The microstructure of poly(vinyl chloride) as revealed by x-ray and light scattering

The Microstructure of Poly(viny1 Chloride) as Revealed by X-Ray and Light Scattering

W. WENIG, Chemische Werke Hiils AG, Zentralbereich Forschung und Entwicklung, 4370 Marl, West Germany

Synopsis

Small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS) as well as small- angle light-scattering (SALS) techniques have been applied to investigate the microstructure of a number of commercial poly(viny1 chloride) (PVC) samples. From the wide-angle x-ray scattering, crystallinity and crystal size parameters have been determined. The crystallinity of the samples investigated range from 5% to 10%. Superstructure parameters such as crystallite thickness, distribution functions of crystallite and amorphous thicknesses, and size of ordered regions have been obtained by an analysis of the SAXS curves using the cluster model. The crystallinity agrees well with the WAXS crystallinities indicating that most of the crystals are lamellar shaped, though some rodlike entities are present in the sample as is shown by the small-angle light scattering. From the SAXS analysis, the microstructure is described as clusters of lamella stacks which are identical with the subprimary particles. Their size is determined to be 220-240 A. Emulsion type PVC also contains lamellar-shaped crystals. The superstructure, however, of this type of PVC is different from that of mass or suspension-polymerized material. The SAXS curve does not reveal any correlation between the crystals.

INTRODUCTION

The morphology and physical properties of poly(viny1 chloride) (PVC) is of increasing interest. Natfa and Corradinil were among the first to investigate PVC; they found the crystal structure of oriented fibers to be orthorhombic with unit-cell dimensions a = 10.4 A, b = 5.3 A, and c = 5.1 A. Wilkes, Folt, and Krimm2 confirmed the existence of an orthorhombic lattice but determined the unit-cell constants to be a = 10.24 A, b = 5.24 A, and c = 5.08 A.

The crystallinity of PVC has been investigated by a number of It has been found that the polymerization temperature is the principal parameter that determines the structure of PVC since the syndiotacticity increases when the polymerization temperature is lowered. Nakajima, Hamada, and Hayashi3 studied the influence of branching on the morphology by infrared measurements on several commercial samples and others polymerized in the presence of benzoyl peroxide. They found that with decreasing polymerization temperature the degree of branching decreases from 0.27 for a sample polymerized at 90°C to zero for one polymerized at -75°C. Concurrently the density, crystallinity, glass- transition temperature, and melting point increase. PVC polymerized at about 5OoC, the temperature a t which much commercial PVC is produced, generally contains only a small fraction of crystallized material. Rehage and Halboth4 estimated the degree of crystallinity of an “atactic” sample from wide-angle x-ray measurements to be 5%. Ohta, Kajiyama, and Takayanagi5 determined the crystallinity from DSC thermograms by calculating the heat of fusion. They found a maximum value of 5% for a sample annealed at 130°C for 3 hr. Naka-

Journal of Polymer Science: Polymer Physics Edition, Vol. 16, 1635-1649 (1978) 0 1978 John Wiley & Sons, Inc. 0098- 1273/78/0016- 1635$01 .OO

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jima, Hamada, and Hayashi3 calculated the degree of crystallinity from density measurements. They found a value of 5%-7% for samples polymerized above 5OOC.

More recently, Gouinlock6 interpreted x-ray measurements on low-molecular-weight (M, = 2300) PVC prepared using chain-transfer agents. The polymerization was carried out a t 52°C with azobisisobutyronitrile as initiator. An “aldehyde” polymer was prepared to a conversion of 3.5% using 0.88 mole n- butyraldehyde per mole of vinyl chloride. The polymer was recovered by addition of the reaction mixture to an excess of methanol. The crystallinity of this sample was determined to be 30%. A similar investigation of a fraction of the whole polymer obtained by the addition of methanol to a 5% polymer solution in tetrahydrofuran yielded a value of 44%. This is due to the higher syndiotacticity of the fraction and indicates that fractionation effects a separation with respect to syndiotactic content. Baker, Maddams, and Preedy7 report x-ray diffraction and infrared absorption results on highly syndiotactic samples made by the urea clathrate method. They confirm the annealing experiments reported earlier by several authors,5.8~~ i.e., an increase of crystallinity with annealing temperature starting from an original value of 63%.

