Molecular motion and orientation distributions in melt-processed, fully aromatic liquid crystalline polyesters from 1H NMR

Solid State Nuclear Magnetic Resonance 12 Ž1998. 97–112

Molecular motion and orientation distributions in melt-processed, fully aromatic liquid crystalline polyesters from 1 H NMR Michael Gentzler, Siddharth Patil, Jeffrey A. Reimer ) , Morton M. Denn Center for AdÕanced Materials, Lawrence Berkeley National Laboratory, Berkeley, CA, USA Department of Chemical Engineering, UniÕersity of California at Berkeley, Berkeley, CA 94720-1462, USA Received 5 January 1998; revised 12 February 1998; accepted 25 February 1998

Abstract Fully-aromatic thermotropic liquid crystalline polymers ŽLCP. containing 4-hydroxybenzoic acid ŽHBA. and 6-hydroxy2-naphthoic acid ŽHNA. were studied with 1 H NMR. A two- or three-parameter nematic director distribution in molten or nearly molten samples was obtained via rigorous simulation of wideline spectral lineshapes. This methodology was further employed to yield the chain director distribution in macroscopic sections derived from a frozen contraction flow. In addition, the dynamic conformation of polymer chains through the melting transition was monitored via lineshape analysis of samples having Žbulk. isotropic director distributions. Extension of rigorous 1 H NMR spectral deconvolution to recently developed solid-state NMR imaging sequences is discussed. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Liquid crystal polymer; Molecular motion; Orientation distribution

1. Introduction Main-chain liquid crystal polymers ŽMLCPs. form a technologically important class of materials that exhibit a variety of interesting mechanical, physical and chemical properties w1–3x. These materials are of fundamental scientific interest because ‘chain stiffness’ results in a propensity to form liquid crystalline phases, particularly nematic phases. The nematic character of many quiescent MLCPs, however, is concealed within microscopic domains w4–6x. The nematic fluid orientation in adjacent domains varies,

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Corresponding author. Tel.: q1-510-642-8011; Fax: q1-510642-4778; E-mail: [email protected]

resulting in samples that appear isotropic when measured on mesoscopic length scales. Deformation greatly affects MLCP domain texture and generally leads to macroscopic orientation in the flow direction at high rates w7,8x. The significant viscosity drop that accompanies ‘nematic domain alignment’ is desirable for injection molding w2,3x; complex flow geometries have regions of both high and low deformation rates Žand regions of shearing and elongation.. Uncontrolled development of order in mold geometries w9–11x leads to undesirable part inhomogeneities, such as peeling surface skins, weak weld lines and warpage w12x. The coupling between domain alignment and deformation is fundamentally not understood w13,14x, and an improved understanding of this relationship is essential

0926-2040r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 6 - 2 0 4 0 Ž 9 8 . 0 0 0 5 6 - 3

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M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

if the technological promise of MLCPs is to be realized. Measurement of the macroscopic fluid alignment and orientation in a complex flow geometry would be useful to theorists trying to develop mesoscopic constitutive relations between fluid stress, order and deformation. These theories consider a length scale just large enough to average over the microscopic nematic disclination texture; fluid order then becomes a continuous field and the ‘mesoscopic order parameter tensor’ Žfor a uniaxial fluid., Sm Ž x, y, z ., can be defined w13x as Sm sSm Ž nm nm y1r3 . .

Ž 1.

MLCP alignment and orientation are characterized by the scalar Sm and the average chain direction or director, nm , respectively. For an isotropic sample, Sm s 0; for an untextured mono-domain sample the bulk measurement of Sm yields the nematic order parameter, Snematic . Demonstrated techniques for observing mesoscopic structure in processed, commercial main-chain LCPs, such as the fully-aromatic copolyesters of 4-hydroxybenzoic acid ŽHBA. and 6-hydroxy-2naphthoic acid ŽHNA., have all required ex situ solid cutting w10,11x or fracture; this is largely due to the fact that these LCP’s are opaque to visible light. In situ studies have been limited to simple geometries; average melt alignment and orientation, in response to shearing w15x and magnetic fields w16,17x, have been studied by X-ray diffraction. Nuclear magnetic resonance ŽNMR. may be an excellent technique for MLCP characterization. NMR has proven very useful for determination of scalar order parameters in mono-domain LC fluids w18x and sidechain LCPs w19x, even under flow w20x. NMR directly yields a local order parameter, S loc , of uniaxial nuclear interaction tensors from a motionally averaged frequency, v , referenced to a spin interaction principle axes systems ŽPAS.. Here, the order parameter depends on the sample orientation in the magnetic field, and is not an absolute measure of local order. S loc s vrvmax sP2 Ž cos b PASyLAB . ,

Ž 2.

where P2 Ž x . s Ž3 x 2 y 1.r2 and P2 Ž x . indicates a time average over the NMR measurement period;

b PAS-LAB is a polar angle between the unique PAS axis and the magnetic field. For a monodomain nematic, the molecular ‘long axis’ ŽLD. and nematic director ŽND. are the relevant intermediate axes; the local order parameter, using the addition theorem for spherical harmonics, is given w1x by S loc s P2 Ž cos Ž b PASyLD . . P2 Ž cos Ž b LDyND . . =P2 Ž cos Ž b NDyLAB . .

Ž 3.

