Willis

An infra-red spectroscopic study of molecular orientation and conformational changes in poly(ethylene terephthalate) A. Cunningham and I. M. Ward Department of Physics, University of Leeds, Leeds LS2 9JT, UK

and H. A. Willis and Veronica Zichy Research Department, Imperial Chem&al Industries Ltd, Plastics Division, Welwyn Garden City, Hefts AL7 1HD, UK (Received 8 March 1974) Polarized infra-red (i.r.) spectroscopy has been used to study the changes in molecular orientation and conformation which occur on drawing poly(ethylene terephthalate) sheets. The i.r. data provided orientation functions (P2(0)~ir where 0 is the angle between the molecular chain axis and the draw direction for these uniaxially oriented sheets. Excellent agreement was obtained between the i.r. orientation functions for absorption bands associated with benzene ring mode vibrations, and orientation functions obtained from optical birefringence. Infra-red orientation functions for absorption bands associated with the trans and gauche conformations of the glycol residue, were then combined with i.r. estimates of the trans/gauche concentrations to examine the changes occurring in drawing. For drawing at 80°C up to a draw ratio of about 3-5, there was good agreement with expectations based on the deformation of a rubberlike network.

INTRODUCTION Although the examination of polymers by infra-red (i.r.) spectroscopy with polarized radiation has been undertaken for many years, it is only comparatively recently that the measurements have been used to obtain an absolute measure of molecular orientation in terms of orientation functions similar to those employed in optical, X-ray diffraction and n.m.r, studies. Most of these quantitative i.r. studies have been carried out on polyethylene, notably by Read, Stein and their collaborators, and extensive measurements have been made on low density polyethylene 1, oxidized polyethylene 1, ethylene-carbon monoxide copolymers ~ and crosslinked amorphous polyethyleneS. The particular value of assessing the i.r. data in terms of orientation functions, rather than dichroic ratios, is that they can then be used to compare with other measures of orientation. In this paper we describe an i.r. spectroscopic study of poly(ethylene terephthalate) (PET) where the i.r. results are combined with measurements of refractive indices to provide quantitative information regarding both molecular orientation and conformational changes. The i.r. data will be analysed using the theoretical results derived in the previous paper 4, which take into account both the reflectivity correction and the internal field effect. There have been several previous i.r. structural studies of oriented PET fibres and films. Two aspects

have been given particular attention. First, there is the molecular orientation. In one way drawn films this is complicated by preferred orientation of the (100) planes of the crystalline regions 5, 6. We have taken particular care to reduce this effect to a minimum in the films prepared for the present investigation. Secondly, there are the changes in rotational isomer content with changing degrees of deformation or draw ratio. It is now generally accepted that these are primarily associated with the trans and gauche isomerism of the ethylene glycol linkage 7-9, and there have been a number of publications where it has been shown that the trans content increases and the gauche content decreases with increasing draw ratio or density 10-12. In the present paper, by combining quantitative measures of both molecular orientation and rotational isomer content, we are able to carry the analysis forward to a greater degree of sophistication than has hitherto been achieved. THEORY As the theory to be used has been described in detail in the previous paper 4, only a brief summary will be given here. The measurements are made with the electric vector of the polarized i.r. radiation along the draw direction (z) or perpendicular to the draw direction in the plane of the film (x). Absorption coefficients kz and kx are then calculated from equation (12) of the previous

POLYMER, 1974, Vol 15, November

749

I.r. study of molecular orientation and conformational changes in PET: A. Cunningham et aL paper, where the absorbance A is given by: A = log10/~=0"4343{~-t