WhitenhaferlO discusses the melting and recrystallization of a solvent-cast film of commercial PVC by interpreting infrared spectra. From the measurements, the presence of crystallites of widely different degrees of perfection is inferred.

The existence of crystals in rigid PVC thus being well established, Straff and Uhlmannll conclude, from small-angle x-ray measurements, that there is an absolute absence of any volume fractions of crystallinity. These authors find a continuous decreasing scattering curve which is described by scattering from heterogeneities of various sizes and concentrations and by scattering of thermal density fluctuations altogether not exceeding a concentration of 0.5%.

In this paper, we discuss the microstructure of several commercial PVC samples as revealed by wide-angle and small-angle x-ray diffraction and by small-angle light scattering. The samples chosen are comparable in molecular weight, polymerization temperature, and density. Bulk-, suspension-, and emulsion-polymerized samples have been investigated. An interpretation of the crystallinity and its implications for supermolecular structure, such as crystallite size and order of crystals in the bulk material, is given.

EXPERIMENTAL

X-Ray Diffraction Measurements

Wide-angle x-ray measurements were performed using a Philips PW 1050l25 powder diffractometer. The incident Cu K , radiation was monochromatized by a Ni filter. The scattering curves were recorded using an electronic step-scan device (PW 1394/PW 1395) to guarantee a minimum counting rate of 5000 counts per point. The step size was 0.05” (20) for a normal run and 0.25’ (20) for a rapid scan. Each sample was measured twice in order to obtain a smoother curve. The air scattering was measured by the method of Gouinlock.6

MICROSTRUCTURE OF PVC 1637

Small-angle x-ray scattering curves have been measured by using a Kratky slit collimation camera. The geometry of the camera was such that a resolution of several thousand angstroms was provided (entrance slit width 60 pm). The Philips generator PW 1010 was equipped with a 2.7 kW Kratky tube. The cooling water for the x-ray tube was controlled to provide a constant primary beam intensity. Cu K , radiation was used and monochromatization was achieved with a Ni filter in conjunction with electronic pulse-height analysis of the output from a proportional counter. Both scattering curve and background intensity were recorded twice for each sample in order to minimize the experimental error. The curves corrected for background scattering were desmeared using the methods of Glatterl2 and of Guinier and Fournet.13J4 Both methods gave essentially the same results.

Light-Scattering Measurements

Light-scattering patterns were obtained from the crystalline samples using an apparatus designed by Stein.15 A 4 mW He-Ne laser source was used in conjunction with a polarizer to ensure complete linear polarization. After the polarized light beam passed through the sample, a second polarizer with polarization axis either perpendicular to that of the first polarizer (H , pattern) or parallel to that of the first polarizer (V, pattern) was used. Samples ca. 150 pm thick were pressed between glass plates in the presenck of an immersion liquid (silicone oil) having approximately the same refractive index as the sample.

Sample Preparation

A quantity of fine PVC powder was placed between the plates of a hydraulic press and pressed to a thin film (thickness d ca. 150 pm) under a pressure of 24.5 MPa and a temperature of 160°C for 2 min. The samples were cooled at ca. 30” C/min. Amorphous samples were prepared by heating the specimens above their melting points. The preparation was done in an electric furnace at 900°C (by “shock heating”), similar to the method described by Smith.lG It was not possible, however, to carry out the treatment originally proposed by Smith because the surfaces of the samples thus prepared were not as smooth as required for the WAXS measurements. The films, therefore, were covered with aluminum foil as holders and placed in the furnace followed by chilling in ice water. An amorphous sample was achieved after treatment for 15 sec in the furnace. Figure 1 shows that the x-ray crystallinity drops with increasing time of heat treatment. The absence of crystallinity is concluded from the disappearance of the diffraction peaks, especially the (110) peak, the angular position of which does not coincide with the first maximum of the halo. These results are confirmed by the change of density as a function of heat treatment (Fig. 2). The density decreases continuously with increasing time of heat treatment up to 15 sec. All amorphous samples were, therefore, prepared by heating for 15 sec in the furnace. Analytical data for the samples investigated are listed in Table I.