Henceforth, the definition for angles will be used as in Fig. 3; i.e., x s b LD-ND and b s b ND-LAB . For a rigid-rod polymer Snematic s P2 Ž cos Ž x . . ; this is easily calculated, provided the fluid orientation, b , is known. Snematic s

S loc P2 Ž cos Ž b PASyLD . . P2 Ž cos Ž b . .

Ž 4.

The relative orientation of the PAS and the long molecular axis will not fluctuate, since the polymer molecules behave like rigid rods Žvalid as long as the persistence length is much larger that the monomer length.. Eq. Ž4. simply states that given the relationship between a spin Hamiltonian PAS system and a molecular axis, and the macroscopic orientation of a sample in a magnetic field, one can determine Snematic via measurement of S loc . One could therefore envision exploiting NMR imaging techniques to characterize order and velocity fields simultaneously in a complex flow field. While optimism abounds in the NMR community regarding the potential for such studies, there are significant challenges that must be overcome to realize the potential of NMR for the study of order in quiescent and flowing main-chain LCP materials. Characterization of main-chain LCP mesoscopic order is not necessarily a simple extension of NMR measurements of S loc . For example, a distribution of splittings or frequencies, P Ž v ., will generally be observed for a given NMR ‘site’ and the director distribution, needed for assessment of Sm and nm , is not the only contributing factor to P Ž v .. Consider the average splitting, ² vrvmax :, as a probe of aÕerage local order: ² S loc : s ² P2 Ž cos Ž b PASyLD . . :i ²P2 Ž cos Ž x . . :i i =² P2 Ž cos Ž b . . :i i i

Ž 5.

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

Note that the three distinct distributions, i, ii, and iii, represent variation in PAS parameters, local motional environments, and nematic ‘domain’ directors, respectively. With appropriate labelling a PAS distribution is not expected. In contrast, site motional heterogeneity should be very common to main-chain LCPs since the most useful melt processed materials are wholly-aromatic random copolymers w1x. Since any ‘dynamic conformation’ distribution is similarly convoluted with the chain orientation distribution, failure to assess P Ž x . moments independently could introduce significant error into determinations of P Ž b . moments. For example, consider only the average mesoscopic alignment, Sm . If the fluid is nominally oriented along the magnetic field direction Sm s ² P2 ŽcosŽ b ..:i i i and Eq. Ž5. yields Sm s

² Sloc : P2 Ž cos Ž b PASyLD . . ²P2 Ž cos Ž x . . :i i

for n5Bz ;

Ž 6. Even for this special case, one must independently d eterm in e th e av erag e m o tio n al facto r ²P2 Ž cos Ž x . . :i i. For the real case, assessing both mesoscopic alignment Ž Sm . and orientation Žnm ., a full director distribution must be determined independently of the full motional amplitude distribution. To our knowledge, this deconvolution of NMR ‘site inhomogeneity’ from S loc distributions has not been realized previously in the literature w23,24x. The simplest approach for characterizing SŽ x, y, z . may be spatially resolved spectroscopy w25x of a well-labeled polymer molecule. With a few carefully chosen sites on each rigid unit in a main-chain LCP, a unique chain orientation distribution function might be obtained and SŽ x, y, z . calculated. In practice, the imaging might involve variations of the proton decoupled, PG dipolar-echo sequence w26x for 13 C or 15 N labels, or a PG quadrupolar-echo sequence for 2 H labels or isolated 1 H pairs. Such schemes, however, can have significant practical difficulties: isotopic labelling chemistry, relatively wide spectral lineshapes for 2 H NMR, and the potential demand for multiple-frequency high-power rf excitation. Furthermore, there may be a large fluid requirement since many ‘mixed flow’ geometries, the simplest of which is a contraction or expansion, require recirculation over the long NMR experimental times.

99

Considering the above, we decided to use natural abundance 1 H as an orientational probe in the commercial, engineering thermotropic MLCP known as Vectra-A, a random copolyester comprised of 73% 4-hydroxybenzoic acid ŽHBA. and 27% 6-hydroxy2-naphthoic acid ŽHNA., as well as copolyesters having other compositions of these same monomers. By exploiting natural abundance 1 H, we obtain excellent signal-to-noise in short experimental times. We have the added advantage of having spin-labels on all chain units. Vectra-A is, however, a random copolymer w27,28x and thus we must also deconvolute anticipated site inhomogeneity. We find that a chain director orientational distribution relative to the magnetic field direction can be extracted from the 1 H spectrum of the molten Žor nearly molten. MLCP; our spectral analysis improves upon previous studies that have failed to account for site inhomogeneity. A molecular model of monomeric motional averaging on the NMR experimental timescale is invoked; the relevant distribution of monomeric fluctuation amplitudes is measured with isotropic samples and then fixed for director determinations on the contraction flow samples. The localized director distributions in a contraction flow are investigated by sectioning a macroscopic sample. The problem of director distribution uniqueness is discussed briefly. Extension of the experiments to spatially-resolved 1 H spectra is discussed, specifically for the MLCP Vectra-A. Density matrix simulations indicate that the Vectra-A monomeric units, a phenyl group with 4 protons and a naphthyl group with 6 protons, behave to a good approximation as isolated 2 and 3 spin systems for modest echo times; with typical gradients, sub-millimeter spatial resolution could eventually be attained. For FT imaging, however, sequences must be devised to obtain pure-phase echoes from both moieties.