2k2 -/ (n+nKBr)2j

(1)

where It, I~ are the incident and transmitted intensities respectively at the peak of the absorption, n and k are the real and imaginary parts of the complex refractive index of the polymer at the free space wavelength )~, and nr:Br is the refractive index of the potassium bromide plates used to contain the sample (assumed constant and real). The thickness of the sample is y0, and the free space wavelength at the absorption peak is )~. The value of k can be found directly from equation (1). This equation is a quadratic in k and has two solutions, one of which may be rejected by inspection, since an approximate value of k can be obtained in the absence of the reflectivity correction term 2k2/(n+n~zBr) 2. These values for kz and kz are then combined with the optical values of nz and nx, to obtain the imaginary parts of the corresponding average complex polarizabilities ( %*) = ( % ).- ~ ( .% ) . and . (.~ * ).= ( ~.) - z ( o ~ ) (see ref 4), using the Lorentz-Lorenz equation. We have: 2 4 4zrN , 6nzkz{n4z + 2n~zk~+ 4n~ - 4k~ + k z + 4}- 1 = _ i f _ ( % ) and

6nxkx{n~ + 2n~k~+ 4n~- 4k~ + k) + 4}-1 = ~ - ( a ~ )

(2)

These polarizabilities, where N is the concentration of absorbing species/unit volume, relate to the distribution of molecular orientations as follows. It is assumed that an individual transition moment direction makes a fixed angle Ora with the chain axis, and that the corresponding chain axis makes an angle 0 with the draw direction. It was shown in the previous paper that for a uniaxially oriented polymer:

~ x

= P2(Om)(P2(O))ir

(3)

It is perhaps worth commenting that this equation is very closely related to the more familiar relationship in terms of the absorbances Az and Ax, which follows directly from the molecular gas approximation without taking into account reflection losses and the internal field effect. In this case we have:

Az--A~ Az~ = P2(Om)(P2(O))lr In these equations P~(Om)=½(3cos2Om-1) and is assumed to be a constant quantity depending only on the molecular structure of the polymer. It is, of course, quite possible that this assumption does not hold if there are changes in molecular conformation on drawing. (P2(O))ir=½(3(cos2O)ir-1), defines the mean value of P2(0), determined by the i.r. method for the molecular chain axes and is the orientation function which we will be primarily concerned with in this paper. The measurement thus provides a direct measure of the product of the constant quantity P2(Om) and the orienta-

751) POLYMER, 1974, Vol 15, November

tion function (P2(0))lr. An absolute measure of the chain axis orientation can therefore be obtained either if Ora is known or if the method can be calibrated by comparison with another method of measuring molecular orientation. In this investigation we have combined the i.r. measurements with refractive index measurements to examine the validity of the i.r. method and to provide a possible measure of absolute calibration. For a transversely isotropic sample, the refractive indices nz and nx can also be used to calculate (P2(0)). Since this is a different measure, we introduce the subscript 'opt'. Following the previous paper, letting n~-I ~=¢i

"e

(4)

(P~(0))opt

(5)

We then have: ¢~ + 2¢~ =

Ae/3e0 can be estimated from measurements on highly oriented samples where (P2(0))--*l. We have used the value 0.105 calculated from data in ref 6. It can be appreciated that if the i.r. method provides an accurate measure of chain axis orientation then a plot of P2(Om)(P2(O))ir against (P2(0))opt will be linear. Moreover, the optical measurements can be regarded as providing a calibration of the i.r. technique, by allowing P2(0m) to be calculated. Alternatively, if an independent estimate of 0m can be obtained (say from crystallographic data) then the i.r. data can be directly converted to an absolute measure of chain axis orientation.