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\ L l t= \

\

I 15: I I I I I I

510 . z - 4 \

i? 5 -

s - 'e

- a'. .' . 2 a\

\ \

0- b - e - I L I I I I I I I I

3 s 21m- k

Ql,389-

L

2 lu

135

- Ivy' I I I '

I ' i \

*' 'h

\ * - * \

't \*

- I I I I 1 1 I 1 I I

Fig. 2. Density versus time of heat treatment in an electric furnace at 900°C (sample A). The density was measured in a gradient column at 25°C.

RESULTS

Wide-Angle X-Ray Diffraction The measurements were run over the angular range 5'45" (28) to allow for the

construction of the base line. The results of two runs were averaged and a smooth curve was drawn. The results are shown in Figure 3, where the diffraction patterns, corrected for air scattering and the amorphous scattering (halo), are displayed. To obtain an amorphous sample, we had to apply high temperatures (7' = 900OC) as already noted. Since all samples decomposed when exposed to temperatures higher than 190°C for longer than a few minutes it proved necessary to heat rapidly to get above the maximum melting point of the crystals before decomposition occurred. This agrees with the experiments of Smith16 but is in contrast to the procedure described by Ohta et al.,5 who molded a sample


TABLE I Polymer Characterization Data

Polym. temp. M w I M n [vI pe

Sample (OC) aw a an b aw c M,, c - 1 c (dlg-1) ( g ~ m - ~ )

A Mass 54 84,000 51,000 83,000 49,000 0.7 0.95 1.4038 B Suspension 57 84,000 50,500 83,000 49,000 0.7 0.98 1.3953 C Emulsion 50 76,500 39,000 75,000 37,500 1.0 0.90 1.3944

a From light scattering, sample dissolved in 50% tetramethylurea and 50% acetone at 25OC. b Osmometric value, sample dissolved in chlorobenzene at 9O"C, measured at 43OC.

Determined by GPC. Dissolved in cyclohexanone at 90°C for 1 hr, measured at 25OC. From density gradient measurements a t 23°C.

1 1 1 1 I I 1 I 1 1 I I

10 20 30 40 50 SCATTERING ANGLE 2 8 1 O -

Fig. 3. Wide-angle x-ray scattering (WAXS) curves of the samples investigated. The curves have been shifted for clarity.

(Ryuron 700 D) at 18OOC for 10 min in a laboratory press and then quenched it in water. This sample was mixed with butyl tin maleate as a stabilizer; however, addition of stabilizer may lead to different results, as shown in Figure 4. We added a dioctyl tin glycolate stabilizer at 5% concentration to our bulk-polymerized sample (sample A ) . This specimen was heated in the 900°C furnace for 15,20, and 25 sec and quenched in ice water. The three samples show identical scattering curves of the type in Figure 4, which differ from the scattering curves of the unstabilized sample. Thus, it is evident that the stabilizer used here does influence the statistics of the interchain distances in the amorphous phase.

The crystallinity is obtained from the ratio of the integral intensity of the crystalline peaks to the total intensity of both amorphous and crystalline scattering (Fig. 5) after correction by the factor17

(1) which accounts for polarization, and Lorentz and geometrical factors.

g = sin28 cos8/(1 + ~ 0 ~ 2 2 8 )

The weight fraction crystallinity is then given by W, = Iosmax Z,(s)g(s)s2 ds/ ~ o s m a x I(s)g(s)s2 ds (2)

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t I I 1 1 I I I I I 1 I

10 20 30 LO 50 SCATTERING ANGLE 281° ----b

Fig. 4. WAXS amorphous scattering of a platicized (dotted line) and unplasticized (solid line) sample. The curve for the unplasticized sample was used as the halo for obtaining the crystallinities of the crystalline samples.

Here Z, (s) is the crystalline scattering intensity at s = 2 sinfl/X, where 8 is half the scattering angle and X is the wavelength of the x-ray beam; Z(s) is the total scattering intensity at s.