2. Experimental 2.1. Materials and methods All NMR spectra were obtained on a home-built solid-state NMR spectrometer operating at 99.7 MHz

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M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

for 1 H resonances. The home-built, static VT-probe, used for all measurements, contained the samples within the NMR coil and exposed to a 11 ATM He or dry nitrogen atmosphere to suppress off-gassing. A nominal 908 pulse of 3 m s, a ringdown delay of 4 m s, and a 1 m s dwell time were used for all experiments. The recycling delay was set to 4–5 = T1 Žsee w33x. for all measurements. All ‘powder’ spectra shown are 128 averaged scans Žexcept the 75r25 330C spectrum: 64 scans.. No shifting or broadening function was applied to the data before Fourier transforming. A zero-order phase correction to within 18 was applied manually. The 1 H probe background signal was checked at room temperature prior to, and following, all measurements involving sample melting. The broad, featureless background signal was always less than 0.5% of the total signal, usually much less than 0.25%. All samples were heated from room temperature to 2808C for measurement. The heating proceeded at 58Crmin above 2208C with no overshoot. Density matrix calculations of the 1 H-NMR spectra for isolated HBA and HNA units following pulsed excitation were programmed in Mathematica Version 3.0 on an SGI Impact2 computer. After formulating the appropriate product basis wave functions for four- and six-coupled spins, an initial density matrix was generated using the Boltzmann distribution. For various pulse schemes the time-independent solution to the Liouville equation, r Ž t . s expŽyŽ ir" . Ht . r Ž0. expŽŽ ir" . Ht ., was calculated. In the case of the solid-echo sequence, the initial density matrix was subject to a pr2 rotation, a delay in which only the dipolar Hamiltonian was allowed to evolve, a second pr2 rotation phase-shifted by 908, followed by another delay with dipolar evolution. In this latter period real and imaginary magnetization was calculated using a 10 m s dwell time. A constant T2 relaxation rate of 300 Hz was assumed throughout. Simulations for the six-coupled spins took several hours of workstation CPU time. The 75r25,73r27 ŽVectra-A900., 58r42 and 30r70 polyŽHBA-HNA. copolyesters were supplied in pellet form by the Hoechst Celanese. All samples were dried under vacuum Ž- 0.1 Torr. at 120–1308C for 36 h before use. ‘Powder’ samples were prepared without net director alignment: polymer pellets were

ground, and premelted in the NMR probe outside of the magnet at 3208C at 11 atmospheres for 20 min, followed by rapid cooling. All data were acquired during discrete temperature ramps in situ. In most cases the time spent at any temperature above 1408C was not more than one hour. The total time at elevated temperatures for some samples may have been many hours; multiple experiments indicate no effects from sample degradation. A frozen capillary flow was obtained with a home-built vacuum molding apparatus described previously w29x. A cylindrical mold acted as the reservoir, or barrel, for a removable capillary, attached at the base, with a 1808 entrance angle. Pressure was applied in the barrel via a flat, brass-tipped piston, driven vertically by an Instron model 1321 servo-hydraulic testing machine. The barrel and capillary had diameters of 0.385Y and 0.064Y and lengths of 5Y and 3.064Y , respectively. Prior to the flow experiment a void-free, solid rod of Vectra-A900 was prepared in the barrel w29x. This rod, having been re-dried, was reinserted into the barrel and the entire apparatus was heated to 3168C under 222 N of piston force. After 5 min, the temperature and force were reduced to 3108C and 44 N, respectively. Flow began by removal of a pin in the capillary exit. To halt the flow quickly, the heater was turned off and water was sprayed at the capillary exit. The estimated centerline cooling times to 2808C for the barrel and capillary were 200 and 10 s, respectively. The shear rates in the barrel and capillary were found to have been 0.067 sy1 and 14.5 sy1, respectively. ŽFrom the force, a viscosity of 165 Pa was calculated; this is half that expected.. The bold rectangles in Fig. 9 indicate cylindrical or annular sections taken from the barrel or capillary. The capillary and barrel wall sections were cut into two and six pieces, respectively, in order to fit into the NMR coil. All sections were placed in the coil with the flow centerline axis parallel to the vertical static magnetic field. The barrel wall pieces were arranged to approximate the expected axial symmetry in the flow system. Sectioning was done with a fine hand saw, with trimming by razor blades. All sections were relatively free of bubbles, which were apparent in a few regions of the barrel due to the low molding pressure.

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

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3. Results

3.1. Polymer motional model Fig. 1d shows the 1 H broad-line NMR spectrum from a purely molten, unaligned sample of 30r70 polyŽHBA-HNA.. Within a resolution of 100 Hz, the lineshape is symmetric and structured. A rigorous spectral simulation is expected to yield more information regarding orientation distributions. To calculate the 1 H NMR spectrum of molten polyŽHBArHNA. we make three assumptions: Ž1.

Fig. 2. Likely rotation axes of melted polyŽHBArHNA. monomers. The possible HNA axes have two extremes, compared to the chosen pseudo para-axis.

Fig. 1. Stages of 1 H spectral simulation Žof unaligned, melted HBArHNA copolyesters.: calculated, dipolar ‘stick’ spectra of spinning HBA and HNA units, aligned along the magnetic field Ža.; powder spectra constructed by interpolation of stick spectra Žb.; least-squared-error, calculated 30r70 HBArHNA spectrum, with parameterized tilt-angle distributions and Gaussian broadening as adjustable parameters Žc.; experimental data Žd.; error of simulation, multiplied by 5 Že..

