direct observation of taut tie molecules in high-strength polyethylene fibers by raman spectroscopy

Direct Observation of Taut Tie Molecules in High-Strength Polyethylene Fibers by

Raman Spectroscopy

KESHAV PRASAD and DAVID T. GRUBB, Department of Materials Science and Engineering, Cornell Uniuersity,

Ithaca, New York 14853

Synopsis

The Raman spectra of four gel-spun high-strength polyethylene fibers were recorded as a function of stress, with detailed study of the 1063 cm-' band. The change in the peak position of this band was linear a t low stresses, but there was little change at high stresses. The center of mass of the band moved linearly with stress until fracture, and the shift per unit stress was almost the same for all the fibers studied at 4.0 + 0.5 cm-'/GPa. The line shape is symmetric at low stresses, and the full width at half maximum increases with stress. When plastic deformation begins the band develops a broad low intensity tail extending to lo00 cm-'. This corresponds to stresses of up to 15 GPa, and the tail contains up to 184% of the band intensity when the maximum stress is applied. Equivalent wide-angle x-ray studies showed no such tail, so the highly stressed material is not crystalline, although it must be in the all-trans form to contribute to the l b a n peak. Such load-bearing extended-chain-disordered material is described as taut tie molecules. The amount is much larger than that usually derived from mechanical modelling, it is essentially all the amorphous material if the DSC crystallinity of 85% is correct. It is thought to be interfibrillar, stressed when fibrils slide past each other in creep. On unloading the fiber, the band became more symmetrical again but did not always return to its initial position at zero stress. The peak moved to a wave number greater than its initial value on unloading and then over time relaxed to its original value. Thus tensile stresses in the disordered material, balanced by compression in the crystals, are slow to relax. Lower molecular weight fibers (M,, = 8 X lo5) had small anelastic effects, probably because they relaxed within the time of the experiment.

INTRODUCTION

Since the discovery of the process of gel drawing or spinning'-3 it has become possible to prepare ultrahigh-molecular-weight polyethylene (PE) fibers and tapes with Young's modulus of 100-200 GPa and tensile strength of 2-5 GPa;4.5 such fibers are now commercially available.6 These values for modulus and strength are very high considering that the theoretical modulus of a PE crystal along the chain direction E, is thought to be about 300 GPa and the theoretical strength of a molecule about 35 GPa.' Few practical materials approach so closely their theoretical mechanical properties. I t is of considerable interest to know the structure that gives such good mechanical properties and to know what mechanisms or defects still keep the properties below their theoretical limits.

The stiffness and strength of the PE crystal in the molecular chain direction is much greater, of the order of 100-fold greater, than that in any other directi0n.7.~ Any slight imperfection in the orientation of the crystals would

Jm~mal of Polymer Science: Part B: Polymer Physics, Vol. 27, 381-403 (1989) 0 1989 John Wiley 8z Sons, Inc. CCC 0098-1273/89/020381-23$04.00

382 PRASAD AND GRUBB

therefore result in a much reduced tensile modulus for the fiber. The stiffness and strength of fully disordered amorphous PE is also low. However it is found that fibers produced with different draw ratios or under different conditions can have the same highly perfect crystal orientation and the same level of crystallinity X , but very different moduli and strengths.lO*ll Other factors must therefore be involved in controlling the mechanical properties of the fiber. In general the properties will depend on the way in which stress is distributed within the material.

Measurement of local stress distribution within a high-modulus fiber would help relate mechanical properties to the structure and predict fiber strength. In prikciple the accurate determination of line position and line shape in wide-angle x-ray diffraction under stress will give the crystal lattice parame- ters and their distribution. These strains and E, give the stress distribution. In practice the x-ray experiments have in the past required large samples and long data collection times, and only the peak position has been measured. Early experiments were described as x-ray crystal modulus determination12* l3

and assumed a homogeneous stress distribution (series model) to derive E, = 200 GPa. More recently, a more sophisticated model was used on melt-drawn high-modulus PE fibers,14 giving E, = 250 GPa and structural information on the samples. A synchrotron source of x-ray radiation at the Cornell High Energy Synchrotron Source (CHESS) has made possible x-ray modulus determination and x-ray line shape studies using a single fiber sample and data collection times of only 1 min,l5'l6 but this paper is concerned with the determination of the distribution of local strains by another method: Raman spectroscopy.

Stress acting on an elastic solid result in reversible changes in interatomic spacings. These changes affect the environment of atoms in the solid, so that in general their vibrational modes are altered. If spectroscopically active modes change their frequency, lines in the IR or Raman spectrum of the material will be affected by tress.'^-^^ The effects are often small, driven by the small anharmonic terms in the oscillator potential. IR studies showed that the shift in position of the band peak is usually to lower frequencies, is often nonlinear, and depends on the sample morphology and history. The band generally increases in width and often has an asymmetric tail extending to lower frequencies.

The shape of an IR spectral band has been used to study the stress distribution in p~lypropylene .~~.~~ The asymmetric tail was assigned to a fraction of the molecules in the samples being stressed to much higher than average values. The stress distribution as a function of time during stress relaxation in this material has been modelled with a combination of tie molecules and crystals using IR spectral data.lg

When polymer chains are extended and aligned in parallel as they are in high-modulus fibers, tensile stress applied along the fiber causes strains in the polymer chains which have regular conformation; bond angles and length must change. This can cause significant shifts in the IR and Raman spectral line positions and ~ h a p e s . ' ~ * ~ ~ - ~ * It is experimentally difficult to use IR spectroscopy for small fiber samples, so Raman spectroscopy is preferred.

with the major features of the crystalline spectrum unambiguously assigned. In the case of PE the Raman spectrum has been described in

OBSERVATION OF TAUT TIE MOLECULES 383

The Raman spectrum of molten PE contains only broad bands, but the high temperature hexagonal or rotator phase has the same spectrum as normal crystalline PE, except for an increase of intensity of a band at 1440 cm-1.32 The rotator phase contains molecules in the all-trans conformation with poor lateral order.