The value of the crystallinity depends on the manner in which the halo is fitted to the scattering of the semicrystalline sample. Since the total integrated intensity of the volume fraction of noncrystalline material in the semicrystalline sample is lower than the total integrated intensity of the 100% amorphous sample, the scattering of the amorphous sample has to be reduced by a factor to fit its WAXS curve to that of the semicrystalline sample. This has been done through a computer program. The result is shown in Figure 5(a). The computer program used did not allow for any overlapping of the halo with the curve of the sample. Many authors, however, fit the halo to the minimum in the semicrystalline curve a t a 28 of about 21°, thus arriving at considerably lower crystallinity than is obtained by the method described above [see Fig. 5(b)]. Although some overlapping occurs, crystallinities obtained by applying the latter method seem to be more reasonable, the more so because these values are in good agreement with crystallinities obtained from density data (Table I). The x-ray crystallinities are listed in Table 11.

Approximate values of crystallite size have been determined from the line profiles of the crystalline peaks by use of the Scherrer equationl8

(3) where Dhkl is the mean dimension of the crystal in the (hkl) direction (perpendicular to the hkl plane); (P - 00) is the integral breadth of the (hkl) reflection corrected for experimental broadening by using a silicone standard; and K is a constant which is commonly set equal to unity. The Scherrer equation does not allow for additional peak broadening caused by lattice distortions and strain and is thus a rather rough measure. The more accurate methods derived by Hose- mannlg and by Wilke and Martis20 cannot be employed here since only a few ill-defined peaks are resolvable. The values obtained by using eq. (3) are, therefore, somewhat too low, permitting only a qualitative discussion.

Dhkl = KX/(P - Po) C O S ~

MICROSTRUCTURE OF PVC

I 1 I I 1 I L

10 20 30 LO 50 SCATTERING ANGLE 2 8 1 O

1641

I ,

d

I I 1 . I b l 10 20 30 10 50

SCATTERING ANGLE 2810 __c

Fig. 5. WAXS curve of sample A demonstrating the construction of the halo into the scattering curve: computer fit of the halo to the curve of the semicrystalline sample (a) avoiding “overlapping” of the two curves. Fit of the halo to the curve of the sample a t 20 = 21” (b).

TABLE I1 Wide-Angle X-Ray Results

Crystallite sizes Crystallinity @)

Sample WC ~(200 .010) D(ll0) D(210,111,201)

A 0.10 39 64 34 B 0.08 42 55 27 c 0.05 43 48 23

Small-Angle X-Ray Scattering Small-angle x-ray intensities are displayed in Figure 6. Inspection reveals

diffraction maxima for all but the emulsion-polymerized sample. The presence of a diffraction peak clearly shows that the scattering elements are partly ordered with an average distance which is connected to the long period derived from the angular position of that peak. The long periods are listed in Table 111. They

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1 I I

B C I ! I ! I ! I ! I \ \ i . I !

s I IO*A*- Fig. 6. Small-angle x-ray scattering curves (desmeared intensity) of the samples investigated.

are not, however, identical with the mean spacing of the superlattice built up by the arrangement of the crystals since these values are derived from a simple application of Bragg’s law.21 The long period agrees better with the real distance of the “lattice planes” if the crystals are situated regularly in an ordered domain. Briimer22 has shown that this cannot be realized with most partially crystalline polymers. It is thus clear that the superlattice repeat unit, as well as other su- perstructural parameters, have to be derived from a quantitative analysis of the SAXS curve^.^^,^^

On the basis of the appearance of a diffraction maximum in the SAXS curve, we assume the crystals to be arranged in small numbers in an ordered fashion. We call these regions of coherent scattering crystals “domains.” A domain is thus made up of N crystals; the domain size, depending on the shape of the crystals, is given by the thicknesses of crystals and amorphous regions between the crystals. Assuming a two-phase system, the one-dimensional electron density distribution p(2) in a domain is given by2* (Fig. 7)

(4) N

n=l ~ ( 2 ) = C ~ n f i ( Z - g n ) + pu - Apub(Z)

n = 2 , . . . , N + 1 n = l


I

I I I I

I- I I I I

I I

I lo I I _ _ - I I iz 91 g2 93 gN 'N.1

Fig. 7. One-dimensional electron density distribution within a crystal domain.