Fig. 3. Schematic definition of b , the local director orientation angle, and x , which quantifies the amplitude of monomer fluctuation, about the local director, on the NMR time-scale.

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intermolecular 1 H dipolar couplings are completely averaged on the NMR timescale of 0.1 ms–10 ms due to translational motion and conformational fluctuations of molten chains; Ž2. all aromatic rings on all chains are spinning rapidly and independently of adjacent rings about an appropriate local axis indicated in Fig. 2 Žsee Appendix A.; Ž3. the 1 H spectrum of a single chain will be dominated by component ring 1 H subspectra. We furthermore assume weak inter-ring proton couplings will only appear as homogeneous broadening. If all aromatic rings are

spinning, it is clear from internuclear distances that the strongest dipolar couplings will be between protons on individual rings. These assumptions will be closely scrutinized later. Fig. 1a shows the 1 H dipolar subspectra for isolated, spinning phenyl and naphthyl groups, with their rotation axes parallel to the static magnetic field. In a high viscosity, ‘polydomain textured’ thermotropic nematic melt, the aromatic rings will not be perfectly aligned with the magnetic field and will be undergoing fluctuations about the local chain

Fig. 4. Experimental 1 H spectra of unaligned HBArHNA copolyesters, close to nominal melting points. Three different compositions were investigated.

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

axis and director. The spectra are therefore scaled by 2 2 Ž 3 cos Ž x .y1 . . Ž 3cos Ž b .y1 . . where x is the NMR 2

2

time-averaged fluctuation amplitude, or ‘tilt-angle,’ and b is the angle between the local director and the static magnetic field, as shown in Fig. 3. The final 1 H dipolar subspectra will reflect the convolution of director orientation distribution and the HBA and HNA tilt-angle distributions due to random chain structure:

HP Ž x .HP Ž b .P Ž cos x . P Ž cos b . 2

2

103

sentative experimental spectra with simulated lineshapes. The single-parameter, monomer tilt-angle distribution functions used in the simulations are shown in Fig. 6A. The parameters which give the best-fit simulation to the data in Fig. 4 are shown vs. temperature in Fig. 7. ŽDetails of the computation are contained in Appendix B.. It is important to establish in which spectra the samples are completely molten and unaligned by the

f HBA l HBA8 Ž n .

q Ž 1 y f HB A . l HNA8 Ž n . d x d b .

Ž 7.

Here l HB 8 AŽ n . and l HNA 8 Ž n . are the sub-spectra in Fig. 1a and f HB A is the HBA copolymer fractional content. As stated in the introduction, since both distribution types simply scale transition energies, spectral deconvolution for a sample of unknown macroscopic alignment and monomer tilt-angle distributions is impossible. In S ection 3.2, w e exam ine m olten polyŽHBArHNA. samples with an isotropic director distribution and, from a least- squares fit, obtain the average tilt-angle for each monomer, x HB A and x HN A , as well as a residual spectral broadening. The unaligned, poly-domain melt is a more appealing starting point than a monodomain; besides the difficulty of attaining a perfect monodomain sample, the director distribution in a monodomain would still be unknown due to slow elastic modes w24x. In Section 3.3, the average tilt-angles and residual broadening are obtained for Vectra-A900 powder at 2808C. Taking these to be fixed parameters in the least squares fit, we obtain the director distribution, P Ž b ., in the frozen, then sectioned, contraction flow samples via deconvolution of 1 H NMR spectra taken at 2808C. Further computational details are found in Appendices B and C. 3.2. Chain conformation in the melt Fig. 4 shows 1 H spectra for 75r25, 58r42 and 30r70 polyŽHBArHNA. at temperatures ranging from below the melting points to 3508C or to a lower temperature at which magnetic-field- induced domain alignment had just begun. Fig. 5 shows repre-

Fig. 5. Comparison of experimental Žsolid. and best-fit simulated Ždashed. 1 H spectra for unaligned 75r25, 58r42 and 30r70 HBArHNA Ža, b and c, respectively.. A fully-melted and incompletely melted spectrum are shown for each composition.

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Fig. 6. Monomer tilt-angle distribution functions investigated. Models ‘A’, ‘B’ and ‘C’ contain one adjustable parameter, the average tilt-angle, per distribution. For these models, homogeneous broadening was the third adjustable parameter used in the fits.

magnetic field. The temperature dependence of the homogeneous broadening clearly indicates the melting of the copolyesters, as that transition is associated with the onset of chain translational motion. For all compositions, the high amount of homogeneous broadening at low temperatures can only be due to strong intermolecular 1 H dipolar interactions between aromatic rings with little relative motion on an NMR timescale. The temperatures at which the broadening has ‘leveled off’ at a nearly constant, low value indicate completely molten samples. The monotonic decrease of the broadening with temperature, and the composition-dependent temperatures at which complete melting is observed, is fully consistent with previous studies of the slow crystallization processes for these polymers w30x. For the 75r25 and 58r42 compositions, at 3508C and 3308C respectively, transient broadening of the lineshape during the data acquisition indicated very slow domain alignment Žwith a time constant of hours. in the magnetic field. Since perfect alignment doubles the average spectral splitting observed in a powder sam-

ple, the slight alignment, apparent in these spectra, produced a sharp decrease in the apparent HNA average tilt-angle. Results for fully molten, unaligned spectra are shown in Table 1. The average tilt-angle for HBA s 15 " 18 for all compositions and melt temperatures. The average HNA tilt-angle increases slightly as HNA content in the LCP increases from 25% to 70%. 3.3. Director distributions in Vectra-A900 mold Fig. 8 shows the experimental and simulated 1 H lineshapes for three sections of the frozen VectraA900 flow near the contraction. ŽThese results are representative of the remaining sections.. Fixed parameters in the spectral fits included the P Ž x . distributions and residual broadening obtained from the spectral fit of a pre-melted powder sample heated from room temperature to 2808C. ŽSee Appendix C.. In general, for a suitably small sample voxel with unknown director alignment, a two parameter spec-

