conformational analysis of the crystal structure for mdi ... · conformational analysis of the...

Conformational Analysis of the Crystal Structure for MDI/BDO Hard Segments of Polyurethane Elastomers

CHRIS W. PATTERSON, DAVID HANSON, ANTONIO REDONDO, STEPHEN L. SCOTT, NEIL HENSON

Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87544

Received 10 November 1997; revised 17 May 1999; accepted 18 May 1999

ABSTRACT: From conformational analysis, we have determined the two lowest energycrystal structures for the hard segments of 4,49-diphenylmethane diisocyanate/1,4-butanediol (MDI/BDO)-based polyurethane elastomer. Both crystal forms give promi-nent X-ray scattering at ;7.6 Å. In one crystal form, (1), there is strong hydrogenbonding between linear chains with a density of 1.30 g/cm3, while in the other form, (2),van der Waals bonding gives rise to a double helix structure with a density of 1.22 g/cm3

and a formation energy 1.6 kJ/mol higher than form (1). The double helix crystal has aunit cell length of 18.8 Å which is about half the 34.7 Å unit cell length of thehydrogen-bonded crystal. The X-ray diffraction predicted for each crystal is presentedand compared with experiment. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys37: 2303–2313, 1999Keywords: atomistic modeling; conformational analysis; hard segments; polyure-thane elastomer; X-ray diffraction

INTRODUCTION

Polyurethane elastomers, based on the hard seg-ment 4,49-diphenylmethane diisocyanate (MDI)and 1,4-butanediol (BDO) denoted by MDI/BDO,have been extensively studied by X-ray scatteringtechniques to determine the possible crystalstructures. Early, wide-angle X-ray studies byBonart et al.1–3 showed an off-meridian reflectionat about 7.9 Å, some 30° from the fiber axis.Bonart et al. proposed that the hydrogen bondingbetween fibers caused the fibers to be staggeredresulting in the alignment of the amine and car-bonyl groups. Such packing is indeed seen inmodel compounds where the crystal structure canbe determined unambiguously.4–6 Wide-angle X-ray studies of oriented thin films of MDI/BDOhave been ambiguous, leading to a number ofdifferent proposed triclinic crystal structures allresulting in staggered chains presumed to arise

from hydrogen bonding.7–11 The densities of theseproposed hard segment crystals range from 1.32to 1.58 g/cm3 compared to the experimental de-termination10,12 of 1.25–1.35 g/cm3. Part of theproblem of assigning a unique crystal structurefrom a given wide-angle X-ray pattern is that thehard segments of MDI/BDO are paracrystalineand give rise to only a few broad diffraction linesfor which assignments are ambiguous. Thus, thesame or similar diffraction patterns have led todifferent crystal assignments by different inves-tigators.

This problem is compounded by the fact thatthere have been no determinations of the struc-ture factors for the X-ray fiber patterns, and in-vestigators have not been able to show that thegiven assignments actually correspond to themost intense scattering. Any complete analyses ofthe wide-angle X-ray results must also explainthe absence of Bragg lines in the data. For anyassignment made, there are typically hundreds oflines of the same scattering order that are notvisible in the diffraction pattern, a point usuallyignored by previous investigators. For example,

Correspondence to: A. Redondo (E-mail: [email protected])Journal of Polymer Science: Part B: Polymer Physics, Vol. 37, 2303–2313 (1999)© 1999 John Wiley & Sons, Inc. CCC 0887-6266/99/172303-11

2303

all investigators have assigned the 7.6–7.9 Åscattering feature to the (004) Bragg diffraction,yet there is no explanation for why the (001),(002), (003), and (005) diffraction peaks are neverseen. This is particularly striking because theredoes not appear to be any selection rule due tocrystal symmetry that would eliminate any ofthese lines (as, for example, one would find inbody-centered and face-centered cubic crystals).Furthermore, there is no explanation for why theBragg lines at (h00) and (0k0) are apparentlynever seen, although they should be quite in-tense. For these reasons, we believe it is impor-tant to show the fiber diffraction pattern resultingfrom a proposed crystal assignment so that theabsence of predicted features in the data becomesobvious.

