Heteronuclear Dipolar Interactions Research Articles

Structural impact of niobium oxide on lithium silicate glasses: Results from advanced interaction-selective solid-state nuclear magnetic resonance and Raman spectroscopy

While niobium-containing oxide glasses are used in many technological applications, especially optical glasses, the exact structural role of Nb and its impact on the structure of covalent/ionic oxide glasses remain incompletely understood. In the present study, this issue is addressed for Nb2O5-containing lithium silicate glasses using 7Li, 29Si, and 93Nb magic-angle-spinning (MAS) and advanced NMR methods sensitive to 7Li–7Li and 7Li–93Nb magnetic dipole-dipole interactions, accompanied by molecular dynamics (MD) and Monte-Carlo (MC) simulations. In glasses along the compositional line (1–y)Li2Si2O5–yNb2O5, 29Si MAS-NMR spectra reveal a gradual silica network repolymerization with increasing y, indicating that the accommodation of the niobium oxide component into the glassy network requires on average about 0.7 equivalents of lithium oxide. Significant 7Li–93Nb interactions were also detected and quantified by Rotational Echo Saturation Pulse Double Resonance (RESPDOR) experiments. Consistent with this finding, profound changes in the local environments of the lithium ions and their spatial distributions are observed in 7Li satellite transition (SATRAS) spectra and 7Li dipolar spin echo decays, whereas 93Nb NMR and Raman spectra suggest the formation of six-coordinated NbO6 polyhedra with both, corner- and edge-sharing connectivity. Results obtained on glasses along a second composition line, SiO2–[(Li2O)1.4(Nb2O5)], confirm the above-described structural concepts. The average homo- and heteronuclear dipolar interaction strengths as expressed by the second moments M2(Li-Li) and M2(Li-Nb) are consistent with random spatial distributions of the lithium and niobium species, with a tendency towards Nb clustering at higher concentrations. All of these results suggest that niobium oxide adopts a network former role in these glasses. The current study defines a comprehensive general strategy for elucidating the structural impact of NMR active intermediate oxides incorporated into silicate glasses.

Theoretical description of pulse induced resonances in the homonuclear PIRATE experiment

Rotor-synchronous π pulses applied to protons (S) enhance homonuclear polarisation transfer between two spins (I) such as 13C or 15N as long as at least a single I–S heteronuclear dipolar-coupling interaction exists. The enhancement is maximum when the chemical-shift difference Δν between two spins equals an integer multiple, n, of the pulse-modulation frequency, which is half the rotor frequency νr. This condition, applied in the Pulse Induced Resonance with Angular dependent Total Enhancement (PIRATE) experiment, can be generalised for any spacing of the pulses k/νr such that Δν=nνr2k . We show, using average Hamiltonian theory (AHT) and Floquet theory, that the resonance conditions promote a second-order recoupling consisting of a cross-term between the homonuclear and heteronuclear dipolar interactions in a three-spin system. The minimum requirement is a coupling between the two I spins and a coupling of one of the I spins to the S spin. The effective Hamiltonian at the resonance conditions contains three-spin operators of the form 2I1±I2∓Sz with a non-zero effective dipolar coupling. Theoretical analysis shows that the effective strength of the resonance conditions decreases with increasing values of k and n. The theory is backed by numerical simulations, and experimental results on fully labelled 13C-glycine demonstrating the efficiency of the different resonance condition for k=1,2 at various spinning frequencies.

Quantifying quadrupole effects in the NMR spectra of spin-1/2 nuclei in rotating solids.

Quantifying the NMR spectra of spin I = 1/2 nuclei coupled to quadrupolar spins (nuclei with spin quantum number, S > 1/2) has remained an arduous task in solid-state magic angle spinning (MAS) NMR experiments. In particular, extraction of chemical shift anisotropy (CSA) tensors from line-shapes of spin I = 1/2 nuclei coupled to quadrupolar spin (S = 1) in MAS experiments has remained challenging owing to the simultaneous presence of both heteronuclear dipolar interactions and quadrupolar interactions. Unlike experiments that involve only spin-1/2 nuclei, both faster spinning frequencies and stronger decoupling field strengths on the quadrupolar spins are essential to average/minimize the contributions from heteronuclear dipolar interactions. To this end, a quantitative theory based on the concept of "effective fields" is proposed to deduce optimal conditions in experiments that involve simultaneous recoupling and decoupling of heteronuclear dipolar interactions. Through analytic expressions, the spectral frequencies and intensities observed in experiments are quantified and rigorously verified. Since extraction of molecular constraints in NMR experiments involves iterative fitting of experimental data, we believe that the analytic expressions derived would speed up and be beneficial in quantifying such experiments.