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Table 1 Average monomer fluctuation amplitudes Žin degrees. and residual spectral broadening for unaligned, fully-m elted polyŽHBArHNA. HBArHNA

T, 8C

a x HB A

a x HNA

G.B., Hz ab

75r25 58r42

310 265 290 310 330 330

14.6 Ž0.15. 14.8 Ž0.2. 15.1 Ž0.2. 15.3 Ž0.2. 15.5 Ž0.2. 15.7 Ž0.35.

14.4 Ž0.5. 16.5 Ž0.25. 15.7 Ž0.3. 15.7 Ž0.3. 16.0 Ž0.3. 18.0 Ž0.15.

481 Ž14. 444 Ž8. 433 Ž9. 454 Ž9. 486 Ž9. 389 Ž5.

30r70 a b

Ž. Denotes fit uncertainty. Expressed as a Gaussian full-width at half-maximum, Hz.

tion; however, because an axially symmetric geometry was chosen, the sections were cut to maintain that symmetry. ŽNote, however, that violation of axial symmetry near the contraction has been observed

Fig. 7. HBA and HNA fluctuation amplitudes, and residual Gaussian 1 H spectral broadening, in polyŽHBArHNA., vs. temperature. The compositions are 75r25 Žopen squares., 58r42 Žfilled circles. and 30r70 Žtriangles. HBArHNA. ŽLines are drawn to connect data points.. Possible melting point ranges Ždue to annealing affects. of the copolymers are shown near the temperature axis.

tral fit, using moment analysis for a transversely isotropic distribution w32x, can extract a Gaussian distribution width Db , where b is the chain director angle from the mean director and bo , the polar angle of the mean director with the static magnetic field. The second Euler angle, fixing the director location on the bo cone, can be obtained from sample symmetry, or in the 3-D case, via spectral fits after a small tilting of the sample or magnetic field axis along orthogonal directions. The sample sections studied here were too large to assume a transversely isotropic director distribu-

Fig. 8. Representative experimental Žsolid. and best-fit, simulated Ždashed. 1 H spectra for three sections of the frozen Vectra-A900 capillary flow. The sections, taken from the capillary Ža., contraction entrance Žb. and barrel wall Žc., are those closest to the contraction plane, shown in Fig. 9.

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Finally, a pseudo-order parameter, Szz ), has been calculated for each section and is shown in Fig. 9 for each location. Szz ) s

H0p r2 d b P Ž b . P2 Ž cos b . sin b H0p r2 d b P Ž b . sin b

Ž 9.

If the LCP section is aligned along the centerline flow axis Ži.e., bo < Db ., then Szz ) s Sm .

3.4. Density matrix simulation of lineshapes Fig. 10 shows the simulated 1 H NMR spectra for isolated HBA and HNA units using the solid-echo pulse sequence. These molecules are aligned with the rotation axis parallel to the static magnetic field. For the HBA unit, there is complete refocussing of the phases after the echo, indicating that it behaves like a two-spin system. In the case of the HNA unit, there

Fig. 9. Schematic of the Vectra-A900 quenched-contraction-flow mold. Piston direction was downward, i.e., from top to bottom in the figure. Director orientation distributions Žobtained from 1 H NMR spectral fits. and calculated centerline order parameters are shown. The bold rectangles indicate cylindrical or annular sections taken from the barrel or capillary for study.

w29x, presumably due to flow instabilities.. The two adjustable parameters describing the P Ž b . distribution for each section are shown in Fig. 9. Unlike the P Ž x . distributions in Fig. 6, the P Ž b . distribution was parameterized with b as an Euler angle so that the true volume-weighted distribution is sin b P Ž b .. The functional form used was exponential, i.e., P Ž b . s exp Ž y< Ž b y b o .
Ž 8. where bo s is the ‘preferred orientation’ and Db is the ‘distribution width.’ Two typical P Ž b . distributions are shown in Fig. 9.

Fig. 10. Fourier-transformed interferograms of proton spin evolution after dipolar evolution during a phase-alternated pair of p r2 pulses. Top: four protons on a benzyl ring. Bottom: six protons on a naphthyl ring. Note the appearance of out-of-phase components in the lower spectrum.

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

is substantial phase-dispersion after the echo. Evolution of the HNA protons under other two-pulse sequences was also simulated; in no case was a pure-phase echo obtained.