EXPERIMENTAL

Sample preparation The starting material for all the samples investigated was isotropic amorphous PET film (intrinsic viscosity 0.61) of thickness 30/~m. This film was prepared by melt extrusion and quenching onto a chill roll. Two series of oriented films were studied. Series (i) was prepared by drawing strips of the isotropic film to a constant draw ratio of 4:1 at temperatures in the range 60°C to 100°C. Series (ii) was prepared by drawing at constant temperature (80°C) to different draw ratios in the range 1.5: 1 to 5: 1. Details of the sample dimensions, and the extensometer crosshead speeds used are listed in Table 1. For convenience a range of cross-head speeds was utilized in the sample preparation. Subsidiary experiments showed that this did not significantly affect the degree of molecular orientation achieved. The sample thicknesses were measured with a precision dial indicator and were checked by near i.r. interference fringe measurements. These results are also shown in Table 1, together with density measurements obtained using a density column prepared from an aqueous solution of sodium bromide and water. Refractive index measurements The measurements of refractive index were undertaken using an image splitting interference microscope (Zeiss Zena Interphako) with accurately calibrated immersion liquids. All measurements were made at 551 nm. The results are shown in Table 2.

I.r. study of molecular orientation and conformational changes in PET: A. Cunningham et al. Table I

Details of sample preparation

Shape

Average thickness after drawing (/zm)

Density

Crosshead

Gauge

Temp. (°C)

Draw ratio

speed (cm/min)

length (cm)

Series (i) 60 65 70 75 80 87 94 100

4:1 4:1 4:1 4:1 4:1 4:1 4:1 4:1

5 5 5 5 5 5 5 5

8 8 8 8 8 4 4 4

3 3 3 3 3 3 3 3

Strip Strip Strip Strip Strip Strip Strip Strip

11.5 12 14 14 16 16 11 12

1.362 1 '362 1 '362 1.358 1.358 1.355 1 '356 1 '356

Series (ii) 80

1.5:1

Unknown (dead-loaded) Unknown

10

3

Taper

25

1-339

10

2-5

Taper

20

1.340

10

2

Taper

14

1.343

10

1-5

Taper

16

1-354

10

1

Taper

16.5

1-356

4 4

1 1

Dumbbell Dumbbell

12-5 12.5 30

1.365 1.365 1.337

80

2.3:1

Width (cm)

(dead-loaded) 80

2.7:1

80

3.4:1

Unknown (dead-loaded) Unknown

(dead-loaded) 80

3.7:1

Unknown

(dead-loaded) 80 80 Isotropic 2C

4.5:1 5:2 1:1

20 20 .

.

.

Infra-red measurements

;a 975crn-~

The i.r. measurements were carried out using a Hilger H800 double beam i.r. spectrometer, with a wire grid polarizer Cambridge Consultants Limited type 1CR 55. The measurements were made at normal incidence and the film sample was sandwiched between potassium bromide plates with a very thin film of Nujol between each surface. This reduces the reflection at the polymer surface, which for an isolated polymer film gives rise to interference fringes. The Nujol forms an approximate match for the refractive index of the polymer and has a low absorption in the region 750-1300cm -1. The wire grid polarizer was assumed to transmit radiation with the electric vector in one plane only, and the chart recorder was calibrated as a linear vertical scale so that the ratio IT/I~ could be determined directly from the curves, using a pseudo-base line as shown in

875cm~

4C o

795cm"1

~

/~

896 Cm-'

{

I

Ln

~- 6C

80

b

875cm

Figure 1.

-~

2C

~ 4C o

E c

/

795 cm-i

6C

.

•k'X• 6cm''

i

For each sample, two spectra were recorded in the normal incidence case, one with the electric vector parallel to the z direction and the other at right angles in the x direction. For each polarization the spectrometer was scanned through the range 750-1100cm -1 at a speed of 42-5 cm-1/min and the slit width was gradually reduced from 0.9 m m at 750 cm -1 to 0-5 m m at 1100 cm -1. Typical examples of such spectra, obtained from a sample of intermediate draw ratio, are shown in Figures la and lb.