The task of deducing the crystal structure froma diffraction pattern is aggravated by the factthat it is now known that the hard segments canoccur in several crystal forms.13–15 It is not knownprecisely which wide-angle X-ray diffraction pat-terns correspond to which crystal forms or evenhow many crystal forms may actually be ex-pressed in the data. Wide-angle X-ray studies byBriber and Thomas13 have shown the appearanceof at least three different types of paracrystals.Type I is found in unstretched samples, Type II instretched samples, and Types II and III occur

upon stretching and annealing. Thus, Type III isincluded in all the previous wide-angle X-raystudies of oriented and annealed thin films andmay itself actually correspond to more than onecrystal form. No determination of the crystalstructure has been attempted for Types I and II.Briber and Thomas13 found that Type III has amore extended fiber than Type II, which corre-sponds to a 4.6 Å line, in agreement with Black-well and Lee.14

Alternatively, Koberstein and Stein16 have in-terpreted small-angle X-ray data to conclude thatthe hard segment microdomains of MDI/BDO arein sheets (laminae) only a few MDI units thick asa result of considerable chain folding. This is incontrast to the original model of Bonart in whichconnected chains are held together by hydrogenbonding.

Finally, we should mention that differentialscanning calorimetry thermograms14,17 showhard segment crystal endotherms at two differenttemperatures which could be attributed to thepresence of two different crystal forms. Appar-ently, the lower temperature endotherm is asso-ciated with the extended crystal Type III form.Overall, we conclude that there is considerableconfusion in the determination of crystal struc-ture from X-ray scattering data for MDI/BDOpolyurethane hard segments.

Table I. Configuration Energies (kJ/mol) and Crystal Structures for Various Geometries of MDI/BDO(HB 5 Hydrogen Bonded)

1. SingleStrand

2. HBDimera-axis

3. HBDimerb-axis

4. DoubleHelixDimer

5. UnconnectedHB Crystal

6. ConnectedHB Crystal

7. DoubleHelix

Crystal

Bonded interactionsBond stretching 171.6 338.6 338.2 339.1 159.1 159.5 160.7Bond bending 108.8 210.6 219.3 218.5 106.7 105.5 105.9Torsional energy 3.8 30.6 19.3 16.3 40.6 37.3 15.9Total bonded 284.2 579.8 576.8 573.9 306.4 302.3 282.5

Nonbonded interactionsvdW repulsion 1117.7 2381.8 2377.6 2451.3 1492.3 1511.1 1466.4vdW dispersion 2529.5 21370.5 21368.4 21511.1 21369.2 21378.9 21339.9Coulomb energy 2555.1 21134.8 21145.7 21112.2 2592.7 2583.5 2570.6Total nonbonded 33.1 2123.5 2136.5 2172.0 2469.6 2451.3 2444.1Total energy 317.3 456.3 440.3 401.9 2163.2 2149.0 2161.6

Crystal structurea (Å) 6.72 6.64 7.26b (Å) 5.66 5.60 8.59c (Å) 36.68 34.73 18.77r (g/cm3) 1.27 1.30 1.22a 113.3° 108.6° 54.3°b 61.3° 68.1° 93.5°g 132.8° 132.8° 82.7°

2304 PATTERSON ET AL.

In this paper, we shall attempt to determine thepossible crystal structures of MDI/BDO hard seg-ments by conformational analysis. There have beennumerous conformational studies of the MDI/BDOmolecules comprising the crystal.6,18–21 Previous in-vestigators, however, did not determine crystalstructure by energy minimization because of thelarge number of atoms in the unit cell and thecomputational difficulty in obtaining convergencefor van der Waals and Coulomb energies betweencells. In this paper, we use the well-documentedcommercial software packages InsightIIt and Dis-covert from Molecular Simulations Inc.22 to accom-plish this task. The use of a widely available com-mercial software package makes it possible for any-one to repeat the calculations with the samestandard molecular potentials. Further, this codehas been benchmarked for numerous other molec-ular crystals and its accuracy documented in theliterature.22 In the next section, we describe theprocedure we used to minimize the energies of themolecular dimers and the molecular crystals ofMDI/BDO in both the hydrogen-bonded and doublehelix conformations. Then, we give the results of theenergy minimization for the dimers followed by theresults for the crystal. Finally, we discuss the crys-tal fiber X-ray spectra resulting from the two crystalforms found previously.

METHOD FOR ENERGY MINIMIZATION

The MSI InsightIIt code assigns an empirical po-tential energy function to each atom from the cvffforcefield22 depending on the element type andthe nature of the chemical bond. The total bondenergy includes the bond stretching, bond bend-ing, and bond torsion (dihedral angle) terms. Em-pirical partial charges are assigned to each of theatoms with the total molecular charge being zero.Consequently, part of the intramolecular energyminimization includes the electrostatic Coulombpotential between atoms. Empirical van derWaals potentials, which include repulsive anddispersive terms, are also assigned to each pair ofatoms. The total nonbond energy is the sum of theCoulomb and van der Waals energies. In Table I,we show the various potential energies for theMDI/BDO minimum configuration.