4. Discussion 4.1. Chain motions Examination of Table 1 shows that the amplitude of fast chain backbone fluctuations for HBA units is less dependent on the polymer composition than that for the HNA units. Since this is a random copolymer, a significant increase in the amplitude of both groups might be expected. On the other hand, the broader HBA tilt-angle distribution indicates that chain sections containing the larger HNA groups may be sterically hindered from large chain fluctuations, resulting in HNA rotations. This is consistent with the HNA group being a larger, ‘crankshaft’ linkage which requires long-length scale chain motions involving multiple monomer units and bond rotations to rotate. These results therefore indicate that cooperative motions involving multiple HNA groups on adjacent chains may be occurring with increasing HNA content. It is interesting that the average monomer tilt-angles monotonically increase with temperature and ‘level out’ at temperatures lower than those at which the Gaussian broadening indicates a fully-melted sample. This is consistent with the tilt-angle being a local measure of chain dynamics. Perhaps the small cocrystalline fraction w33x has extensiÕe ‘solid’ dipolar couplings, thereby compromising the assumption of uniform Gaussian broadening. It seems clear, however, that the onset of translational motion upon melting is accompanied by an increase in the amplitude of off-axis chain fluctuations. It is difficult to access the qualitative accuracy of the average tilt-angles obtained from spectral fits below apparent melting temperatures. However, the monotonic rise with temperature is encouraging. We note the change in tilt-angle with melting is greater for the minority unit than the major component. For 30r70 polyŽHBArHNA., the HBA and HNA angles

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change from 6.58 to 15.58, and 158 to 188, respectively, between 2658C and 3308C. For 75r25 polyŽHBArHNA. at 2658C, almost 308C below the nominal melting point, the HBA tilt-angle is about 18 less than the melt value, whereas the HNA value is nearly 78. These results seem to suggest that, below the melting point, the majority monomer has considerable Žnearly melt-like. off-axis chain motion, probably due to cooperative motions andror beneficial chain packing. The minority unit appears somewhat excluded from these large amplitude chain fluctuations. As previously mentioned, the rotation axis of the naphthalene is not defined by a unique set of bond rotations. We have found that changing the axis to either extreme depicted in Fig. 2 does not affect any of the trends or conclusions discussed above. Fig. 11 shows that the HNA subspectral width, not the lineshape, is sensitive to the orientation of the assumed HNA rotation axis. Therefore, these other axis orientations significantly alter only the absolute value of the HNA tilt-angle, not the HBA tilt-angle or homogeneous broadening. Table 2 shows results of spectral simulations using a rotation axis orientation of y98 for melted polyŽHBArHNA.. Further details are given in Appendix A.

Fig. 11. Variation of theoretical 1 H dipolar powder lineshapes for a rotating naphthyl group with different rotation axes ŽSee Fig. 2.. The lineshapes have normalized areas and are not broadened or scaled.

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Table 2 H spectral fit results for unaligned, fully-melted polyŽHBArHNA. assuming an extreme naphthyl rotation axis, y98 from the pseudo it para-axis. ŽSee Fig. 2.

1

HBArHNA

T, 8C

a x HB A

a x HNA

G.B., Hz ab

75r25 58r42

310 265 290 310 330 330

14.6 Ž0.15. 15.1 Ž0.2. 15.3 Ž0.2. 15.5 Ž0.2. 15.7 Ž0.2. 16.5 Ž0.4.

7.6 Ž0.5. 10.3 Ž0.5. 10.0 Ž0.5. 10.0 Ž0.6. 10.2 Ž0.6. 13.0 Ž0.2.

439 Ž15. 408 Ž9. 399 Ž10. 417 Ž11. 451 Ž9. 355 Ž5.

30r70 a b

Ž. Denotes fit uncertainty. Expressed as a Gaussian full-width at half-maximum, Hz.

4.2. Director distributions The success of the NMR spectral lineshape simulation strategy is evident from Fig. 9. Moderate alignment along the flow axis is observed in the capillary, along the barrel walls, and at the top of the barrel. Alignment in the capillary was expected, both from the strain of the contraction and from the modest shear rate Žat the region II–III boundary of the shear flow curve w34x.. Alignment at the barrel walls, with little in the center, is the classical ‘skin core’ morphology w35x. At the top of the barrel, alignment is presumably due to ‘fountain flow’ caused by the moving piston; this flow should be purely extensional along the centerline. Limitations of this technique are apparent. Firstly, the 1 H NMR lineshape is least sensitive to alignment orthogonal to the magnetic field axis, since the lineshape does not reflect the sign of Ž3)cosŽ b . y 1., making the spectral scaling a non-unique function of b . Two additional measurements obtained with tilted sample orientations Žnecessary for 3-D director alignments. would improve the accuracy of the derived director distributions. Secondly, melt alignment under the body force of the magnetic field is likely to complicate melt phase studies w16,17x. However, the analysis works well with incompletely melted samples. It is perhaps surprising that solid-state orientation can be measured just below the melting temperature of the polymer with the spectral simulation based on a model of molten LCPs. The nominal melting temperature of Vectra-A900 is 2828C; however, complete melting occurs approximately at 3158C, owing to the presence of high melting crystallites w33,36x.