Heteronuclear and homonuclear radio-frequency-driven recoupling.

The radio-frequency-driven recoupling (RFDR) pulse sequence is used in magic-angle spinning (MAS) NMR to recouple homonuclear dipolar interactions. Here we show simultaneous recoupling of both the heteronuclear and homonuclear dipolar interactions by applying RFDR pulses on two channels. We demonstrate the method, called HETeronuclear RFDR (HET-RFDR), on microcrystalline SH3 samples at 10 and 55.555 kHz MAS. Numerical simulations of both HET-RFDR and standard RFDR sequences allow for better understanding of the influence of offsets and paths of magnetization transfers for both HET-RFDR and RFDR experiments, as well as the crucial role of XY phase cycling.

Through-space 11 B-27 Al correlation: Influence of the recoupling channel.

Through-space heteronuclear correlation (D-HETCOR) experiments based on heteronuclear multiple-quantum correlation (D-HMQC) and refocused insensitive nuclei enhanced by polarization transfer (D-RINEPT) sequences have been proven to be useful approaches for the detection of the spatial proximity between half-integer quadrupolar nuclei in solids under magic-angle spinning (MAS) conditions. The corresponding pulse sequences employ coherence transfers mediated by heteronuclear dipolar interactions, which are reintroduced under MAS by radiofrequency irradiation of only one of the two correlated nuclei. We investigate herein using numerical simulations of spin dynamics and solid-state NMR experiments on magnesium aluminoborate glass how the choice of the channel to which the heteronuclear dipolar recoupling is applied affects the transfer efficiency of D-HMQC and D-RINEPT sequences between 11 B and 27 Al nuclei. Experimental results show that maximum transfer efficiency is achieved when the recoupling scheme is applied to the channel, for which the spin magnetization is parallel to the B0 axis in average.

A modification of γ-encoded RN symmetry pulses for increasing the scaling factor and more accurate measurements of the strong heteronuclear dipolar couplings

Symmetry based γ-encoded RNnν elements are broadly used in magic-angle spinning solid-state NMR experiments to achieve selective recoupling of the heteronuclear dipolar interactions. The recoupled dipolar couplings in such experiments are scaled by a factor, Ksc, which theoretically depends on the chosen symmetry numbers N, n, and ν. However, the maximum theoretical value of Ksc for γ-encoded RNnν pulses is limited to ~0.25, resulting in long RNnν experiment times. Also, the dependence of Ksc on the experimental parameters can result in systematic errors in the experimental determination of the dipolar couplings, especially at low and moderate MAS rates. In this manuscript, we investigate the use of MODifiEd RNnν symmetry (MODERNnν(ϕM)) pulses that increase the dipolar scaling factor by at least 1.45 fold compared to γ-encoded RNnν. The second advantage of MODERNnν(ϕM) pulses with respect to traditional RNnν pulses is the reduced influence of experimental parameters on Ksc, which allows for more accurate measurement of short-range distances. The robustness of MODERNnν(ϕM) is compared with γ-encoded R1423 symmetry pulses. The enhanced performance is demonstrated on two uniformly-13C-enriched samples, N-acetyl valine and the microcrystalline protein GB1, at a 31.111 kHz MAS rate.

Assessment of new symmetry-based dipolar recoupling schemes for homonuclear magnetization exchange between quadrupolar nuclei in two-dimensional correlation MAS NMR