where pc, pa, and pu are, respectively, the electron densities within a crystal and of amorphous material, and the mean electron density of the domain environ- ment. The scattering amplitude is derived as

F ( s ) = J p ( Z ) exp(-2aisZ) dZ N

n=l = c f n exp(-2aisgn) + pU6(s - 0) - Ap,B(s) (9)

where

and 1

2TU B ( S ) = Jb(Z) exp(-z~isZ) dZ = - [ I - exp(-2?risgN+J (11)

From (91, using (10) and (ll), we derive the expression for the scattered inten- sity24

where f r and f , , are the Fourier transforms of the normalized thickness distribution functions, H ( x ) and H ( y ) , of the crystals and amorphous interfacial regions, respectively,

m

f x = H ( x ) exp(-2~isx) d x ; f y = J a H ( y ) exp(-2~isx) dx 0

f z = f r f y (13 )

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The linear crystallinity & is connected with the mean thickness X of the crystals and the mean thickness 7 of the amorphous regions by

7 = - & ) 1 4 c (14) The fluctuation parameters used for the calculation of the intensity curves are

(15) where A2T, A2Y denote, respectively, the mean-square fluctuations of crystal and amorphous thicknesses. The repeat unit of crystals in the superlattice is

d = T + Y (16) The size of a domain in the z direction is given by

D = N d (17) Superstructure parameters are obtained by fitting the theoretical calculated intensity functions to the experimental curves. An example of a curve fit is displayed in Figure 8 for sample A. The fitting procedure has been performed such that the deviation of the theoretical curve from the experimental curve, given by

g, = A2Y/y2, g = A2--2 y YIY

I

5 I 104A-'-

Fig. 8. SAXS curve of sample A (solid line). The model calculated curve (dotted line) has been fitted to the experimental curve.


does not exceed 5%.

and of the Gaussian type21>25 The thickness distribution functions employed are assumed to be symmetrical

(19) and the corresponding expression for H ( y ) .

The superstructure parameters obtained with this model are listed in Table 111. They cannot be varied independently since the thicknesses X, 7 are connected by the repeat unit d [eq. (16)] determined by the peak position and connected with the linear crystallinity [eq. (14)l. The most sensitive parameter is the number N of crystals in a doman which determines primarily the height of the diffraction maximum while the width is mainly given by the fluctuation of the phase with the highest volume fraction which is g y for all samples investigated.

Inspection of Table I11 shows that the model crystallinities CpC calculated with the model are much higher than the weight crystallinities W, (Table 11), obtained from the WAXS measurements. This indicates that the crystals cluster together in stacks forming isolated particles surrounded by amorphous material.

The values of the fluctuation parameters g, and gy seem rather odd. The thickness distribution functions [eq. (19)], however, reveal that the thickness distributions have comparable widths (Fig. 9). This indicates a statistical dis- persion of crystals in the amorphous matrix and influences the particle structure, as will be discussed later.

H ( x ) = [ 1 / ( 2 ~ A ~ X ) ~ / ~ l exp-[(x - X)2/2A2X]

Small-Angle Light Scattering

The H, pattern for the small-angle light scattering of sample A is shown in Figure 10. This type of scattering has been found for all the samples investigated including the emulsion type PVC, which does not show a diffraction maximum in the SAXS curve. It has been shown by Rhodes and Stein26 that such scattering is produced by an assembly of randomly oriented rods.27

DISCUSSION

The results of both the WAXS and SAXS experiments permit conclusions to be drawn concerning the morphology of PVC. Some controversy on this point is found in the literature. Neilson and Jabarin28 propose a nodular structure based on a discussion of the SAXS of thin PVC films of a material with a mo-

TABLE 111 Samll-Angle X-Ray Results

Long Super lattice repeat perioda unitb Superstructure parametersb

L+ d X P D Sample (A) (A) (A) (A) g, g, 4c N (A)

A 154 116 21 95 0.4 0.06 0.18 1.9 220 B 156 110 21 89 0.4 0.05 0.19 2.2 240 C ...

a Derived from the angular position of the diffraction peak by applying Bragg's law. Obtained from model calculations of SAXS curves.