With sufficiently slow heating to 2808C, annealing occurs above 2308C, thereby increasing the melting point w30,31x. We observed no changes in the NMR lineshape during the hour that the samples were held at 2808C for analysis. Furthermore, we note that these LCPs are known for retention of alignment at elevated temperatures w37x. We conclude that the dynamic LCP melt model used for the NMR simulation appears suitable for general use as long as the residual broadening parameter Žwhich indicates crystallinity. is less than about 1 kHz. Molecular alignment in completely solidified, drawn HBArHNA tapes has been previously characterized with moment analysis of 1 H NMR free induction decays w38x. This type of analysis is relatively limited and impractical because it requires significant sample reorientation to obtain ‘spectral 2nd-moment’ functions to extract distributions. We believe that the near-melt data contain considerably more information. 4.3. Prospects for solid state imaging The crude solid sectioning used here is desirable for demonstration of the spectral analysis only. In principle, this approach can be combined with solidstate imaging sequences like the magic-sandwich echo w39x to achieve truly non-invasive 3-D spatially resolved director distributions. In situ observation of molten LCP alignment under flow would then be possible. This methodology would be uniquely suited to blends or composites containing these LCPs. Much work remains to implement imaging. Fig. 10 shows that simple spin echoes could be used in conjunction with pulse gradients only for the VectraA phenyl protons. The napthal protons do not produce pure phase echoes with any simple pulse scheme, and thus deconvolution of phase accumulation due to applied gradients from phase accumulation due to dipole evolution would be necessary. We note, however, that our simulations indicate that, to first order, the naphthyl protons may be treated as three protons located on a line, a system for which analytical solutions for the dipolar spectra are available w40x. These solutions, along with other work w21,22x are expected to give us insight into simple pulse schemes so that, with typical gradients, submillimeter spatial resolution could eventually be attained.

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

5. Conclusions A fully-aromatic thermotropic liquid crystalline polymer was studied with 1 H NMR. The distribution of local nematic directors in macroscopic sections of a frozen contraction flow has been determined by analysis of wideline 1 H NMR lineshapes. The director distributions are consistent with expectations. This technique should be of use with non-invasive NMR imaging sequences to examine melts Žor solidified melts. in situ; explicit imaging sequences, however, are not obvious. The local dynamic conformation of polyŽHBAHNA. chains in the melt has been studied with 1 H lineshape analysis of samples with bulk isotropic director distributions. The onset of melting is clearly indicated by the onset of chain translational motion, fast on the NMR timescale, and a jump in chain twisting amplitudes, particular for the minority monomer unit. In the melt, the average off-axis fluctuation amplitude for the HBA unit was 158 " 28 for all compositions. The amplitudes for these HBA motions appear to be relatively heterogeneous. In contrast, the average off-axis fluctuation amplitude for the HNA unit increased by 3–58 as the copolyester HNA content increased from 25% to 70%.

Acknowledgements This work was supported by the Director, Office of Energy Research, Office of Basic Energy Science, Materials Science Division, U.S. Department of Energy, under contract No. DE-AC03-76SF00098. MG gratefully acknowledges an AT & T graduate fellowship.

Appendix A Previous workers w41x have attributed the ‘beta’ and ‘gamma’ glass transitions to activation of HBA and HNA unit rotational motions. From the transition temperatures, it is clear that both HNA and HBA rings, near melt temperatures, will be undergoing rotations fast on an NMR timescale of 0.1–10 kHz w33x.

109

The magnitudes of the monomer tilt-angles obtained are quantitative, rather than semi-quantitative, if we have complete confidence in the orientation of the chosen ring spinning axes in Fig. 2. For the HBA unit, the phenyl ring para-axis is the appropriate axis for rotation if the ring rotates rapidly and independently of the ester group near melt temperatures. In polyŽHBA., a significant fraction of phenyl rings are rapidly flipping at approximately 1008C below the melting point, where ester group rotation begins w42x. In contrast, there seems to be a correlation to the onset of phenyl and carbonyl motions in polyŽHBArHNA. w41,43x and similar polyesters w44x. However, the composition-independence of the gamma glass transition indicates the associated motion is highly localized at HBA units. Phenyl ring rotation does not require perturbation of adjacent monomer units, unlike rotation of a rigid phenyl-ester unit. ŽEven if the ring does rotate rigidly with the ester group, the effective phenyl rotation axis will still be within 118 of the 1–4 ring axis, based on likely crankshaft chain motions. The magnitude of tilt-angles obtained for the phenyl rings would then presumably reflect a contribution from the off-axis averaging of this motion.. For the HNA unit, NMR measurements of labeled 52r42 Žapproximately 308C below the melting point. and 30r70 polyŽHBArHNA. Žapproximately 1008C below the melting point. indicate rapid naphthyl ring rotations and ester group reorientations respectively w45x. Relaxation measurements on LC polyesters with different naphthyl ester linkages suggest the naphthyl ring and neighboring carbonyl group in polyŽHBArHNA. undergo coordinated rotational motion at the ‘beta’ transition. Hence, a range of possible rotation axes, depending on the orientation of the carbonyl group to the ring, is possible. In the Table 3 Normalized, least-squared error: HBArHNA composition Žtemperature. Model

75r25 Ž3108C.

58r42 Ž2908C.

30r70 Ž3308C.

A B C D E

21 21 44 56 56

24 25 46 87 91

20 36 24 126 137

110

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

two extremes, the carbonyl and naphthyl ring are coplanar, with the rotation axis approximately y98 or 78 relative to the pseudo para-axis of the naphthyl ring, as shown in Fig. 2. Although the y98 axis may be more probable for an extended chain, it is not clear if either extreme is favored at melt temperatures. Therefore, an angle of 08 is used for our calculations. Comparison of Tables 1 and 2 show that the rotation axis choice does not affect our conclusions.