We provide an extensive experimental and numerical evaluation of MQ-phase (S)M supercycles with M={3,4} of three groups of symmetry-based homonuclear dipolar recoupling rf-pulse sequences, S={SR22p1,SR441,SRNNN/2}, for establishing proximities among half-integer spin quadrupolar nuclei under moderately fast magic-angle-spinning (MAS) conditions in single-quantum–single-quantum (1Q–1Q) correlation NMR experiments. The relative merits of the (S)M schemes for variations in resonance offsets and rf-amplitude errors were assessed by numerically simulated magnetization transfers in spin-3/2 pairs with variable isotropic chemical shifts and quadrupolar coupling constants. Experimental demonstrations of 23Na (spin-3/2) NMR on Na2MoO4·2H2O and 27Al (spin-5/2) NMR on AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O] are presented at 14.1 T and 24 kHz MAS. We recommend using the (SR221)3 or (SR221)4 supercycles for samples that exhibit small chemical-shift dispersions (<3 kHz), and any (SRNNN/2)3 scheme with N⩾10 for larger spreads of isotropic chemical shifts. However, because the (SRNNN/2)3 sequences recouple heteronuclear dipolar interactions, their application to proton-bearing samples requires high-power proton decoupling during the mixing period. Alternatively, the (SR241)3 and (SR241)4 schemes may be employed in the absence of proton decoupling, but with poorer compensation to resonance-offsets and rf-amplitude errors.

Rationalization of solid-state NMR multi-pulse decoupling strategies: Coupling of spin I = ½ and half-integer quadrupolar nuclei.

In this paper we undertake a study of the decoupling efficiency of the Multiple-Pulse (MP) scheme, and a rationalization of its parameterization and of the choice of instrumental set up. This decoupling scheme is known to remove the broadening of spin-1/2 spectra I, produced by the heteronuclear scalar interaction with a half-integer quadrupolar nucleus S, without reintroducing heteronuclear dipolar interaction. The resulting resolution enhancement depends on the set-up of the length of the series of pulses and delays of the MP, and some intrinsic material and instrumental parameters. Firstly through a numerical approach, this study investigates the influence of the main intrinsic material parameters (heteronuclear dipolar and J coupling, quadrupolar interaction, spin nature) and instrumental parameters (spinning rate, pulse field strength) on efficiency and resolution enhancement of the scalar decoupling scheme. A guideline is then proposed to obtain quickly and easily the best resolution enhancement via the rationalization of the instrumental and parameter set up. It is then illustrated and tested through experimental data, probing the efficiency of MP-decoupling set up using this guideline. Various spin systems were tested (31P-51V in VOPO4, 31P-93Nb in NbOPO4, 119Sn-17O in Y2Sn2O7), combined with simulations results.

Observation of proximities between spin-1/2 and quadrupolar nuclei in solids: Improved robustness to chemical shielding using adiabatic symmetry-based recoupling

We introduce a novel heteronuclear dipolar recoupling based on the R21−1 symmetry, which uses the tanh/tan (tt) shaped pulse as a basic inversion element and is denoted R21−1(tt). Using first-order average Hamiltonian theory, we show that this sequence is non-γ-encoded and that it reintroduces the |m| = 1 spatial component of the Chemical Shift Anisotropy (CSA) of the irradiated isotope and its heteronuclear dipolar interactions. Using numerical simulations and one-dimensional (1D) 27Al-{31P} through-space D-HMQC (Dipolar Heteronuclear Multiple-Quantum Correlation) experiments on VPI-5, we compare the performances of this recoupling to those of other non-γ-encoded |m| = 1 heteronuclear recoupling schemes: REDOR (Rotational-Echo DOuble Resonance), SFAM (Simultaneous Frequency and Amplitude Modulation) and R42−1(tt). Such comparison indicates that the R21−1(tt) scheme is more robust to CSA, offset and radiofrequency field inhomogeneities than the other schemes. We take advantage of the high robustness of R21−1(tt) to CSA and offset to demonstrate the possibility to correlate the signals of 207Pb isotope with those of neighboring half-integer spin quadrupolar nuclei. Such approach is demonstrated experimentally by acquiring 11B-{207Pb} D-HMQC 2D spectra of Pb4O(BO3)2 crystalline powder.