The effect of stress on the IR and Raman spectra of high-modulus PE fibers and tapes has been previously studied at stresses up to 0.4 GPa.26 The specimens studied had been extruded in the solid state and had high modulus but relatively low ~ t r e n g t h . ~ ~ , ~ The changes in the Raman active C-C stretching modes were measured as changes in the wave number of the peak position ap = dfik/da [(wave number v" = l/(wavelength in cm)]. The shift of the C-C asymmetric stretch band at 1063 cm-' was linear at low stresses, ap = -11.2 cm-'/GPa, deviating from linearity at stresses > 0.15 GPa. Asymmetry and broadening of the band shape were seen at higher stresses and were recognized as being due to nonuniform stresses on the chains, as in the IR e ~ p e r i m e n t s . ~ ~ , ~ ~ The C-C symmetric stretch at 1127 em-' was measured up to 0.2 GPa, and ap was -5.9 cm-'/GPa in that range.

The vibrational frequencies in PE were calculated by Wool et a1.26 as a function of stress using conformational energy minimization methods. Both harmonic and Morse potential energy functions for the C-C stretching modes in the valence force fields were used. The stress was assumed to be homogeneous within the specimen, and so the load on a molecule was calcu- lated by dividing the applied load by the cross-sectional area of the PE chain. To minimize the effects of inhomogenous stresses, the experimental data obtained at lower stresses were compared with theory. A peak shift of - 11.2 cm- '/GPa, identical to the experimental results, was calculated for the C - C asymmetric stretch using a one-dimensional linear coupled diatomic anhar- rnonic oscillator model.

The materials tested in the experiments reported here are high-modulus gel-spun fibers of polyethylene supplied by Allied C0rp."9~~ They are very strong, which allows stresses up to 2.5 GPa to be applied, producing strains of over 1% in the crystals and comparatively large changes in the Raman sp t r a . The fibers tested were made under similar processing condition^,^^ so the effects of the molecular weight, strength, and modulus could be examined. It is found that measurement of the Raman spectrum under stress is not equivalent to measurement of the wide-angle x-ray diffraction lines under stress; the two techniques are complementary.

EXPERIMENTAL METHODS

The samples used were two commercial polyethylene fibers (Spectra 1W and Spectra W) and two experimental fibers obtained from Allied Corpora- tion. We will call these fibers D, E, F, and G in this paper. Their specifications are outlined in Table I. All fibers had been gel-spun from ultra high-molecu- lar-weight PE,11,36 leading to a very high degree of molecular orientation. The degree of crystallinity of all the samples was about 0.85 as measured by differential scanning calorimetry. The processing parameters of these fibers are largely unknown to us, except that all were similar.36 Fibers D and E have the same molecular weight, 2.5 million, but D is heat treated and drawn

384 PRASAD AND GRUBB

TABLE I Properties of Extended Chain PE fibers

MW Diameter Strength" Modulus" Modulusb Sample x 106 (Pm) (GP4 (GPa) (GP4

D 2.5 27 3.1 180 74 E 2.5 38 2.7 125 42 F 0.8 38 2.4 110 60 G 0.8 40 2.4 110 60

" Data supplied by Allied Corporation, strain rate 0.02 s- l .

bExperimental data, strain rate 0.003 s-', strain 0.01.

further to produce higher modulus and strength. The molecular weight of Fibers F and G is "only" 800,000. Fibers E, F and G have a nominal diameter of 38 pm compared with 27 pm for D. The strength of similar gel-spun PE fibers has been found to increase with decreasing diameter,37 and with increas- ing molecular weight.4, l1

The cross-sectional area of each fiber was determined using the vibroscope technique, ASTM D1577. This area, determined for individual fibers, was used in calculating the stress on the fiber, instead of the area calculated using the nominal diameter specified by Allied Corporation. PE fiber cannot be mounted by normal tabbing methods, so special capstan inserts were usedm (Fig. 1). Each end of the fiber was clamped between the two jaws and wound several times on it. The specimen tightened around the capstans at the start of the test, and no slippage was observed at high stresses. The specimen failed between the jaws, and no jaw breaks were observed. For tensile tests the capstan inserts were fitted into the standard pneumatic grips of an Instron model 1122 tensile testing machine. The fibers were strained at a rate of 3 x lop3 s-l and the modulus calculated at 1% strain.

In the s t ress-Wan and x-ray scattering experiments, the capstan inserts were mounted in a small strain frame designed to fit on a microscope stage. Strain was applied in a stair case fashion, i.e., the fiber was rapidly extended to a particular strain value and allowed to stress relax until the stress stabilized. At high stresses stress relaxation was considerable, and the step of the strain was increased to overstress the fiber. The stress was counted as being stable when it remained constant within f60 MPa over the Raman data collection time of 100 sec. Each step in the stair case took about 10 minutes, with the time taken for the stress to stabilize increasing at higher stresses. During loading the average rate of increase of stress, including relaxation time in the total, was about 0.2 MPa/s. This corresponds to average strain rates in the range 10-6-10-5 s-'.

All fibers used in this study were subjected to cyclic loading. The fibers were unloaded in a similar staircase fashion at about twice the rate, as fewer data points were taken and the load on the fiber stabilized much faster. The fiber was then either immediately reloaded or allowed to relax overnight at zero stress before more spectra were recorded. This was to study the effect of long-term relaxation at zero stress. Raman spectra were recorded on a SPEX 1877 triplemate spectrometer,

using a Coherent Nova 90-5 Ar' laser with a maximum power of 2 W in the

OBSERVATION OF TAUT TIE MOLECULES 385

( b) Fig. 1. Special capstan jaws, exploded (a) and together (side view) (b).

514.5 nm line. A tunable excitation filter was used to reject spurious lines and background. Scattering was examined at 135O to the direction of the incident radiation (45' backscattering geometry; Fig. 2). The beam was focused using a Leitz microscope to about 100 pm, and a field stop was used to restrict the area of collection to that of the size of the fiber. The power at the sample was about 100 mW. The spectrometer was equipped with a 1800 grooves/mm holographic grating, and the slit was set for optimum spectral resolution. The detection system was a diode array, an EG & G optical multi-channel ana- lyzer, and an IBM XT personal computer. A detection time of 100 s was regularly used.