Absorption band assignments 80

pseudo base lin~"~ ~ -~. ~

.1 . /

Figure 1 The infra-red spectrum of PET in the region 700-1000 cm -z. Electric vector parallel to (a) z direction or (b) x direction

The detailed assignment of the absorption bands in the i.r. spectrum of PET has been the subject of much attention and controversy. Some of this stems from the proposal originally made by one of us 7-9, that the major differences between the i.r. spectra of amorphous and partly crystalline samples of PET are due to rotational

POLYMER, 1974, Vol 15, November

1'51

I.r. study of molecular orientation and conformational changes in PET: A. Cunningham et al. isomerism of the 0

CH2

/\/

\/

CHz

O

group. Crystallographic studies lz, showed that the conformation of this group in the crystalline regions is trans. It was proposed that in the amorphous regions the gauche conformation of this group is present as well as the trans conformation. Although this proposal was initially not generally accepted TM 15, in most later paperslZ, 16-18 there is a general consensus that certain absorption bands can be identified with the trans and gauche conformations. In this paper we have chosen the 975 cm -1 trans band and the 896 cm -1 gauche band for quantitative analysis. It is also valuable to analyse the behaviour of absorption bands associated with the terephthalate group, and more particularly the benzene ring. Here we have chosen the 795 cm -1 and 875 cm -1 bands. The 875 cm -1 band has the added advantage that it can be assigned with some certainty to an out-of-plane C - H deformation vibration, in which the transition moment vector lies normal to the plane of the benzene ring. From the crystallographic data lz, 0m the angle which the transition moment vector makes with the chain axis would then be about 86 °.

RESULTS AND DISCUSSION The optical measurements of the refractive indices nz and nx were used to calculate the refractive index of the isotropic polymer ni8o, on the basis of averaging the polarizabilities and assuming that the samples were transversely isotropic. As before, the Lorentz-Lorenz equation is used to relate polarizabilities and refractive index. We have:

where/~ and p0 are the densities of the isotropic polymer and the oriented film respectively. Table 2 shows that the predicted values of nl8o correspond very closely to the experimental value of 1.582, confirming that these samples are transversely isotropic to a very good approximation. The optical data have also been used to calculate the overall molecular orientation function (P2(O)ovt) on the basis of equations (4) and (5) above, and the results are shown in Table 2. The i.r. measurements on the bands at 875, 795 and 896cm -1 were first used to calculate the absorbances Az and Ax, corrected for reflection at the interfaces using equation (1). These absorbances were then used to calculate the quantities Cz and ~x, on the basis of equations (4). Finally values of the i.r. orientation function product P2(Om)(P2(O))ir were calculated using equation (3). It is also possible to calculate the orientation functions ignoring the local field correction, by assuming that (c¢*)ocn'2-1, i.e. (~")ocnk. Values of P2(Om)(P2(O))ir so calculated for the 875cm -1 band are shown in

Figure 4. Compar&on of the i.r. and optical orientation functions The 875 and 795cm -1 bands are both associated with vibrations of the benzene ring. They are therefore not directly affected by conformational changes in the same way as the 975 and 896 cm -1 bands, and might be expected to give an indication of the overall chain orientation. The optical orientation functions are derived on the premise that they relate to the orientation of an extended repeat unit. Figures 2 and 3 show values

,%

n~so - 1 1 p, t n ~ - 1 , 2 ( n ~ - l)] n ~ s o - 2 - 3 p0 ~ n z ~ - v ~ ] 0"20

Table 2

Refractive index measurements

Temp. (°C)

Draw ratio

nz

nx

ni (predicted) (Ps(O))opt

,_ .0"15

Series (i) 60 65 70 75 80 87 94 100

4:1 4:1 4:1 4:1 4:1 4:1 4:1 4:1

1-713t 1.709 1-703 1-695 1.679 1.660 1.620 1-587

1.540 1,540 1-542 1.540 1-549 1-555 1.570 1.576

1-582 1.590 1.580 1.579 1.580 1.580 1.576 1.570

0.729 0.715 0.682 0-663 0.557 0-453 0.219" 0-049*

1-5:1 2.3:1 2.7:1 3.4 ."1 3.7:1 4.5:1 5:1 ~

1- 592 1" 621 1" 623 1.658 1" 684 1" 704 1.705 1.582

1" 576 1.563 1.563 1.553 1" 547 1" 540 1" 540 1 "582

1.580 1- 580 1- 580 1- 578 1.581 1" 578 0-578 1 "582

0.071 0- 256 0" 264 0.455 0.586 0.696 0" 700 0

-$ V


Series (ii) 80 80 80 80 80 80 80

Isotropic

* These samples were not used in the subsequent i.r. analysis because of the poor predicted value of ni "l'These values were obtained by extrapolation of the higher temperature nz data