Engineering spin Hamiltonians using multiple pulse sequences in solid state NMR spectroscopy

Multiple pulse sequences are often used to manipulate spin Hamiltonians in solid-state nuclear magnetic resonance spectroscopy. In this paper, we analyze multiple pulse sequences using the well-known average Hamiltonian theory. We first expand the resulting average Hamiltonian into a reachable set of sub-Hamiltonians and then develop a general procedure using both flip-angle and phase of the applied pulses as control variables to select any of those sub-Hamiltonians. We use this method to analyze solid-echo based sequences and to design new proton-proton homonuclear decoupling sequences in static solids. It is found that this newly designed decoupling scheme, in the presence of finite pulse length, effectively suppresses the 1H–1H homonuclear dipolar interactions while establishes variable scaling factors on the heteronuclear dipolar interactions and chemical shift interactions, depending on the flip-angle of the applied pulses. When the pulse flip-angle is close to 54.7°, this sequence possesses a large scaling factor with relatively low average decoupling field. When the pulse flip-angle becomes ∼120°, the scaling factor is almost zero. A static 15N-acetyl-valine crystal sample has been used as an example to confirm and validate the performance of this new decoupling scheme.

Design and construction of a quadruple-resonance MAS NMR probe for investigation of extensively deuterated biomolecules

Extensive deuteration is frequently used in solid-state NMR studies of biomolecules because it dramatically reduces both homonuclear (1H-1H) and heteronuclear (1H-13C and 1H-15N) dipolar interactions. This approach greatly improves resolution, enables low-power rf decoupling, and facilitates 1H-detected experiments even in rigid solids at moderate MAS rates. However, the resolution enhancement is obtained at some cost due the reduced abundance of protons available for polarization transfer. Although deuterium is a useful spin-1 NMR nucleus, in typical experiments the deuterons are not directly utilized because the available probes are usually triple-tuned to 1H,13C and 15N. Here we describe a 1H/13C/2H/15N MAS ssNMR probe designed for solid-state NMR of extensively deuterated biomolecules. The probe utilizes coaxial coils, with a modified Alderman-Grant resonator for the 1H channel, and a multiply resonant solenoid for 13C/2H/15N. A coaxial tuning-tube design is used for all four channels in order to efficiently utilize the constrained physical space available inside the magnet bore. Isolation among the channels is likewise achieved using short, adjustable transmission line elements. We present benchmarks illustrating the tuning of each channel and isolation among them and the magnetic field profiles at each frequency of interest. Finally, representative NMR data are shown demonstrating the performance of both the detection and decoupling circuits.

Microsecond Time Scale Proton Rotating-Frame Relaxation under Magic Angle Spinning.

This paper deals with the theoretical foundation of proton magic angle spinning rotating-frame relaxation (R1ρ) and establishes the range of validity and accuracy of the presented approach to describe low-amplitude microsecond time scale motion in the solid state. Beside heteronuclear dipolar and chemical shift anisotropy interactions, a major source of relaxation for protons is the homonuclear dipolar interaction. For this latter relaxation process, no general analytical equation has been published until now, which would describe the R1ρ relaxation at any spinning speed, spin-lock field, or tilt angle. To validate the derived equations, we compared the analytical relaxation rates, obtained by solving the master equation within the framework of Redfield theory, with numerically simulated relaxation rates. We found that for small opening angles (∼10°), the relaxation rates obtained with stochastic Liouville simulations agree well with the analytical Redfield relaxation rates for a large range of motional correlation times. However, deviations around the rotary-resonance conditions highlight the fact that Redfield treatment of the solid-state relaxation rates can only provide qualitative insights into the microsecond time scale motion.

Rotational resonance for a heteronuclear spin pair under magic-angle spinning in solid-state NMR.

Rotational resonance (R2) is one of the widely applied techniques in solid-state NMR for recoupling a homonuclear dipolar interaction under magic-angle spinning (MAS). R2 occurs as the result of interference between the difference of the chemical shifts and MAS. In this work, we extend R2 to a heteronuclear dipolar interaction in the interaction frame of RF irradiation. Based on the average Hamiltonian theory, we show that the recoupling of the heteronuclear dipolar (I-S) interaction occurs at the recoupling conditions written as ΩI'±ΩS'=kωr (k=0,±1,±2), where ΩX' is the RF offset for spin-X (X = I or S) scaled by RF irradiation. The new recoupling sequence for a heteronuclear spin pair is referred to as offset-driven cross polarization along the z axis (OD-CPZ). With the robustness for RF inhomogeneity and ten recoupling conditions to choose, OD-CPZ can be a useful frequency-selective cross polarization method. Experiments and numerical simulations are shown with the results of the theoretical analysis.