LASER SPEX TRIPLEMATE

SPECTROMETER

Fig. 2. Micro Raman system with 45" illumination.

386 PRASAD AND GRUBB

Wide-angle x-ray scattering studies were performed at CHESS on the A-1 beam line, which uses a wiggler magnet and a double focussing monochroma- tor to produce a highly parallel beam of x-rays, wavelength 1.5 A, with 5 X 10" photons/s in a 0.3 X 1 mm2 spot at the detector plane. In these experiments a 500 pm pinhole collimator was used. The (002) meridional reflection was recorded using a Braun position-sensitive detector placed at an angle of 28, = 75' to the direction of the incident beam. The sample-to-detec- tor distance was 304 mm, corresponding to a detector resolution of 0.2 prads. The fiber was mounted in a small strain frame with the fiber direction at an angle 8 , - 90 = -52.8' to the direction of the incident beam, to put the (002) planes in the diffracting position.

The b a n data was transferred to a PRIME computer, and the spectral region 1000-1500 cm-' was selected for further analysis. Several fitting procedures were used on the data. A third-order polynomial baseline was drawn and the 1063 cm-' band of the subtracted data set was fitted to a Gauss-Lorentz sum f u n c t i ~ n ~ ~ . ~ using a nonlinear least square fitting routine. Equation (1) represents the total of the baseline and the fitting function.

y = a + bx + cx2 + d X 3

where p is the peak position, i the intensity, f the fraction of Gaussian component, and wg and wl the Gaussian and Lorentzian full width at half maximum, respectively. Since this fitting function is symmetric, the procedure suppresses any asymmetry in the band.

Two further data analysis procedures were used to deal with the asymmetry of the band. First the mean position (center of mass) of the band was found; differences between mean and peak positions indicate asymmetry. Second, a symmetric function fitted to one side of the band only was compared with the data. In both procedures the first step was to subtract a polynomial baseline, which was not a trivial operation. To get the mean position of the band, C(position x height)/C height was calculated. This result was very sensitive to the baseline curve chosen, since a small discrepancy far from the peak position has a large effect. A plot of Cption(position x height) versus position was made for each data curve, and if a significant part of the total sum arose from regions that the eye would take to be noise in the original data, the background was redrawn or the integration limits changed to prevent this. To fit one side of the data only, the side at higher wave numbers was separated and duplicated by folding over the peak position to produce a truly symmetric peak. A Gauss-Lorentz sum function was fitted to this, and this function was superimposed on the original data. The amount of asymmetry was given by the integrated intensity of the difference between the fitted function and the original data.

If the peak position is all that is required, a much simpler procedure is to pick the maximum intensity data point of the baseline subtracted and smoothed data set. This gave the same peak position as all of the more complex curve fittings, but of course ignored the band shape.

OBSERVATION OF TAUT TIE MOLECULES 387

900 1000 1100 1200 1300 1400 1500 1600

I I

900 1000 1100 1200 1300 1400 1500 1600 Wovenumber cm-'

Fig. 3. Raman spectrum of fiber D in the 1OOO-1500 cm-' region at 0 and 2.4 GPa stress.

RESULTS The Raman spectrum of fiber D in the 1000-1500 cm-' region is shown in

Figure 3 at zero stress and at 2.4 GPa. The spectra are vertically separated for clarity. The assignments of some of the major bands are given in Table 11. The 1063 cm-' band was chosen for detailed study because it shows the largest peak shift per unit stress. The 1295 cm-' peak is sharp and well separated from all others but shifts very little under stress. The bands between 1400 and 1500 cm-' are overlapping so that band shape would be impossible to determine. Even the 1127 cm-' band, which seems well sepa- rated in Figure 3, can overlap the 1063 cm-' band a t high stresses.

The 1063 cm-' band is assigned to the C-C asymmetrical stretching mode in PE and has been observed by most previous workers at or near 1063 cm-'.31741.42 The same band was chosen in the previous study of the effect of stress on the Raman spectrum of PE,26 but in this case it was observed at 1059 cm-'. To make sure that the peak position at zero applied stress was well defined, we recorded the Raman spectra of several very different samples of linear polyethylenes. These were single crystal mats crystallized at 80 and W"C, material crystallized at high pressure to form extended chain crystals, gel-spun fibers, and also a parafk C32Ha. The

TABLE I1 PE Vibrational Frequencies and Their Assignments in the 1OOO-1500 cm-' Region

Wave number (an-') Assignment

1063 1127 1295 1418 1440 1463

C-C a s p str, B, C- C a s p str, Ag

CH, twist, &g CH, bend, Ag CH, bend, A, CH, bend, %,

388 PRASAD AND GRUBB

1064

1062 r I

1060 n E 2 1058 > P

1056

1054

Peak position

0

* \

1064

1062 - I

E,

5 s

1060 &

P

n

1058 c

1056

1054

0.0 0.5 1 .o 1.5 2.0 2.5 Stress, GPa

Fig. 4. Mean and peak frequency of the C-C asymmetric stretching mode of fiber D as a function of stress (loading).

relative intensities of the bands in the Raman spectra of these samples were different, but the shape and position of the bands were identical. The mean wavenumber of the C-C asymmetric stretch Raman band was 1064 f 0.4 cm-‘. Further results and discussion relate to this band, which will still be called the “1063 cm-’” band.

Consider now the effects of loading. A plot of the peak position Cp versus stress during loading shows an initial linear portion for all fibers. The slope of this curve is the peak shift per unit stress, called the peak frequency shift factor, ap. Then at a well-defined stress value which we call the break point the peak shift deviates from its initial linearity and the effect of stress on the peak position Fp becomes very small. That is, a p is small at higher stresses.