These calculations, in agreement with Black-well et al.,19,20 indicate that the energy minimumfor MDI/BDO corresponds to all trans carbonbonds in the BDO segment as shown in Figure 1.Furthermore, the urethane group of the MDI is in

the same plane with the nearest benzene ring aspreviously noted.21 The benzene rings in the MDIsegments form planes which intersect at 90°. Forthe minimum energy configuration, the urethanebonds occur on alternate sides of the benzenerings for each MDI unit and on alternate sides ofthe BDO link between MDI units. In Figure 1, wehave used two MDI units and have artificiallytruncated the polymer chain with hydrogens aftertwo carbons of the BDO extender. This comprisesthe unit cell in a hydrogen-bonded crystal, and weshall use this unit for comparison. This modelunit can be readily extended to make the hydro-gen-bonded crystal by deleting the terminal hy-drogens. The energy minimization calculationsfor the conformation shown in Figure 1 are incomplete agreement with previous conforma-

Figure 1. Strand of MDI/BDO containing two MDIunits used to build the crystal cell. The ends are cappedwith hydrogens when the cells are unconnected. Ener-gies are given in Table I (column 1).

CRYSTAL STRUCTURE OF POLYURETHANE ELASTOMERS 2305

tional analyses of MDI/BDO which have been re-ported by numerous authors.18–21 The energiesfor this MDI/BDO unit are shown in Table I (col-umn 1).

In this work, we are interested in the dimerand crystal conformations that arise from inter-actions between MDI/BDO molecules andchains. These interactions are entirely due tononbonding and electrostatic interactions thatare treated in the crystal energy minimizationusing Ewald summation methods. In practice, itis necessary to try many initial configurationsof the molecular MDI/BDO and crystal unitcells in order to sample the large configuration

space. The MSI InsightIIt program will alterthe crystal parameters and the molecular bondsin order to minimize the energy. The minimiza-tions were performed at constant pressure withall degrees of freedom allowed to relax. Still, thetwo lowest energy configurations found were atleast 20 kJ/mol below all others. To accomplishthe minimizations, it is much easier to leave thestrands unconnected and unbonded lengthwisebetween adjacent cells in order to sample con-figuration space rapidly and to observe wherethe molecular ends prefer to go. The resultinggeometry then suggests the connectivity be-tween cells to form the linear chains.

Figure 2. Dimers formed from the single strands shown in Figure 1. The hydrogenbonding of the strands occurs along two different axes corresponding to (a) and (b) onlyto the extent that the benzene rings are in the same plane. Energies are given in TableI (columns 2–3).


MOLECULAR MDI/BDO DIMERS

Bonart1–3 originally proposed by that the MDI/BDO chain was staggered about 30° in the crystalin order to accommodate the hydrogen bondingbetween the NH and OC in the urethane bond.The staggering actually occurs in both axes per-pendicular to the chain axis. In order to show this,we exhibit the dimer configuration correspondingto the energy minimum for the crystal a- andb-axes, respectively [see Fig. 2(a) and (b)]. Thestaggering is evident in both Figure 2(a) and (b)where the alignment of NH and OC between mol-ecules occurs twice in each figure for each MDI/BDO molecule, corresponding to the two differentsets of planes containing the benzene rings inMDI. In Table I (columns 2–3) we compare theenergies for the two hydrogen-bonded configura-tions shown in Figure 2.

The energy of the hydrogen-bonded dimer inFigure 2(b) is 16 kJ/mol lower than that of thehydrogen-bonded dimer in Figure 2(a). The inter-action energy is dominated by the van der Waalsenergy between the benzene rings and the Cou-lombic hydrogen bonding. The maximum van derWaals energy between two adjacent benzenerings is about 20 kJ/mol, similar to that of ahydrogen bond. However, it is much easier toalign the two planes of the benzene rings than thetwo axes of the NH and OC. For this reason, thedimer configuration which minimizes the energyis mostly determined by the alignment of the ben-zene rings, leading to similar contributions to thetotal energy in both Figure 2(a) and (b), as shownin Table I (columns 2–3). The energy for Figure2(b) is somewhat lower because the urethanebonds at the ends of the molecules can bend toalign the NH and OC. In Figure 2(a), the ure-thane bonds are in the middle of the moleculesand alignment is poor because the urethanebonds are not in the same plane.