Solvent signal suppression for high-resolution MAS-DNP

Dynamic nuclear polarization (DNP) has become a powerful tool to substantially increase the sensitivity of high-field magic angle spinning (MAS) solid-state NMR experiments. The addition of dissolved hyperpolarizing agents usually results in the presence of solvent signals that can overlap and obscure those of interest from the analyte. Here, two methods are proposed to suppress DNP solvent signals: a Forced Echo Dephasing experiment (FEDex) and TRAnsfer of Populations in DOuble Resonance Echo Dephasing (TRAPDORED) NMR. These methods reintroduce a heteronuclear dipolar interaction that is specific to the solvent, thereby forcing a dephasing of recoupled solvent spins and leaving acquired NMR spectra free of associated resonance overlap with the analyte. The potency of these methods is demonstrated on sample types common to MAS-DNP experiments, namely a frozen solution (of l-proline) and a powdered solid (progesterone), both containing deuterated glycerol as a DNP solvent. The proposed methods are efficient, simple to implement, compatible with other NMR experiments, and extendable past spectral editing for just DNP solvents. The sensitivity gains from MAS-DNP in conjunction with FEDex or TRAPDORED then permits rapid and uninterrupted sample analysis.

Site-resolved multiple-quantum filtered correlations and distance measurements by magic-angle spinning NMR: Theory and applications to spins with weak to vanishing quadrupolar couplings

We discuss and analyze four magic-angle spinning solid-state NMR methods that can be used to measure internuclear distances and to obtain correlation spectra between a spin I = 1/2 and a half-integer spin S > 1/2 having a small quadrupolar coupling constant. Three of the methods are based on the heteronuclear multiple-quantum and single-quantum correlation experiments, that is, high rank tensors that involve the half spin and the quadrupolar spin are generated. Here, both zero and single-quantum coherence of the half spins are allowed and various coherence orders of the quadrupolar spin are generated, and filtered, via active recoupling of the dipolar interaction. As a result of generating coherence orders larger than one, the spectral resolution for the quadrupolar nucleus increases linearly with the coherence order. Since the formation of high rank tensors is independent of the existence of a finite quadrupolar interaction, these experiments are also suitable to materials in which there is high symmetry around the quadrupolar spin. A fourth experiment is based on the initial quadrupolar-driven excitation of symmetric high order coherences (up to p = 2S, where S is the spin number) and subsequently generating by the heteronuclear dipolar interaction higher rank (l + 1 or higher) tensors that involve also the half spins. Due to the nature of this technique, it also provides information on the relative orientations of the quadrupolar and dipolar interaction tensors. For the ideal case in which the pulses are sufficiently strong with respect to other interactions, we derive analytical expressions for all experiments as well as for the transferred echo double resonance experiment involving a quadrupolar spin. We show by comparison of the fitting of simulations and the analytical expressions to experimental data that the analytical expressions are sufficiently accurate to provide experimental (7)Li-(13)C distances in a complex of lithium, glycine, and water. Discussion of the regime for which such an approach is valid is given.

Two-dimensional proton-detected (35)Cl/(1)H correlation solid-state NMR experiment under fast magic angle sample spinning: application to pharmaceutical compounds.

The determination of structure of hydrochloride salts of active pharmaceutical ingredients (HCl APIs) utilizing (35)Cl solid-state NMR studies has been of considerable interest in the recent past. Until now these studies relied on the (35)Cl direct observation method which has its own limitations in terms of the sensitivity and resolution due to the quadrupolar nature and the low gyromagnetic ratio of (35)Cl. In this contribution we demonstrate the two-dimensional (2D) (35)Cl/(1)H correlation measurement by using the proton detection-based (indirect observation of (35)Cl via(1)H) approach under fast magic angle sample spinning (MAS: 70 kHz). The main advantages of this approach over the direct observation method are highlighted in the present study. We have employed heteronuclear magnetization transfer through the recoupling of (35)Cl-(1)H heteronuclear dipolar interactions. The applicability of (35)Cl indirect detection method is first demonstrated on hydrochloride salts of amino acids, l-tyrosine·HCl and l-histidine·HCl·H2O following which the 2D (35)Cl/(1)H correlations are obtained for HCl APIs, procainamide HCl (Proc) and aminoguanidine HCl (Amin). On the basis of separation between the central transition (CT) and satellite transition (ST) peaks, and the shape/width of CT powder patterns, it is also shown that the quadrupolar parameters which are useful for the elucidation of the molecular structure can be determined. Moreover, the (35)Cl/(1)H correlations provide the precise determination of (1)H chemical shifts of nearby (35)Cl nuclei.