When the mean position of the band F, is plotted instead of the peak position, there is more scatter because of the influence of background noise, especially in fibers F and G, but there is no longer a break point. Instead there is a linear relation between mean band position and stress at all stresses; dFJda = a, is constant. Figures 4 and 5 show the peak frequency of the C-C asymmetric stretching mode as a function of stress during loading of fibers D and E, respectively. Figures 6 and 7 show similar data for fibers F and G. Table I11 summarks the break points and the frequency shift factors a p and a, of all four fibers during loading. The mean position critically depends on the form of baseline and the integration limits chosen as explained in the experimental section. a, is therefore not accurate to more than f0.2 at best, and it should not be taken from Table I11 that fibers D, E, and F are identical while G is different. All fibers give a similar mean shift factor am = - 4.0 & 0.5.

The experimental frequency shift factor for the peak position a p in the linear region of the Raman frequency-stress curve (column 2, Table 111) was very nearly the same for fibers D, E, and G. Fiber F, which has low molecular weight and low modulus, showed a slightly larger shift factor (Fig. 6). In the reported case of extruded high modulus PE,26 ap was much larger: -11.2 cm-’/GPa. At stresses greater than the break point stress, a p is

OBSERVATION OF TAUT TIE MOLECULES 389

1064

- I 6 1062

n L 0

5 g 1060 3

1058

Peak position

1064

- 1062 '6

n L 0

2 1060 5

3

1058

0.0 0.5 1 .o 1.5 Stress, GPa

Fig. 5. Mean and peak frequency of the C-C asymmetric stretching mode of fiber E as a function of stress (loading).

reduced substantially, but it no longer corresponds to the whole of the specimen. As the shift is being compared with the macroscopically applied stress, the shift of the mean position is clearly more appropriate. The total frequency shift of the band is about 8 cm-' for fiber D and about 4-5 cm-' for the rest of the fibers.

The break point (the stress at which the peak shift deviates from linearity) increases with the strength of the material. It is about 0.9 GPa for high- strength fiber D, dropping to about 0.5 GPa for fibers E and F. Since fiber G was not loaded to very high stresses, it is difficult to observe any break point. In the extruded PE used by Wool et al., which had an initial Youngs modulus of 33 GPa and a strength of less than 1 GPa, a,, deviated from linearity at about 0.15 GPa.26 The PE fibers undergo significant plastic flow at stresses

r 1065

1065

c I 6 1063

k n

? 1061

5 P

c

1063 '5 t, n

$ 1061

3

1059

1059

0.0 0.5 1 .o 1.5 Stress, GPa

Fig. 6. Mean and peak frequency of the C-C asymmetric stretching mode of fiber F as a function of stress (loading).

390 PRASAD AND GRUBB

1064

- '5 1062

n L V

$ 1060

3

1050

Peak position

Mean position \

1064

- I

1062 6 n L V

5 1060 8

3

. 1058

0.0 0.5 1 .o 1.5 Stress, GPO

Fig. 7. Mean and peak frequency of the C-C asymmetric stretching mode of fiber G as a function of stress (loading).

above the break point stress, since increasing strain was required to maintain the stress. Mechanical testing at a low but constant strain rate showed no discontinuity at the (( break point" stress, but a steady increase of irreversible deformation and decrease of slope of the stress-strain curve.

The change in peak shape on loading is clearly seen in Figures 3 and 8 and the data corresponds to fiber D. The spectra are again vertically separated for clarity. Stress has caused the band to shift to lower wave numbers and to broaden. The peak intensity falls, and a low intensity tail appears at low frequency, in the region 1000-1050 cm-'. The tail is not very clear in the raw data, even a t the highest stresses.

Figure 8 shows a sequence of processed and normalized data curves from the same specimen, each with the continuous line derived from fitting the right- hand half of the band with a symmetric function as described in the experi- mental section. Initially at zero stress the band appears to be completely symmetric, and the line is still an excellent fit to the data at a stress of 0.68 GPa, just below the break point. Remember that the data points to the left of the peak in Figure 8 were not used in the procedure that gave the continuous lines. Above the break point at 1.38 GPa and at the maximum stress the line is

TABLE111 Summary of Stress versus Frequency-shift Behavior on Loading Extended Chain

Polyethylene Fibers

Frequency shift factor Frequency shift factor Break pointa Type of peak [(cm . GPa)-'] of mean [(cm . GPa)-'] ( G W

Fiber D - 3.7 - 3.9 0.9 Fiber E - 3.5 - 3.9 0.5 Fiber F - 4.3 - 3.9 0.5 Fiber G - 3.6 - 4.5 0.5

Extruded PEb - 11.2 - 0.15

astress at which frequency shift becomes nonlinear. bRef. 26: modulus = 33 GPa, strength < 1 GPa.

OBSERVATION OF TAUT TIE MOLECULES 391

I I I I

1000 1020 1040 1060 1080 1100 Wavenumber cm-'

Fig. 8. Background subtracted and normalized data curves from sample D. The continuous line is derived from fitting the right-hand half of the curve to a symmetric function.

still an excellent fit for the upper 70% of the peak. Thus the band consists of a symmetric peak and, above the break point, an asymmetric tail. The full width at half maximum of the Raman band is therefore given accurately by the full width at half maximum (fwhm) of the Gauss-Lorentz function, but this only relates to the sharp part of the distribution, not the tail.

The nearby 1127 cm-' band changes in position and shape with stress in the same way as the 1063 cm-' band. The peak wave number of the 1127 cm-' band falls with stress at low stresses, at about 2.5 cm-'/GPa. I t then stabilizes at high stresses and a tail develops, making the peak asymmetric. This indicates that the tails relate to the original peaks. It would be improba- ble, for example, that the tail on the 1063 cm-' band should come from a broad peak at 1043 cm-' that was not observable at low stress and for a similar broad peak to appear just below the 1127 cm-' band at the same stress. The tail on the 1127 cm-' band extends almost to the 1063 cm-' band. This will affect the baseline drawn, and thus the values of the mean band positions Fm at the highest stresses, in Figure 4 for example, are not so reliable.