The minimum energy configuration for thedimer, however, is formed by a double helix ge-ometry of the two MDI/BDO chains shown in Fig-ure 3. To our knowledge, this has not been previ-ously reported The individual strands in Figure 3are the same as in Figures 1 and 2, except theBDO chain extender has one gauche bond be-tween the middle two carbon atoms. The gauchebond requires an additional 15 kJ/mol of energy.However, this energy penalty is more than com-pensated by the nearly perfect alignment of thebenzene rings resulting in a lower van der Waalsenergy. In Table I (column 4), we find that the

energy for the double helix dimer is 38.4 kJ/mollower than that for the hydrogen-bonded dimershown in Figure 2(b). Despite the additional 15kJ/mol of energy for the carbon gauche bond, thetotal energy due to bonded interactions for thedouble helix dimer is even lower than the hydro-gen-bonded strand dimer in Figure 2(b) by 2.9kJ/mol. This is because the double helix has muchless distortion of the bond and dihedral angles toaccommodate the benzene ring interactions. Infact, the total energy due to bonded interactions

Figure 3. Dimer formed from two strands inter-twined in a double helix. Because the benzene rings ofthe diphenylmethane are facing each other in the twostrands, there is no hydrogen bonding. Energies aregiven in Table I (column 4).


when molecules are separated remains at 573.9kJ/mol, so there is virtually no distortion of themolecules as they form the double helix dimer. Bycontrast, the bonded interaction energy of thehydrogen-bonded dimer in Figure 2(b) is 8.4 kJ/mol higher than that for the separated molecules.

There is no hydrogen bonding in the doublehelix because the urethane bonds for the two mol-ecules are always in parallel planes separated byabout 4 Å. Thus, as Table I (columns 2, 3 and 4)show, the Coulomb contribution to the total en-ergy for the double helix dimer in Figure 3 is23–34 kJ/mol higher than that of the hydrogen-bonded dimers in Figure 2. However, because ofthe excellent alignment of the benzene rings, thevan der Waals contribution (repulsive and disper-sive) to the total energy for the double helix dimeris 69–71 kJ/mol lower than that of the hydrogen-

bonded dimers. For connected chains, the energydifferences between the two dimers are multi-plied by the number of pairs of MDI units in eachchain.

HARD SEGMENT MDI/BDO CRYSTALSTRUCTURE

We now compare the crystal energies for the hy-drogen-bonded and double helix conformationsand determine the X-ray fiber pattern for theresulting crystals. Although the double helix con-figuration has a lower energy than the hydrogen-bonded dimer, this is not the case for the crystal.In the crystal, the hydrogen bonds of the singlestrand will occur along both transverse crystalaxes, not just in one direction as for the dimer. As

Figure 4. Crystal made from unconnected single strands with hydrogen bondingbetween cells. (a) View along the b-axis; (b) view along the a-axis. Energies and crystalstructure are given in Table I (column 5).


a result, we find the hydrogen-bonded crystal en-ergy is 1.6 kJ/mol lower than the double helixcrystal, a value less than the accuracy of the code.The energies and crystal parameters for the hy-drogen-bonded unconnected chains are given inTable I (column 5). In Figure 4, we show thehydrogen-bonded crystal conformation in the un-connected chain in which there are only two MDIunits. From this figure, it is seen that the chain ismost readily extended along the c-directionwithin the same cell along the a-axis, but in anadjacent cell along the b-axis. Thus, the fiber axiswill not be along the c-axis, but slightly tiltedtoward the b-axis which is 132.8° from the c-axis.

With this information, we now connect the mol-ecules in the unit cells in the manner suggestedby Figure 4 to determine the hydrogen-bonded

connected chain crystal cell conformation. Theenergies and crystal parameters for this hydro-gen-bonded conformation are given in Table I (col-umn 6). Note that, with their ends constrained,the energy for the hydrogen-bonded connectedchain is higher by 14.2 kJ/mol than the hydrogen-bonded unconnected chain crystal. The bondedinteraction contributions to the total energiesstay nearly the same, but the nonbonded energyincreases by nearly 18 kJ/mol because the ends ofthe molecules are joined to the adjacent cell alongthe c-axis. The principal difference is that thecrystal cell shortens in the c-direction because itis now directly bonded to adjacent molecules toform the fiber chain. This connection is shown inFigure 5(a) and (b), which should be compared tothe dimers shown in Figure 2(a) and (b), respec-