Water dynamics on ice and hydrate lattices studied by second-order central-line stimulated-echo oxygen-17 nuclear magnetic resonance.

Oxygen-17 stimulated-echo spectroscopy is a novel nuclear magnetic resonance (NMR) technique that allows one to investigate the time scale and geometry of ultraslow molecular motions in materials containing oxygen. The method is based on detecting orientationally encoded frequency changes within oxygen's central-transition NMR line that are caused by second-order quadrupolar interactions. In addition to the latter, the present theoretical analysis of various two-pulse echo and stimulated-echo pulse sequences takes also heteronuclear dipolar interactions into account. As an experimental example, the ultraslow water motion in polycrystals of tetrahydrofuran clathrate hydrate is studied via two-time oxygen-17 stimulated-echo correlation functions. The resulting correlation times and those of hexagonal ice are similar to those from previous deuteron NMR measurements. Calculations of the echo functions' final-state correlations for various motional models are compared with the experimental data of the clathrate hydrate. It is found that a six-site model including the oxygen-proton dipolar interaction describes the present results.

Measuring 19F shift anisotropies and 1H–19F dipolar interactions with ultrafast MAS NMR

A new 19F anisotropic–isotropic shift correlation experiment is described that operates with ultrafast MAS, resulting in good resolution of isotropic 19F shifts in the detection dimension. The new experiment makes use of a recoupling sequence designed using symmetry principles that reintroduces the 19F chemical shift anisotropy in the indirect dimension. The situations in which the new experiment is appropriate are discussed, and the 19F shift anisotropy parameters in poly(difluoroethylene) (PVDF) are measured. In addition, similar recoupling sequences are shown to be effective for measuring 1H–19F distances via the heteronuclear dipolar interaction. This is demonstrated by application to a recently synthesized zirconium phosphonate material that contains one-dimensional chains linked by H–F hydrogen bonds.

Probing Molecular Mobility in Nanostructured Composites by Heteronuclear Dipolar NMR Spectroscopy

Conformational and reorientational dynamics of surfactant molecules confined within solid inorganic frameworks of nanostructured composites are studied by solid-state NMR. Since the organic part in the nanocomposites exhibits a great variation in the local molecular mobility, a significant challenge in these materials is to develop an experimental method efficient both for nearly immobilized and for highly dynamic flexible molecules. We introduce a dipolar recoupling NMR technique to study local molecular motion via heteronuclear dipolar spin interactions in a wide range of coupling constant values. The approach is efficient in both rigid and mobile molecules. The method is applied to ordered nanostructured composites to obtain model-independent information on the local molecular dynamics. On the basis of experimentally determined local order parameters of the molecular segments, we put forward physical models for the motion of surfactant molecules in nanoconfined assemblies. In composites with lamellar structure, the hydrocarbon chains adopt well-ordered essentially all-trans conformations and, depending on sample composition, undergo either small-angle wobbling or free rotation around the long molecular axes. In contrast, surfactant molecules in hexagonal mesoporous silica exhibit highly dynamic conformationally disordered chains.

Morphology, mechanical properties and thermal degradation kinetics of PMMA-zirconia nanocomposites prepared by melt compounding

Zirconia nanoparticles were synthesized by means of a sol-gel method and embedded in poly(methyl methacry- late) (PMMA) by melt compounding. The zirconia was well dispersed in the PMMA matrix, with only a few clusters, espe- cially for the highest investigated zirconia content. NMR results showed heteronuclear dipolar interactions involving the carbons and the surrounding hydrogen nuclei. The effect of the amount of zirconia, in the range of 1-5!wt%, on the thermo- mechanical properties and thermal degradation kinetics of PMMA was also investigated by means of dynamic mechanical analysis (DMA), thermogravimetric analyses (TGA), and Fourier-transform infrared spectroscopy (FTIR). The presence of zirconia showed a decrease in the storage and loss moduli at lower temperatures, probably due to a plasticization effect. The presence of zirconia in PMMA slightly increased its thermal stability, but the activation energies of thermal degradation for the nanocomposites were significantly lower, at degrees of conversion higher than 0.3, than those of pure PMMA.