For comparison with Figure 8, Figure 9 shows wide-angle x-ray data for the (002) meridional reflection of a fiber of sample D at stresses of 0.27 GPa and 1.84 GPa. It is immediately clear that there is no tail on either side of the peak, either at low or high applied stress. There is no nearby interfering line, and the background is less noisy, so curve fitting is easier and more reliable than in the Raman spectra. The same fitting procedures were used on the x-ray data as on the Raman spectra. Table IV summarizes the results; the peak and mean position, which are identical, fwhm, and the tail area of the (002) reflection at the two stresses shown in Figure 9. The apparent crystal modulus can be calculated as A(sin e)/(Aa x sin 8) = 300 GPa, but this is not the true crystal modulus E,.7* 149 l6

The change in fwhm with stress in fiber D is shown in Figure 10, along with the integral breadth of the band and the fractional intensity of the tail region. The intensity of the tail region was determined as the integral of the difference between the data and the lines in Figure 8 and normalized by

392 PRASAD AND GRUBB

0.27 GPa

73 74 75 76 77 Angle (20 degrees)

Fig. 9. WAXS data for the (002) meridional reflection of a single fiber of sample D.

TABLE IV Summary of the Effect of Stress on (002) Meridiond Reflection in Fiber D

Stress Peak position Mean position fwhm Area of tail as (GPa) (20 degrees) (20 degrees) (degrees) percent of total peak

0.27 75.3 75.29 0.23 0.47 1.83 74.84 74.82 0.61 0.29

16 - I

6 - 14 5 0

12 D o

10 m

8

A 20

P) a - 15

Y

b

10 n I : :

1 . 3 I

0.0 0.5 1.0 1.5 2.0 2.5 Stress, GPa

Fig. 10. Change in fwhm (A), integral breadth of the band (O), and the intensity of the tail (m) with stress in fiber D.

OBSERVATION OF TAUT TIE MOLECULES 393

1065

1063 c

1061 B n E

Y 1059

s 1057

1061 ' n k a) E

1059 2 B g

1057

1055

. ' \ \ \D

1055 0.0 0.5 1.0 1.5 .2.0 2.5

Stress. GPa

Fig. 11. Peak (a) and mean (b) frequency of the C- C asymmetric stretching mode of fiber D subjected to cyclic loading: (m) loading, (A) unloading, (0) reloading.

dividing by the total integrated intensity of the band. As expected from the noisy baselines in Figure 8, the results show a good deal of scatter. A t low stresses the fwhm and the integral breadth increase linearly and at the same rate. Then at around 1 GPa the rate of increase rises, but the integral breadth increases more then the fwhm. A t the highest stresses there is more scatter, but the fwhm stabilizes while the integral breadth increases slowly again. The integral breadth will rise faster as the tail develops. Figure 10 also shows that for fiber D on loading there is little indication of tail until about 1 GPa, close to the break point of 0.9 GPa, and then the intensity in the tail increases steadily, reaching 18% at 2.4 GPa.

So f a r the data described has come from the first loading of the fiber samples. Now we consider the effects on the Raman spectrum of unloading and reloading. Data for the effects of cyclic loading on fibers D, E, F, and G are given in figures ll,, 12, 13, and 14, respectively. These figures relate to experiments where the stress was cycled with no long pause at either zero stress or the maximum stress. Each of them shows the peak position fip in the upper part (a) and the mean band position fim in the lower part (b). The dashed lines are straight line fits to the loading data, which have already appeared in Figures 4-7. The solid lines are fits to all the remaining data; the unloading, reloading, and reunloading parts of the cycles do not give distin- guishable curves. The dashed lines in the upper sections stop at the break point, because at higher stresses the shift of peak position is no longer linear. The solid line fits extend to the maximum applied stress because there was no longer any indication of a break point in any of the data.

Thus on unloading and reloading the fibers the shift of the 1063 cm- C - C asymmetrical stretch peak was linear and did not follow the original loading curve. aP was larger for fibers D and E than for the lower molecular weight fibers F and G. The wave number of the peak on unloading the fiber to zero

394 PRASAD AND GRUBB

I lorn

1066

1064 - I ' 1062 8 n E $ 1060 > s

1058

1064 - 1062 '

E 1060 g

z

n 8 a)

B 1058

1056

* 1056 ' 1

0.0 0.5 1 .o 1.5

Stress, GPa

Fig. 12. Peak (a) and mean (b) frequency of the C- C asymmetric stretching mode of fiber E subjected to cyclic loading: (w) loading, (A) unloading, (0) reloading.

stress was higher than the wave number at the start of the loading process. The mean position of the band also shifted linearly with stress on unloading. It followed the equivalent loading curve quite closely, but the mean position on unloading was systematically at a higher wave number than the mean position at the same stress during loading.

The position of the Raman peak during reloading depended on the time between the unloading and reloading cycles. If the fiber was reloaded immedi-

1066

1064 - I ' 1062 8 n E $ 1060 > s

1058

1.064 c

1058

1056

1056 ' I

0.0 0.5 1 .o 1.5 Stress, GPa

Fig. 13. Peak (a) and mean (b) frequency of the C- C asymmetric stretching mode of fiber F subjected to cyclic loading: Q loading, (A) unloading, (0) reloading.

OBSERVATION OF TAUT TIE MOLECULES 395

1066

1064 L

I

1062 e n E $ 1060 > s

1058

I 1066

1064 - I

1062 ‘ n b a) E

s 1060

>

1058

1056

t 1056 ‘ I

0.0 0.5 1 .o 1.5 Stress, GPO

Fig. 14. Peak (a) and mean (b) frequency of the C- C asymmetric stretching mode of fiber G subjected to cyclic loading: (m) loading, (A) unloading.

ately after unloading, the reloading curve was closer to the unloading curve. On the other hand if the fiber was allowed to relax for a while, the reloading curve was closer to the loading curve. On allowing the fiber to relax overnight the peak position at zero stress returned to its original value for all four fibers. If the loading was limited to stresses below the break point, no hysteresis was observed. In all of the cyclic loading experiments, the effects were most clearly seen in fiber D, the strongest fiber. Fibers F and G could not be loaded far above their break point, so deviations from linear behavior were small.