752 POLYMER, 1974, Vol 15, November

0"05

0

I

d.2

I

I

0-4

I

d.6

I

o'.e

gP2 (el> opt Figure 2 Values of P=(Sm)(P=(8))ir for the 875cm -1 band as a function of (P2(e))opt. O, Series (i); I I , series (ii)

I.r. study of molecular orientation and conformational changes in PET: A. Cunningham et al. degree of anisotropy in absorbance. In the case of the 875 cm - t band, if it is assumed that the optical measurements provide an absolute calibration, the value of Om is found to be 85 ° . This agrees well with the value expected on the basis of the band assignment*. Hence we can make the following identity, (P2(O))~[ 5=

-

0

-

4

0

d

2

~

(P2(0))opt.

~- -0-3

,a.,,, V

"~-0-2 a.,,,

•

v

-o.i

0

I

I

0.2

I

I

I

I

04 0.6 opt

Figure 3 Values of P~(Srn)(P~(O)>ir for function of (P2(8)>opt. O, Series (i); II,

I

I

I

0.8

1.0

the 795em-1 band as a series (ii)

These results were obtained using the Lorentz-Lorenz internal field correction. Figure 4 shows a comparison of the optical orientation functions with those deduced from the i.r. data for the 875cm -1 band ignoring the local field correction. The solid line shows the expected correlation for Ore= 85 °. The experimental correlation is now less good, and it appears that the value of (P2(0)} is an underestimate. These results give some support for the validity of our treatment. The orientation behaviour of the 975 and 896cm -1 bands associated with the trans and gauche conformations respectively, is much more complicated than for the 875 and 795cm -1 bands. Figure 5 shows values of P2(Om)(P2(O))ir for the 975 cm -1 trans band as a function of (P2(0))opt. In this case there is not a linear relationship, but the trans orientation function increases rapidly for low optical orientation function values to achieve an almost constant value for (P2(0))ovt>0"5. This result shows that the orientation of the trans conformation is not representative of the overall chain axis orientation. Figure 6 shows the corresponding results for the 896 cm -1 * In view of the possible errors in A~13~0 such close agreement may well be fortuitous.

/

_o.,

/

[

/o,

I

~

0

0'2

0'4

0"6

0,8

f:onrrC:ic~7oOf<(~:(~,e>l?3:;(~;SUlllBt::blea,:~i~ ignoring the

o/

o.o

0'3

I-0

internal field

of P2(Om)(P2(O)>ir plotted as a function of (P2(0)>opt for the 875 and 795cm -1 bands respectively, for the two series of oriented samples. There is an excellent linear relationship between these two parameters for both bands, confirming that both are measuring similar quantities. The greater consistency of the results for

the 875cm -z band can be attributed to its greater B

....

O l~

O

, 0.2

~

, 0.4

,

~ 0-6

,

, O18

I-©

oPt Figure 5 Values of P~(Om)(P~(O))irfor the 975cm-1 trans band as a function

of(P2(O)>opt.(3, Series(i); II, series (ii)

POLYMER, 1974, Vol 15, November "/53

I.r. study of molecular orientation and conformational changes in PET: A. Cunningham et al.