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x , y - Fig. 9. Thickness distribution functions of crystals and amorphous regions of sample A.

(a) (b) Fig. 10. Small-angle light-scattering pattern (H , ) of sample A . I t is typical for all investigated

samples. The radial densitometer tracing (in the 45' direction) indicates an intensity distribution which may be attributed t.o an assembly of randomly oriented rods.

lecular weight Mu = 104,000 and a stabilizer concentration less than 1%. Con- trary to our investigations, their SAXS curves decrease monotonically without showing diffraction maximum. Sizes of scattering elements are calculated from Guinier plots. Gezovich and Gei129 explained their micrographs on the basis of a nodular structure and discuss a lamellalike morphology. Bort, Zegelman,


and Kargin30 find, by use of electron microscopy, a structure composed of both lamellas and elongated particles, which are built up by “rolled up’’ lamellas. The lamellas are identified as monocrystals, the polymer chains being arranged in a planar zigzag perpendicular to the lamellar surface. The crystal thickness in the chain direction was found to be 25-75 A, the lamellas appearing in stacks. Apart from these two morphologies, there is a tendency to build up axialites and spherulites, as found earlier by Clark3l and also by Utsuo and Stein.32

No conclusive interpretation could be given as to whether the structural elements consist of elongated nodular particles or of crystal lamellas.

From our experiments, we conclude that the superstructure mainly consists of lamellar-shaped crystals. The values of the crystal size parameters listed in Tables I and I1 clearly show that the sizes in the (hkO) direction are two to three times larger than the thicknesses in the (001) direction. Hence, the crystals appear to have a lamellar form. This readily explains the SAXS as being produced by a stack of lamellas arranged in cluster^.^^,^^ From light scattering (Fig. lo), it is certain that rodlike entities are present in the sample. This would either support the model of Bort et al., assuming deformed lamellas, or is due to crystals which grow preferentially in one direction, thus adopting an elongated form. The fact, however, that the crystallinities obtained from the SAXS are higher than those obtained from the WAXS experiments indicates that most of the crystals are in the lamellar form. This is even more the case since the linear crystallinity derived from the SAXS is calculated on the basis of a lamella cluster model, assuming the crystal sizes perpendicular to the chain direction too large compared to the thickness.23 Hence, we conclude that only a few rodlike scatterers are present in the sample.

From these results we propose a superstructure model describing the fine structure of the primary particles. The basic elements of these particles, the subprimary particles, are identical with the lamella stacks, the clusters (Fig. 11). The size of the subprimary particles is 230-240 A and varies so that no inter- particle interference occurs in the SAXS curves. The superstructure of the emulsion type PVC is different from that of the other samples, which may be due to the different polymerization process. Although the shape of the crystals appears not to be different, the supermolecular order is disturbed and no correlation exists between the crystals.

The molecular arrangement within the crystals cannot be directly derived from the measurements presented here. The width of the WAXS peaks may indicate a low degree of perfection in the crystals. The presence of isolated nodules is not very reasonable although they may have been incorporated into the crystals

primary particles sub -primary particles

Fig. 11. Superstructure model of bulk PVC.

1648 WENIG

according to a molecular model proposed by Yeh33 for stretched natural rubber. The assumption of crystallites composed of arrays of micro para crystal^,^^-^^ as has been found in PVC gels,37 remains to be proved.

CONCLUSIONS

1) The crystallinity of PVC, polymerized by various processes at about 5OoC, ranges between 5% and 10%.

2) The crystals grow in lamellalike fashion although some elongated particles, made up of deformed lamellas or grown in elongated form, occur.

3) The crystal lamellas cluster together in stacks containing an average of two crystals.

4) The submicroparticles are identical with the clusters of lamellas. Their size is 220-240 A.

5) Emulsion-prepared PVC contains the same type of crystals as bulk- or suspension-polymerized material. The superstructure, however, is disturbed and no correlation occurs between the lamellar crystals.

The author wishes to thank Dr. R. Hammel, Dr. K. Meyer, and W. Holtrup for providing the GPC, viscosity, and density data. The assistance of R. Janosch, M. Steiner, U. Maykotter, and B. Hotzel is gratefully acknowledged.