DISCUSSION

The frequency of a band in a Raman spectrum of a polymer depends on the exact shape of the molecule and on its e n v i r ~ n m e n t . ~ - ~ ~ Whe n the shift in wave number of a spectral line AF with the applied stress u was found to be approximately linear, the slope dF/du was at first assumed to be a material constant.” Then the shift was found to depend on the sample, and dF/dr,, where E , is the strain of the oscillating chain, was recognized as the true constant. In terms of local stress on a chain, a,, the shift factor dF/du, = a, will also be a constant as long as the chain modulus E, remains constant. The chain modulus may change with temperature and fall at very high strains altering Neglecting these effects in the experiments described here, in all-trans PE chains there is a linear relationship between the local stress in the molecular chain direction and the vibrational frequency of the “1063 an - ’’ Raman band.

The line shape of the Raman band is then directly related to stress distribution in the sample. The mean position of the band corresponds to the

396 PRASAD AND GRUBB

mean chain stress and the peak position to the most probable chain stress. If noise could be sufficiently reduced, deconvolution of the line shape at zero applied stress would allow the exact stress distribution to be obtained, as in the IR case.21

In high-modulus fibers all the crystals are well aligned with the chains along the fiber axis. The material stiffness is so high that the contribution of the poorly aligned or not all-trans chains can be neglected. The applied load is then equal to the sum of all the loads on the all-trans chains in a cross section. This is the same as the mean stress 6, on these chains times their cross-sec- tional area. The applied stress u = 6, x fa, where fa is the fractional cross-sec- tional area of the fiber taken up by the aligned all-trans chains. fa will depend on the total volume fraction of the all-trans chains f and on the fiber structure. The shift of the mean of the band position a, = dF,/du = ao/fa. In any all-trans extended chain polymer X , < f I fa < 1 (ignoring the differ- ence between volume fraction crystallinity and mass fraction crystallinity). When these conditions are met in a high-modulus sample, a, could fall in the narrow range a, - a,/X,. But only if the distribution of stress is symmetrical about 6, will the shift of the peak position a,, = am.

Figures 4-7 show that a , is a constant for each fiber, up to an applied stress of 2.4 GPa for fiber D (Fig. 4) and also to the maximum stress attainable in the other fibers. (See Table I11 for a summary of the results.) This means that each fiber has a constant value of fa throughout the testing, and that the data analysis procedures have captured all of the 1063 cm-’ band, or a constant fraction of it. If many chains were stretched into the all-trans conformation during deformation of the fiber, fa would increase and a, fall. If some chains were stressed to more than 15 GPa as the applied stress increased, they would oscillate at below lo00 cm-’, outside the integration limits used in calculating the mean band position. The mean shift would be underestimated, and a , would fall. The constancy of a, is also a confirma- tion that a, remains constant to at least 15 GPa, corresponding to the highest observed frequency shift (unless a fall in E, at high strains increased a, just enough to balance an increase in fa or underestimation of a,).

From Figures 4-7 there are two distinct stress regions with different behavior of the Raman band. Up to a certain stress level, 0.5 or 0.9 GPa (column 3 of Table 111), the peak position of the band shifts linearly with the applied stress. In this linear range, the frequency shift of the peak position with applied stress ap is essentially the same as that of the mean band position am, and the band remains symmetric. The fwhm and the integral breadth of the band increase linearly and at the same rate in this region (Fig. 10). A linear increase of width with stress is expected for a constant fiber structure. The stress distribution will increase in proportion to the applied stress. For example if one portion of a chain carries 1.5-fold the applied stress u, in a fixed structure it will always carry 1.5 X u. The width of the 1063 cm-l band increases by 2.5 cm-’/GPa at low stresses (Fig. lo), a width which is 60% of the applied stress. Asymmetry of the stress distribution and therefore of the band shape would be required if the width of the distribution ap- proached the mean, since compressive stresses would not be generated or sustained in a stretched polymer fiber. In this case the distribution is narrow enough to allow an essentially symmetric band.

OBSERVATION OF TAUT TIE MOLECULES 397

In contrast, at stresses above the break point the peak position changes only a little with applied stress, and the band becomes asymmetric. Its form is similar to that previously found for polypropylene samples in IR.23924 The 1063 cm- ’ band becomes bimodal, containing a comparatively sharp symmet- ric peak and a low broad tail extending to low wave numbers (Fig. 8). The broad tail is a small but increasing fraction of the material (Fig. 10) which has much higher and less uniform strains. This is a distinct second system of load-bearing material. Wool et al. saw a deviation from an approximately linear effect of stress on the same 1063 cm-’ band at 0.2 GPa in extruded PE and their Figure 826 shows the beginnings of a low-frequency tail in the 1063 cm-’ band at high stress.

A reduction of ap at high stress has also been observed in “as-spun” poly(p-phenylene benzobisthiazole) (PBT) fibers by Day et al.46 PBT is a highly ordered rigid rod polymer with an apparently simple fibrous s t r ~ c t u r e . ~ ~ - ~ ~ At strains greater than 1% no change in Raman peak position is seen with a further increase in strain, and the measured macroscopic stress falls with time. Heat-treated fibers of PBT do not yield, and a p remains constant until failure. The nonlinear behavior of the Raman peak was said to be due to yield.46 The published Raman spectra of stressed “as-spun” PBT fibers46 are distinctly asymmetric. We can therefore assume that changes in a p are due to band asymmetry even when no measurement of peak shape has been made.

How do these Raman results compare with those of x-ray measurement of crystal strain under stress? Previously published data on the effects of stress on the (002) reflection refer only to the peak position. This has been found to shift linearly with applied stress at low stresses and then become nonlinear at about 0.15 GPa for a range of fibers with moduli in the range 3-15 GPa.l23l3 The peak position does not change much with stress at higher stresses, so the apparent crystal modulus increases greatly above this stress. No explanation was given for these observations, which are identical in form to the Raman results. We might expect this behavior to be due to asymmetry of the x-ray diffraction line.