Figure 5. Crystals made from connected single strands with hydrogen bonding be-tween cells. Strands are connected in adjacent b-cells. (a) View along the b-axis; (b) viewalong the a-axis. Energies and crystal structure are given in Table I (column 6).


tively. As already noted, the hydrogen-bondeddimers do not form in the same plane as theirhydrogen bonds and, in fact, the angle betweenthe a- and b-axis, g, is 132.8° for both the long andshort hydrogen-bonded crystal. This large angleis in disagreement with previous crystal struc-tures inferred from the X-ray diffraction assign-ments. The density of the hydrogen-bonded crys-tal chain increases from 1.27 to 1.30 g/cm3 whenthe strands are connected, which compares favor-ably with the experimental value12 of 1.28 g/cm3.

In Figure 6, we show the calculated X-ray dif-fraction fiber pattern of the crystal in the confor-mation of Figure 5. The lowest order diffractionangles and distances for the peaks are summa-rized in Table II. For ease of calculation, we as-sumed that the fiber is along the c-axis so that thefiber plot is symmetrical about the horizontalaxis. The three progressions of maxima seen ineach quadrant are consistent with what is seen inan experimental fiber X-ray diffraction pattern11

shown in Figure 7. This diffraction pattern wasobtained for a MDI-BDO-based polyurethaneelastomer containing ;50% hard segments, ori-ented by stretching 700% and annealed at 130°Cfor 7 days. The calculated progression (Fig. 6)emanating from the horizontal is quite compli-cated because of the near overlap of doublets aris-ing from the (-1 0 1) and the (0 -1 1) progressions.Because of this overlap, it is very difficult to de-rive the crystal structure from the X-ray line po-sitions alone without also comparing the fiberpattern intensities. Also, the progression (10,)occurs near the observed peak at 4.6 Å at about65° from the vertical. The main discrepancy ofthis plot with experiment is that the ab plane is

23° from the c-axis. As a result, the (004) diffrac-tion peak occurs at 23° rather than the observedvalue of 37°. The (004) peak also occurs at d 5 8.0Å rather than the observed value of 7.6 Å. Fur-thermore, the calculated fiber pattern shows dif-fraction peaks for (001), (002), and (003) whichare not seen in experiment, however, these arecalculated to be five times weaker than the (004)peak.

In Figure 8, we show the crystal structure forthe double helix of unconnected chains and inTable I (column 7), we list the energies and crys-tal parameters. In comparing the conformationalenergies of unconnected hydrogen-bonded anddouble helix crystals (Table I, columns 5 and 7),we see that the Coulomb interaction energy isgreater for the double helix structure, a conse-quence of the absence of hydrogen bonds. On theother hand, the double helix crystal has a lowertorsional strain than does the hydrogen-bondedcrystal, analogous to the double helix vs. the hy-drogen-bonded dimer comparison (Table I, col-umns 2–3 and 4). We did not determine the con-

Table II. Calculated X-Ray Diffraction Peaks forConformation of Figure 5

MillerIndices

Distance(Å)

Angle(degrees)

0 01 32.1 230 02 16.0 230 03 10.7 230 04 8.0 230 05 6.4 230211 4.1 830212 4.1 760213 3.9 700214 3.8 640215 3.6 590 11 4.0 830 12 3.9 770 13 3.7 710 14 3.5 660 15 3.3 62

21 01 4.5 8221 02 4.3 7621 03 4.0 7021 04 3.7 6521 05 3.5 60

1 01 4.9 821 02 4.9 741 03 4.7 661 04 4.6 581 05 4.3 52

Figure 6. X-ray fiber pattern of crystal made fromconnected single strands in


nected chain crystal because of the difficulty inchoosing how the ends of the double helix willconnect in adjacent cells. Because of the difficultyin dealing with such a large number of possibili-ties, this task will be deferred to future work. Wewould like to stress that the 1.6 kJ/mol energydifference between the unconnected double helixand hydrogen-bonded crystals should not be con-sidered significant since the accuracy of the codeis at best about 4 kJ/mol for these types of energydifferences.