(P2(0)>opt= 1)

-0"2 .L q. (3)

"f

C

,

(Y

+O'1 L

0

0.2

0"4

0-6

0"8

1.0

for both the trans and gauche bands. If we combine these extrapolations (shown in Figure 7) with the assumption that there is 100 ~ trans concentration at full overall orientation, we have a very simple picture. The extrapolation of the 975cm -1 band then gives us the value of the polarizability for 100~o trans concentration; hence we can find the trans concentration for an isotropic sample and thus the corresponding gauche concentration. We are then able to calculate the trans and gauche concentrations for each sample, which, of course, should total 100~. In fact, we chose the value of 40 for 100K trans concentration, which gave the best overall fit to the data so that the sum of the trans and gauche concentration totalled as close to 100~o as a least squares fit would provide. Table 3 lists these intermediate concentration values and it can be seen that there is very good internal consistency. A remarkable result, which is not to be expected, is that absolute values obtained for the polarizabilities of the trans and gauche species by this fitting procedure are identical. It can readily be appreciated that this is so

opt

//

Figure 6 Values of P2(Sm)irfor the 896cm -z gauche band

0'1~:

as a function of (P2(0)>opt. O, Series (i); I I , series (ii)

gauche conformation band. In this case a completely different pattern is observed. The gauche orientation function is small and positive for (P2(0))opt<0-45 and then becomes negative, the numerical value increasing rapidly in the highly oriented samples. These results, taken together, suggest the following. First, that the molecular segments which contain the trans conformation possess at low overall orientation much higher orientation than those segments which contain the gauche conformation. Secondly, that up to (P2(O))opt~0.45 the gauche orientation distribution is very close to isotropic. There is even an indication that the gauche segments for low orientation may be oriented transversely to the draw direction. However, it is difficult to study the 896cm -1 band quantitatively in terms of orientation because it overlaps with the strong 875 cm -1 band. The i.r. data must therefore be regarded as inconclusive in this particular detail. Finally, it is clear that at high degrees of overall molecular orientation there is appreciable alignment of the gauche segments. The concentration of the absorbing groups The concentration of the absorbing groups can be estimated from a calculated value of 40. It was found that the calculated values of 40 for the 875 and 795cm -1 bands are approximately constant for all degrees of molecular orientation. This result is an expected one, since these bands have been assigned to vibrational modes which are independent of the conformational state of the molecule. On the other hand, the values of 40 for the 975 cm -1 trans band and 896cm -1 gauche band show a strong dependence on the degree of overall molecular orientation. This can be seen in Figure 7 where 40 is shown as a function of (P2(8))opt, and we observe a smooth increase in trans content and a smooth decrease in gauche content with increasing overall molecular orientation. We have attempted to make the extrapolations of 4o t o full overall molecular orientation (i.e.

754 POLYMER, 1974, Vol 15, November

/ /

I00

/

E o,2

/

c

0

I

0.2

g

r 0

'zY'" t s °

!

0

=

%0

$y" S I S

0.03

o

!so

2"

0.06

75

2s

I

I

0.4

I

I

I

0-6

I

I

08-

U

0

J.o

opt

Figure 7 Values of ~o and concentration for the trans conformation (975cm -1 band) and the gauche conformation (896cm -1 band) as a function of opt. - - - - , trans; , gauche. O, Series (i); I--1, series (ii) Tab/e 3 trans and gauche concentrations

(P~(O)~>opt 0"0 O"1 O"2 O"3 0"4 O"5 0.6 0-7 0"8

0.9 1.0

% trans % gauche (xi) (yi)

(xi"l-yi)

24 28 3£ 38 44 50 58 68

76 72 67 61 56 49 42 34

100 100 99 99 100 99 100 102

77

24

101

88 100

13 0

101 100

I.r. study of molecular orientation and conformational changes in PET: A. Cunningham et al. by noting that the q~0 curves for the trans and gauche species (Figure 7) cross at a point corresponding to 50 ~ trans. It should perhaps be pointed out that although the absolute values of the polarizabilities of the trans and gauche species are identical for the present series of samples this may not hold for other samples where high degrees of crystallinity are obtained. In the samples examined here the crystallinities were always very low, and usually less than 10~o.