To determine line shape a single fiber sample must be used. In a bundle of fibers unequal loading is difficult to avoid, and it would spread the reflection in an unpredictable manner. One vital result from a series of measurements of the (002) WAXS line profile of a single stressed fiber16 has been shown in Figure 9. It is that at stresses where a large fraction (15-20%;) of the Raman band is in the asymmetric tail, the (002) x-ray reflection remains completely symmetric. The continuous lines in Figure 9 seem to have been drawn through the data points, but as in Figure 8 they were obtained by fitting to only the right half of the data. No asymmetry is visible. The calculations used to derive the values for asymmetric fraction of the Raman band, shown in Figure 10, were applied to the x-ray peaks. They indicated asymmetries of 0.5% or less, which are probably due to noise.

The x-ray experiments do not detect the highly stressed material shown in the tail of the Raman peak, but its presence is implied by the sudden increase of apparent crystal l3 Either the crystals suddenly get very stiff as strain increases, which is unreasonable, or something else carries the increas- ing load. The difference between x-ray and Raman experiments is that in

398 PRASAD AND GRUBB

x-ray diffraction sensitivity increases with the regularly organized volume, whereas the Raman spectrum is equally sensitive to isolated chains and chains in crystals. We therefore take the highly stressed chains to be real but not detectable in x-ray experiments because they are not crystalline.

In wide-angle x-ray scattering from PE, the form and intensity of the (002) peak depends on the size of the crystal in all directions. A crystal containing long chains has a well-defined (002) spacing and thus a reflection at a well-defined angle, 28. However, if the crystal is very narrow, a cluster of a few chains, the diffracted x-ray intensity is spread out laterally. When the spread is greater than the width of the detector, signal is lost and the narrow crystals are underrepresented in the x-ray data. An isolated all-trans chain could hardly be detected; about 0.3% of the diffracted intensity might enter the detector with the geometry used here. In contrast to this, the calculations of the Raman frequencies of PE were made using a single isolated chain,26 and Strobl has found that the rotator phase of PE, containing all-trans chains in poor lateral order, has essentially the same Raman spectrum as the or- thorhombic form. In particular, the 1063 cm-’ band has the same position and intensity . 32

Thus the second system that carries load in PE after some plastic deforma- tion has occurred consists of noncrystalline all-trans chains, commonly called taut tie m o l e c ~ l e s . ~ - ~ ~ They could be in small regular clusters, 2-3 nm across, but these would not give sharp x-ray diffraction, a definition of crystallinity. In fiber D at high stresses the taut tie molecules carry almost half the applied load. This approaches the model of Prevorsek for stiff Nylon 6 and PET fibers where the “extended noncrystalline molecules” are the major load-bearing s y ~ t e m . ~ ~ ~ ~ ~ The primary load bearing system is of course the crystals in the system, which produce the sharp peak in the Raman band, which shifts with stress as the x-ray reflection does. The constancy of a , implies that the taut tie molecules also contribute to the Raman band at low applied stresses but are then under stresses close to that of the crystals. Without absolute intensity measurement of the Raman bands, it was not possible to show this directly. According to S t r0b1~~ the 1440 cm-’ band is associated with the presence of disordered material, since it is entirely absent in the Raman spectrum of pressure crystallized PE. In Figure 3 it can be seen that the relative peak intensity of this band falls as stress increases. This might indicate that the degree of disorder in the fiber is reduced; this would not be too surprising, since stretching an extended PE chain will increase the energy required to form defects.

On unloading and reloading the fiber the shift of both the Raman peak and mean band positions are linear with stress. They are not identical, so some asymmetry remains even when it cannot be seen directly in the data. With no “break point” in any but the first loading curve, it seems that once the system of taut tie molecules has been overstressed by plastic flow, and the structure is changed, i t does not change back. This is not strictly correct, since an overnight hold at zero stress returns the sample to its original condition. Time-dependent differences in the stress distribution among chains was also observed in the IR spectral studies of p~lypropylene .~~!~~ They were of the expected form: the stress became equalized among the chains as the highly overstressed chains relaxed.

OBSERVATION OF TAUT TIE MOLECULES 399

The difference in ap for different fibers during unloading is thought to be a rate effect, where the higher-molecular-weight materials have longer relax- ation times. The smaller difference between the loading and unloading curves (and thus the smaller slope of the unloading curve) in fibers F and G may be because these lower-molecular-weight fibers relax faster than the average strain rate during unloading. That is, at each step in the unloading they relax before the Raman spectrum is recorded.

When the external applied stress has been reduced to zero, the position of the peak does not return to its original value, but to one about 1 cm-’ higher. Repeated trials using a range of sample types showed that the vibrational frequency observed at zero stress immediately after unloading was not within the range observed for PE which had never been stressed. The frequency shift of + 1 cm-l corresponds to a compressive stress of about 0.25 GPa. The loaded taut tie molecules are slow to relax, so that if the rate of unloading and reloading could be increased, the Raman shift would more and more corre- spond to the true elastic response of the structure since it is above the break point. At complete unloading the crystals are in compression to balance the residual unrelaxed tension in the second load bearing system.

How can we relate this new information to the structure of high modulus fibers? First, the fact that there is a significant change in the stress distribu- tion associated with the onset of plastic deformation indicates a structural change, a different deformation mode at high stresses. No previous models have specifically considered this; most are purely elastic. They should there- fore be compared with the data only at low stresses. At low applied stresses the all-trans chains are stressed in the same way whether they are in crystals or not. The blocks in structural models usually labelled “crystal” and “amorphous” should therefore be called “all-trans ” and “disordered.”

A t low stresses a p = a, = dF/du and was the same for all our samples. This means that co/u is constant, although the fiber modulus €/a is not. This result is equivalent to the x-ray result that similar lattice moduli cc/u are found in samples of different moduli, which was taken as evidence for a series rn~del.’.’~~ l3 This simplest mechanical model for stress distribution, where the all-trans and the disordered chains are under the Same stress, a, = u, predicts that dF/du = ao, a constant. I t also predicts that the fiber is much softer than observed: E = EJ(l - f ), where E, is the modulus of disordered chains.

