high CP, no INEPT).

These cases can however often be distinguished by simple visual inspection or complementary X-ray scattering measurements.

3.1 Surfactants and lipids

While X-ray scattering is unrivalled for investigating crystal symmetries and repeat distances in materials exhibiting periodicity on the atomic and nanometer length scales, NMR offers unique insights into dynamic and non-periodic parts of the structure. Using the relations between molecular dynamics and CP and INEPT signal intensities described in the sections above, the approach has been applied to surfactant systems for studying phase behavior [9], self-association in clay minerals [61], and templating of inorganic mesoporous materials [62] and nanocrystals [63], [64], [65].

In common with surfactants, polar lipids consist of hydrophilic and hydrophobic parts that lead to self-assembly into primarily bilayer structures. Although the importance of lipids in molecular biology can hardly be overstated, they have in comparison to proteins received far less attention in the literature—presumably because of their dynamics and structural disorder (see Fig. 1) that make them difficult to study with scattering techniques, requiring periodicity, or conventional NMR techniques applicable to molecules and supramolecular aggregates with well-defined distances between pairs of atoms. Since the first demonstration of INEPT to achieve ¹³C signal enhancement for lipid membranes in the mid-90s [66, 67] and more detailed comparisons between the signal intensities obtained by DP, CP, INEPT, and nuclear Overhauser effect (NOE) [46], the DP-CP-INEPT approach has been applied in numerous studies of molecular dynamics, chain conformations, and phase behavior in lipid systems of varying chemical complexity [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], including the presence of proteins [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], as well as in intact cells [84, 94] and cortical bone [95].

3.2 Polysaccharides

In nature polysaccharides often occur as poorly crystalline solids or water-swollen networks with appreciable internal dynamics and low structural order. The power of solid-state NMR for characterization of solid polysaccharides is firmly established, in particular for studies of cellulose polymorphism [96], local structure in disordered solids [97], and spatial proximity between various macromolecules [98]. Despite its relative simplicity in comparison to modern multidimensional solid-state NMR techniques, DP-CP-INEPT has found an important niche for screening and chemical characterization of co-existing solid and liquid fractions in technically relevant reaction media for cellulose dissolution and regeneration [99], [100], [101], [102], [103], [104] as well as monitoring the gelatinization of starch during the cooking of spaghetti and other food products [105].

3.3 Proteins

There is a long history of NMR spectroscopy for determining atomic-resolution structures of proteins in solution [106], embedded in lipid membranes [107], and as solid fibrils [108]. Studies of nominally solid proteins with various one- and multidimensional NMR methods incorporating INEPT rather than CP blocks have demonstrated the ubiquity and biological relevance of dynamic and structurally disordered protein fragments extending from more solid fibril cores [109], [110], [111] or membranes [112]. Consequently, numerous NMR studies of proteins in fibrillar forms or embedded in membranes are currently performed with complementary CP and INEPT versions of the pulse sequences in order to not miss potentially important parts of the proteins that may be invisible with the conventional CP-based solid-state NMR methods [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [123], [124], [125], [126], [127], [128], [129].

Most protein NMR studies are performed on samples isotopically labeled with ¹³C and ¹⁵N, to improve the signal-to-noise ratio, and using multidimensional sequences to resolve a sufficient number of individual molecular site to allow for unambiguous determination of the molecular structure. For a multidimensional pulse sequence, each of the CP or INEPT blocks filters the signal as in Fig. 2c, Fig. 3, and Fig. 4, and with multiple transfer steps, as in a conventional 2D ¹H–¹³C HSQC sequence with separate ¹H → ¹³C and ¹³C → ¹H INEPT blocks, the region of the dynamics space with maximum signal enhancement is smaller than for the simple 1D sequences in Fig. 2a. Despite the added complexity with multidimensional sequences, the theoretical polarization transfer efficiencies are useful starting points for interpreting the observed signal intensities in terms of approximate values of the dynamics parameters τ _c, |S _CH|, and τ _s defined in Fig. 2b.

3.4 Stratum corneum

The importance of using experimental methods capable of characterizing both solid and liquid components has been demonstrated with a series of DP-CP-INEPT studies of the stratum corneum at conditions relevant for understanding the molecular mechanisms behind the excellent barrier and mechanical properties of the skin as well as for applications in drug delivery, cosmetics, and skin diseases [130], [131], [132], [133], [134], [135], [136], [137], [138], [139], [140], [141], [142], [143]. While X-ray scattering and electron microscopy studies have given important information about periodic structures formed by the keratin filaments within the corneocytes as well as chain packing and layering of the solid lipids [19], the DP-CP-INEPT approach has enabled detection and characterization of flexible protein domains and fluid lipids that, although being only a small fraction of the total protein and lipid content, appear to have a decisive influence on barrier and mechanical properties. The data in Fig. 7 shows that at low hydration level and temperature most of the stratum corneum components are solid except for a small fraction of fluid lipids. Increasing the temperature mainly melts lipids while increasing the water content primarily swells the terminal domains of the keratin filaments. At the highest water content and temperature, all lipids are melted and only the keratin filament cores remain solid, preserving the mechanical integrity of the material.

Fig. 7:

Experimental ¹³C MAS NMR data for stratum corneum as a function of water content and temperature using acquisition parameters as in Fig. 5 except for 68 kHz ¹H decoupling during ¹³C detection. Assignments in the top right panel indicate the main peaks from selected carbons of the serine (Ser), glycine (Gly), leucine (Leu), and lysine (Lys) amino acid residues of the keratin, as well as the terminal, penultimate, and middle-of-chain carbons of the lipid hydrocarbon chains (ωCH₃, (ω–1)CH₂, and (CH₂) _n ). The observed CP (blue) and INEPT (red) signal intensities are visualized by color coding of the schematic illustrations of keratin filaments and lipids. (Reproduced from Ref. [130] with permission from the authors.)

3.5 Miscellaneous

In addition to the numerous studies of surfactants, lipids, and proteins, DP-CP-INEPT has been applied for obtaining site-resolved information about molecular dynamics in various polymer systems [144], [145], [146], [147], self-assembled materials [148, 149], and deep eutectic solvents [150].