References

1. G. Natta and P. Corradini, J. Polym. Sci., 20,251 (1956). 2. C. E. Wilkes, V. L. Folt, and S. Krimm, Macromolecules, 6,235 (1973). 3. A. Nakajima, H. Hamada, and S. Hayashi, Makromol. Chem., 95,40 (1966). 4. G. Rehage and H. Halboth, Makromol. Chem., 119,235 (1968). 5. S. Ohta, T. Kajiyama, and M. Takanayagi, Polym. Eng. Sci., 16,465 (1976). 6. E. V. Gouinlock, J. Polym. Sci. Polym. Phys. Ed., 13,961 (1975). 7. C. Baker, W. F. Maddams, and J. E. Preedy, J. Polym. Sci. Polym. Phys. Ed., 15, 1041

8. K. H. Illers, Makromol. Chem., 127,1(1969). 9. A. Gray and M. Gilbert, Polymer, 17,44 (1976).

(1977).

10. D. E. Whitenhafer, preprint. 11. R. S. Straff and D. R. Uhlmann, J. Polym. Sci. Polym. Phys. Ed., 14,353 (1976). 12. 0. Glatter, J. Appl. Crystallogr., 7,147 (1974). 13. A. Guinier and G. Fournet, J. Phys. Radium, 8,345 (1947). 14. R. Bramer and W. Wenig, Kolloid. Z. Z. Polym., 250,414 (1972). 15. R. S. Stein, Newer Methods of Polymer Characterization, Wiley, New York, 1964, Chap.

16. R. R. Smith, Second International Symposium on Polyvinyl Chloride, Lyon-Villeurbanne

17. K. Sagel, Tabellen zur Rijntgenstrukturanalyse, Springer-Verlag, Berlin, 1958, pp. 77-78. 18. L. E. Alexander, X-Ray Diffraction Methods in Polymer Science, Wiley, New York, 1969,

19. R. Hosemann, H. CaEkoviE, and W. Wilke, Naturwiss. 54,278 (1967). 20. W. Wilke and K. W. Martis, Colloid Polym. Sci., 252,718 (1974). 21. R. Bramer, Colloid Polym. Sci., 252,504 (1974). 22. R. Bramer, Thesis, Universitat Ulm, 1973. 23. H. G. Kilian and W. Wenig, J. Macromol. Sci. Phys. B, 9(3), 463 (1974). 24. W. Wenig and R. Bramer, Colloid Polym. Sci., 256,125-132 (1978). 25. W. Wenig, F. E. Karasz, and W. J. MacKnight, J. Appl. Phys., 46,4194 (1975). 26. M. B. Rhodes and R. S. Stein, J. Polym. Sci. A-2, 7,1539 (1969). 27. A. Misra, Thesis, University of Massachusetts, Amherst, Mass., 1974. 28. G. F. Neilson and S. A. Jabarib, J. Appl. Phys., 46,1175 (1975).

IV.

(France), July 5-9,1976 (unpublished).

Chap. 7.


29. D. M. Gezovich and P. H. Geil, Int. J. Polym. Muter., 1.3 (1971). 30. D. N. Bort, V. I. Zegelman, and V. A. Kargin, Vysokomol. Soedin., X(6), 1292 (1968). 31. R. J. Clark, J . Polym. Sci., 51, S71 (1961). 32. A. Utsuo and R. S. Stein, Polym. Lett., 3,49 (1965). 33. D. Luch and G. S. Y. Yeh, J. Polym. Sci. Polym. Phys. Ed., 11,467 (1973). 34. B. Steffen, Phys. Reu. B, 13(8), 3227 (1976). 35. B. Steffen and R. Hosemann, Phys. Rev. B, 13(8), 3232 (1976). 36. G. S. Y. Yeh, R. Hosemann, J. Loboda-CaEkoviC, and H. CaEkoviC, Polymer, 17. 309

37. W. Wenig, unpublished results. (1976).

Received September 16,1977 Revised January 23,1978

Documents

The microstructure of poly(vinyl chloride) as revealed by x-ray and light scattering