If the all-trans and disordered chains are in parallel, so that the all-trans chains are continuous through the fiber, uo = u/ f and E = f X E, (when k:, -=x E J , so dF/du = aJf a 1/E. If at low applied stress where aP is constant and the band asymmetry is small, a p = dF/du. It is then possible to compare our results with those of Wool et a1.26 Their values of a p for the 1063 and 1127 cm-’ bands are 2-3 times larger than ours and were obtained with a sample 2-3 times softer. I t seems that dF/du = 1/E after all. X-ray results on a range of hot-drawn PE fibers55 support this view, for the apparent lattice modulus cc/u dropped as the sample modulus rose.

The above discussion assumes that the stiff chains are perfectly aligned. Samples with imperfect alignment will have other deformation modes active, and this may affect dF/du. An example of this is the rigid rod polymer poly(para-phenylene terephthalamide) (PPTA). We found that in PPTA fibers

400 PRASAD AND GRUBB

ap is constant until fracture, but in different fibers (Kevlar 49 and Kevlar 29, Du Pont) ap increases in proportion to the macroscopic modulus. A recent paper by S. van der Zwaag et a1.% using PPTA fibers of a range of moduli spun by Akzo Laboratories reports this linear relationship and explains that both modulus and frequency shift factor depend on orientation. Misoriented regions rotate towards the fiber axis under tensile stress. This adds to the compliance but has no effect on the Raman spectrum. As the orientation improves, a larger portion of the applied stress deforms the chemical bonds, increasing ap. Since no increase in dF/da with modulus is seen here, misalign- ment is not considered.

Neither the series nor the parallel models can fit all the mechanical data available, and a range of more complex models has been used. Takayanagi models may have some continuous crystalsl4? 57-59 or have crystals linked by thin disordered regions which may contain taut tie m o l e c ~ l e s . ~ ~ ~ ~ ~ ~ ~ - ~ Taut tie molecules with modulus E, are mechanically identical to the continuous crystals. These more complex models generally predict a bimodal or more complex distribution of stress in the all-trans chains, which is not observed experimentally. They generally do not predict a constant dF/da for samples with different modulus, but they do not require it to vary; free structural variables can affect modulus at constant f and not affect dF/da.

In Peterlin’s mode150-52 tie molecules may appear in series with crystals, linking them to form a microfibril, or they may join microfibrils together. The amount and location depends on the material and on the draw ratio. Once a fibrous structure is formed, further deformation is said to occur by the sliding of fibrils past each other, so that the number of tie molecules which link fibrils increases strongly with draw ratio. All high-modulus PE fibers are very highly drawn, so a large amount of interfibrillar ties is expected. Mechanical mod- elling indicates that there are few ties between the crystals. A particularly specific recent model for gel-drawn PE fibers derived from a range of data has microfibrils 20 nm in diameter containing crystals 70 nm long separated by 4-nm-long disordered regions. The disordered regions contain 150 taut tie molecules, which make up about 13% of the chains in the fibril cross section.62,m Thus a = 4/70, b = 0.13, and the taut tie molecules are less than 1% of the total volume and very highly stressed. Nevertheless they limit the stiffness and strength of the fibril and the fiber.

At high stresses, above the “break point,” the fibers undergo significant plastic flow and the stress on the crystals no longer increases. This requires there to be a weak material in series with the crystals which begins viscous flow a t the break point stress. The intercrystalline regions with their tie molecules fit this requirement, since they are predicted to be the weakest part of the fiber. The few all-trans chains in these regions would not be detectable. Increasing loads above this point are carried by a system of taut tie molecules, which are stressed much more than the crystals. They must then be in parallel with the combination of crystals and flowing material, to experience the increasing strain. This is in agreement with x-ray modulus experiments on other high-modulus PE fibers over a range of temperature^.'^ A fall in apparent crystal modulus at higher temperatures was interpreted as due to softening of a noncrystalline load-bearing system in parallel with the crystals.

OBSERVATION OF TAUT TIE MOLECULES 401

If the taut tie molecules were mechanically continuous through the entire sample and had modulus E,, then they would have higher strains and stresses than the crystals at any applied stress. Some amount of disordered material in series with these taut tie molecules is required to keep their stress to that of the crystals before plastic flow. The rest of the disordered material will be in parallel with the whole structure so far described, limiting the modulus and making the total add to 1005%. This is only possible if the normal DSC derived value for crystallinity is accepted as being fa r too high owing to order in the noncrystalline ~ g i 0 n s . l ~

SUMMARY The stress distribution and the deformation mode in high-modulus fibers

can be studied by Raman spectroscopy under stress. The results show that the pattern of stress distribution changes at high stresses when plastic deforma- tion becomes significant, and this seems to be a general phenomenon, not limited to gel-spun PE fibers. In the high-stress region, noncrystalline chains and taut tie molecules are more highly stressed than the crystals and carry a significant fraction of the load. This makes interpretation of x-ray diffraction under stress difficult, unless parallel Raman experiments are carried out. In a gel-spun PE fiber, Spectra 1W at 2.4 GPa, the overstressed taut tie molecules comprise 20% of the total number of all-truns chains, and are stressed up to at least 15 GPa, and carry half the total load on the fiber.

Since the crystallinity of these fibers is 0.85, there does not seem room for this fraction of taut tie molecules, but order in noncrystalline regions will increase the calculated crystallinity. The crystals go into compression when the fiber is unloaded from the high-stress region. This means that tensile stresses in the taut tie molecules are slow to relax, and they must be mechanically in parallel with the crystals. X-ray modulus experiments on other high-modulus PE fibers have shown that normal crystallinity measure- ments overestimate the crystal fraction, because of order in noncrystalline regions whicn are mechanically in parallel with the ~rystals. '~ Structurally this places them between microfibrils rather than between crystals in mi- crofibrils, where they will be highly stressed as the fibrils slip past each other during plastic deformation.

The authors are grateful to the National Science Foundation-Materials Research Center for financial support of this work. They thank Keith Brister of Cornell University for assistance with Raman experiments, R. Wincklhofer of Allied Corporation for supplying the fibers used in this study, and W. W. Adams of AFWAL/MLBP for the loan of the x-ray detector system. Peter Lee of the Department of Materials Science and Engineering, Cornell University, did some of the preliminary work.

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R.eceived January 15, 1988 Accepted August 1, 1988