Appendix B B.1. Isotropic samples Fig. 1b shows the spinning, single ring spectra for bulk, isotropic samples. All transitions are now overlapping Pake w46x powder patterns. Fig. 1c shows the final spectrum reflecting the tilt-angle distributions and homogeneous Gaussian broadening, chosen to yield the best fit to the data in Fig. 1d. The difference spectrum Žscaled by 5 = . is Fig. 1e. This calculation of the ‘distribution-heavy’ polyŽHBArHNA. melt spectrum, with minimal assumptions, is a significant task by itself. Analogous NMR studies are rare w24,47x. B.2. P( x ) functions Initial trial fitting had indicated that an excellent fit to the data could be obtained with a total of three, non-trivial adjustable parameters. Five different sets of tilt-angle distribution functions, shown in Fig. 6, were examined. Sets ‘D’ and ‘E’ have three adjustable parameters; Gaussian, homogeneous broadening was not used. A melt 1 H spectrum for each composition Žat a temperaturef Tm Žnominal. q

308C. was normalized and fit, employing these models. The relative least squared error with the optimal simulation is tabulated in Table 3. It is clear from Table 3 that model A gives the best overall spectral fit. Also, the least-squares error does not show a trend with copolymer composition. For model B, the fit error increases with HNA copolymer composition, indicating perhaps a poor choice for the form of HNA distribution function. The trends Žor lack thereof. with composition for the all the models, especially A–C, suggest the phenyl ring distribution is broader than that of the naphthyl ring. The poor fits obtained with the three parameter tilt-angle distributions are consistent with the fact that the Gaussian broadening is needed. B.3. Residual broadening The residual homogeneous broadening in the completely molten spectra is presumably due to small couplings not accounted for in the simulation of aromatic ring subspectra. These include the small intramolecular 1 H dipolar couplings between adjacent aromatic rings, the spread of the proton chemical shifts, and proton chemical shift anisotropies. A second moment calculation w48x to determine residual dipolar couplings has been done. The results, summarized in Table 4, indicate that an average field of 0.27–0.30 kHz full-width, half-maximum Ždepending on composition. is expected. An additional contribution of 0.27 kHz full-width, half-maximum is estimated from the spread of solution chemical shifts w49x and an estimated chemical shift anisotropy of 3.5 ppm for a spinning ring w50x. Since the sum of these contributions is reasonably close to the observed 0.45 " 0.07 kHz for all melt temperatures and compositions, we can conclude that the crystal-tonematic transition is associated with the disappear-

Table 4 Residual 1 H dipolar second moment from protons on adjacent monomer units ²Ž Dn . 2 : expressed as a Gaussian full-width at half-maximum, Hz Chain Sequence ‘X’, Protons

HBA-X-HBA

HNA-X-HNA

HBA-X-HNA

HBA, all four HNA, 1,3,5,7 HBA, 4,8

319 304 160

325 307 165

320, 323 ŽHNA close. not calculated not calculated

M. Gentzler et al.r Solid State Nuclear Magnetic Resonance 12 (1998) 97–112

111

ance of intermolecular 1 H dipolar couplings, i.e., the onset of chain translational motion. Also, the homogeneous spectral broadening is much less than the spectral width of 10–15 kHz, justifying our approximation of the chemical shift dispersion and intramolecular, inter-ring dipolar couplings as minor perturbations to the aromatic ring 1 H spectra.

for HBA and HNA, respectively, and residual gaussian ŽFWHM. broadening of 523 Hz. All calculations were done with Mathematica on a 8100r100 Power Macintosh. Least squares fitting was done over a 50 kHz spectral window Žapprox. 490 points.. The calculated marginal standard deviations are the uncertainties reported.

Appendix C

References

C.1. Lineshape simulation and fit details

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First-order perturbation theory w51x was used to obtain the spectrum of an isolated spinning aromatic ring oriented parallel to the magnetic field. Pake powder pattern spectra were produced by interpolation w52x, using 64 grid points for the polar angle integration with a 2048 point, 125 kHz sweepwidth spectral axis. Ideal bond angles and bond lengths of 1.40 A and 1.07 A for C–C and C–H bonds, respectively, were used. For powder spectral fitting, scaled P Ž x . spectra for 64 x values between 0 and 548 are pre-calculated for each monomer. These spectra are homogeneously broadened to reflect the experimental inherent line width due mostly to the susceptibility of the titanium probe head. ŽThis was measured with a water sample, equal in size to the polymer samples, which gave a Lorentzian line with a 300 Hz full-width at half-maximum.. During the least squares fit, these scaled spectra are summed and weighted according to the form of the P Ž x HB A . and P Ž x HNA . distributions of the current iteration. Before comparison with the data, this total spectrum is Fourier transformed, apodized with a Gaussian, left-shifted by the experimental ring-down time, inverse Fourier transformed, baseline corrected and centered. The fit therefore had three adjustable parameters: the residual Gaussian broadening, the average HBA tilt-angle, and the average HNA tilt-angle. Fixed parameters are the LCPE composition, susceptibility broadening, left shift, spectral center and molecular structure. For spectral fitting to obtain P Ž b ., a similar procedure is used. In this case, scaled Pake spectra for 64 b values, between 0 and 908, are pre-calculated for each monomer. Additional fixed parameters included the average tilt-angles of 15.38 and 18.18

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