Relationship between molecular orientation and changes in molecular conformation It has already been remarked that the gauche orientation is very low over most of the orientation range. This implies that the overall molecular orientation arises largely from those molecular chains possessing the trans conformation. Moreover, at high overall molecular orientation there is little further increase in the trans orientation. The values of the orientation function for the 975 cm -1 trans band, lr trans × P2(0~an') can be extrapolated to give a constant value for high overall molecular orientation. If it is assumed that this value corresponds to complete orientation of the trans conformers, this gives a value for 0- -t'a"" of 32 °. m With this result we can then calculate absolute values of irtrans for intermediate degrees of overall molecular orientation. These results are shown in Table 4. Furthermore, recalling that the orientation of the gauche conformers is very small, it can be suggested that to a good first approximation the optical orientation function (Pz(O)>opt which reflects the overall orientation is given by: opt =

f transir trans

where titans is the trans mass fraction. The results shown in Table 4 confirm that this is a reasonable approximation. A more remarkable feature of all the results, however, is the exact similarity of the data for the two series of samples, and this suggests that there is a unique relationship between the concentration of trans and gauche conformers and the overall orientation as revealed by optical measurements or by the orientation of the 875 or 795cm-Z bands. A possible explanation of this remarkable result is that both the conformational content and the molecular orientation relate only to the overall strain, irrespective of the temperature and conditions of draw. This explanation would certainly hold for a given temperature if the drawing process can be regarded as the extension Table 4 Comparison of opt with ftransir trans (P2(O)>opt 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

lrtrans ftransir trans 0"0 0.2 0.4 0.6 0.8 0.9 0.9(5) 1 "0 1-0 1 "0 1.0

0.0 0"06 0.13 0"23 0-35 0"45 0"55 0-68 0.77 0.88 1.00

I'0

K O A

~05 V

Draw r a t i o ~ 4 0

0

I

/

I0

20

k2_ /

.....

30

Figure 8 Plot of

opt against [A2-(1/A)] for series (ii) (samples drawn to a series of draw ratios at 80°C)

~

0'4

8 o-3 0"2 b O'l c

'

0

l

I

2

I

3

I

4

I

I

5

I

i

i

6

7

Figure 9 The change in trans conformation for series (ii) as a function of [1/3{,V+(2/A)}-t]

of a rubberlike network, and we will discuss two pieces of evidence which support this view. First, there is the development of orientation in a rubberlike network. If it is assumed that the network can be considered as a network of freely jointed chains of identical links 19 (the so-called random links), it can be shown z0 that the orientation function randora link for the random links is given by: < P 2 ( 0 ) > r a n d o m link = ~

A --

+ terms in N-z, etc.

where N is the number of random links between the network junction points (the entanglements) and h is the extension or draw ratio. Stress-optical data on PET in the temperature range 60--90°C showed 2a that the behaviour fitted this model to a good approximation, and a value of about 6 was obtained for N. A plot of the present 80°C results for , based on the values obtained for the overall molecular orientation, is shown in Figure 8. It can be seen that there is a good linear relationship between and [Az-(1/A)] up to a draw ratio A of 3.5, and this gives a value for N of about 5, in reasonable agreement with the previous stress-optical results. A second piece of evidence comes from a consideration of the conformational content as a function of draw ratio. According to Abe and Flory z2, the average

POLYMER, 1974, Vol 15, N o v e m b e r

755

I.r. study of molecular

orientation

and conformational

changes

in PET:

A. Cunningham

et al.

molecular orientation by polarized Raman spectroscopy and polarized fluorescence are also presented. CONCLUSIONS (1) Polarized infra-red spectroscopy can provide accurate measures of overall molecular orientation in PET. There is confirmation that corrections for reflectivity and the internal field effect are required. (2) The combination of measurements of molecular orientation with concentration of conformers can throw light on the deformation mechanisms occurring during drawing.