The fiber diffraction pattern for the unconnecteddouble helix chain is shown in Figure 9. Because thelength of the crystal cell for the double helix (18.8 Å)is half that of the hydrogen-bonded cell (34.7 Å),the previous diffraction peaks at (004) and (002)are now equivalent to (002) and (001), and none ofthe previous odd (00,) are possible. Also, the (002)diffraction is now at 37° with d 5 7.5 Å in agree-ment with experiment. The diffraction peaks at(001) and (002) for the double helix are, by far, thestrongest Bragg diffractions. The diffraction pro-gressions near the horizontal are not seen in thiscase. Assuming the hard segments to be purely ofa double helix unconnected chain nature leads toa calculated density of 1.22 g/cm3, somewhat

lower than the experimental value10,12 of 1.28g/cm3. Presumably, the calculated density wouldincrease if the chains were connected

CONCLUSIONS

In this work, we have determined the minimumenergy conformations of single chains of MDI/BDO using the Molecular Simulations Inc.22

codes, and these results are in agreement withthose of previous investigators.18–21 We thenfound the minimum energy conformations fordimers of MDI/BDO. The lowest energy conforma-tion was found to be a double helix made up of twostrands of MDI/BDO with a gauche bond betweenthe middle two carbons of BDO. Despite the 15-kJ/mol energy penalty associated with the gauchebond, the double helix has lower total energy be-cause it enables the two dimethylbenzene rings ineach strand to face each other giving rise to astrong van der Waals attraction. We then usedthe same energy-minimization techniques to de-termine the lowest two crystal energies of theMDI/BDO hard segments. We computed the fiberX-ray patterns for these two lowest energy crystal

Figure 7. X-ray diffraction photograph for MDI/BDO/PTMA stretched 700% andannealed at 130°C for 7 d (from Ref. 11 with permission).


conformations in order to compare them to exper-imental data. The calculated energies for the twocrystals differ by about 2 kJ/mol, well within theaccuracy of the calculations, and are lower thanall other calculated conformations by about 20kJ/mol. One crystal was strongly hydrogenbonded between strands while the other formed adouble helix with only van der Waals bonding.

Our procedure, finding the minimum energyconformation, differs fundamentally from previ-ous methods that attempted to infer the crystalstructure from observed fiber X-ray diffractionpattern. The interpretation of fiber diffractionpatterns of MDI/BDO is difficult because of theambiguity in assigning Bragg lines to the dataand because the samples can be mixtures of sev-eral polymorphs of MDI/BDO. The main difficulty

Figure 9. X-ray fiber pattern of crystal made fromunconnected double helices in Figure 7.

Figure 8. Crystal made from unconnected double helices with no hydrogen bonding.Cell length is about half that of hydrogen-bonded crystal of Figures 4 and 5. (a) and (b)represent two different views of the unit cell. Energies and crystal structure are givenin Table I (column 7).


in our procedure is that we cannot be certain thatwe have determined the absolute energy mini-mum (i.e., that we have examined all possibilitiesof molecular orientation and crystal cells). De-spite this drawback, the fiber X-ray patterns cal-culated for our crystal conformations do show rea-sonable agreement with the observed X-ray pat-tern. The hydrogen-bonded crystals give rise tocalculated patterns near the horizontal quite sim-ilar to observations, but have a (004) peak at 23°instead of 37 at d 5 8.0 Å instead of d 5 7.6 Å.Also, the calculations predict weaker peaks at(001), (002), and (003), which are not seen in theexperimental data. The double helix crystal givesrise to fiber X-ray diffraction (002) peaks at ex-actly 37° and d 5 7.5 Å, but the predicted (001)line at d 5 3.75 Å is not observed experimentally,nor does the double helix crystal account for otherpeaks near the horizontal.

It is interesting to note that, before crystalliza-tion occurs in the hard segments, the MDI/BDOunits are likely to be in double helix dimers asthis conformation is about 38 kJ/mol lower inenergy than any other hydrogen-bonded pair.This suggests that before a hydrogen-bondedcrystal can form, the temperature must be in-creased to separate the double helices alreadyformed This may provide an explanation for thehigh annealing temperatures required to createType III crystals. Also, the two hard segmentendotherms observed in the differential scanningcalorimetry14,17 data could arise from double he-lix crystals where one endotherm would corre-spond to the short-range helical structure and theother endotherm to the long-range crystal struc-ture. Finally, the small-angle X-ray data ofKoberstein and Stein16 indicate that the hardsegments form in sheets due to chain folding. Itappears that the shorter crystal cell of the doublehelix conformation would be ideally suited to formsheets if the cells were only connected by onestrand instead of two so that the fibers werefolded along the c-axes. In this case, one wouldnot expect to see c-axis layer lines originatingfrom long double helix fibers.

The authors would like to thank Dr. Russell Pack formany interesting discussions and suggestions. Thiswork was partially carried out under the auspices of

the Los Alamos Laboratory Directed Research and De-velopment program.

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