0.6w a 0 h 0 5

-

0.3-

ACKNOWLEDGEMENTS

I

2

I

I

I

3 Draw

I

4 ratio,

I

t

I

5

A

of draw ratio, showing fit to rubberlike (number of random links, N=4*8) network (-) at low draw ratios and turn over to pseudo-affine deformation

Figure

70

(Pz(B))ept

scheme (- ---)

as a function

at high draw ratios

change in the content of a particular conformer, Amtrans, say, relates to the extensional strain h, by an equation of the form:

where v is the total number of chains in the network and DZ is a constant of proportionality which can in theory be calculated provided that the internal energies of the different conformational states is defined. In Figure 9 the change in the concentration of the tram conformer is plotted as a function of [l/3 x (h2+ (2/h)} - l] for series (ii). Again a reasonable straight line relationship is obtained up to a draw ratio of about 35. These results suggest, therefore, that it is not unreasonable to obtain a good correlation between molecular orientation and conformer content in the low draw ratio range where the extension of the polymer is akin to that of a rubberlike network. It is perhaps more remarkable that the correlation holds to high draw ratios where the behaviour fits the pseudo-affine deformation scheme23 more closely, as shown by the broken line in Figure IO. This aspect will be discussed in detail in a future paper, where measurements of

756

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During the period of this research A. C. held a Science Research Council CAPS studentship. We are indebted to Imperial Chemical Industries, Plastics Division as the industrial sponsor. We also wish to thank Mr P. I. Vincent for useful discussions and for assistance with sample preparation, and to Dr G. R. Davies for his advice on some of the theoretical aspects. REFERENCES 1 Read, B. E. and Stein, R. S. Macromolecules 1968, 1, 116 2 Phillips, P. J., Wilkes, G. L., Delf, B. W. and Stein, R. S. J. Polym. Sci. (A-2) 1971, 9, 499 3 Read; B. E. and Hughes, D. A. Polymer 1972,13,495 4 Cunningham A.. Davies. G. R. and Ward. I. M. Polvmer 1974,15, 143 . ’ 5 Heffelfinger, C. J. and Burton, R. C. J. Polym. Sci. 1960, 47, 289 6 Kashiwagi, M., Cunningham, A., Manuel, A. J. and Ward, I. M. Polymer 1973,14,111 7 Ward, I.-M. Chem. I&i. 1956, p 905 8 Ward, I. M. Chem. Ind. 1957, p 1102 9 Grime, D. and Ward, I. M. Trans. Faraday Sot. 1958, 54, 959 10 Miller, R. G. J. and Willis, H. A. J. Polym. Sci. 1956, 19,485 11 Farrow. G. and Ward. I. M. Polvmer 1960.1.330 12 Schmidt, P. G. J. PO&m. Sci. (2) 1963, l,‘li71 13 Daubeny, R. de P., Bunn, C. W. and Brown, C. J. Proc. R. Sot. (A) 1954,226,531 14 Liang, C. Y. and Krimm, S. J. Mol. Spectros. 1959, 3, 554 15 Boye, C. A. .7. Polym. Sci. 1961,55,261 16 K&m, S. Adv. Pblym. Sci. 1960, 2, 51 17 Daniel. W. W. and Kitson. R. E. J. Polvm. Sci. 1958.I 33.I 161 18 Miyakk, A. J. Polym. Sci. ,1959, 38, 419 19 Kuhn, W. and Griin, W. Kolloid-2. 1942, 101, 248 20 Roe, R. J. and Krigbaum, W. R. J. Appl. Phys. 1964,35,2215 21 Pinnock P. R. and Ward. I. M. Trans. Furuduv Sot. 1966. 62, 1308 22 Abe, Y. and Flory, P. J. J. Chem. Phys. 1970,52,2814 23 Ward, I. M. ‘Mechanical Properties of Solid Polymers’, Wiley, London, 1971, p 258