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JOURNAL OF POLYMER SCIENCE: PART A-2
VOL. 7, 983-992 (1969)
Birefringence of Native Cellulosic Fibers. Spiral Structure of Cotton
Part 11.
li. R. IiRISHNA IYER, P. NEELATiAKTAS, and T. R ADH A N
Synopsis Interferometric studies have been made on cotton fibers as well as on twisted nylon filaments. The results so obtained provide strong evidence that the fibrils in the cotton fiber become less inclined to the fiber axis as one proceeds from the surface to the core. Also, studies on twisted nylon filaments by the fiber refractometer and Becke line techniques indicate that the latter, as practiced in this laboratory, does give values of refractive index which are heavily weighted towards the fiber periphery.
INTRODUCTION The well-known fiber refractometer of Freeman and Preston' has been improved in the authors' laboratory so that its scope can be extended to cover variable natural fibers such as cotton.2 By using this improved instrument, i t becomes possible to measure the mean value of each refractive index in a parallel pad of fibers. An estimate can also be made of the variability in the refractive index among fibers or length elements within fibre^.^ The results obtained on cotton differed in two respects from those obtained by earlier workers who used the Becke line m e t h ~ d . ~ . ~ The extraordinary refractive index n and consequently the birefringence A n were higher; the variability in refractive index also appeared to be more than could be surmised from B e c k line results which indicate next to no variability. By following the a r g ~ m e n t ~ofs Preston et al.,6J these differences were tentatively attributed to the differences between the surface and the interior of the fiber. The Beckr line method gives an estimate of the refractive index near the fiber surface, while the refractometer result represents some sort of average through all the layers of the fiber. Since cotton has a spiral s t r u c t ~ r eand ~ * ~the fibrils in the inner layers may be more oriented than those along the surface, the refractometer value for the extraordinary refractive index could be higher than the Becke line result. The higher variability of refractive index could likewise be due to variations among individual fibers in the spiral arrangement of fibrils from the surface to the core, to which the refractometer is sensitive. However, these explanations are questionable in the light of other earlier work. li'aust1° has adduced reasons to believe that the Becke line refractive indices are 983
984
KRISHNA, IYER, NEELAKANTAN, RADHAKRISHNAN
not superficial. This belief is strengthened by certain interferometric observations of McLean." There is also a view that the fibrils in different layers of cotton may be deposited in spirals of equal angle12 rather than equal pitch.13 I n the present paper, a critical analysis of the situation is attempted with the help of data gathered in three ways: (1) with the improved fiber refractometer, (2) by the Becke line method, and (S) by interferometry of single fibers.
EXPERIMENTAL Samples The fibers studied were ramie, cotton, and filaments of viscose and nylon. Eight varieties of cotton were chosen on the basis of x-ray angle to represent a large spread in orientation. The viscose and nylon filaments were included since they were fibers with no spiral structure, lumen, etc. However, certain experiments were conducted with nylon filaments twisted so as to simulate a spiral structure. Full particulars of the method and the extent of twisting will be given later.
Measurements by the Refractometer The details of measurement are fully described in earlier papers2s3 and will not be repeated here. It will only be remarked that the samples were in the form of a pad of highly parallelized fibers immersed in a "matching" liquid and illuminated by polarized, collimated white light. The irradiated portion consisted of about 1 cm length of the pad consisting of a few thousand fibers. Prior to immersion, the samples were conditioned a t 65% R H and during measurement, the temperature was controlled within 30 f 0.1"C.
Measurements by the Becke Line Method Contrary to the usual practice, as many as a hundred fibers were examined by this method. A somewhat elaborate procedure3 was used to estimate not only the mean, but the coefficient of variation (CV) of the refractive index. Fibers used for this measurement were also conditioned a t 65% R H and tested a t 30°C.
Measurements by the Interferometer Multiple-beam interferometry, employing fringes of equal chromatic order,14was adopted in the present investigation. Since earlier ~ o r k e r s ~ ~ ~ ~ ~ have fully described the method, only a few aspects will be mentioned here. The interferometer plates were thin glass pieces, each about 2 cm in diameter and cut from a good photographic plate. These plates were coated with aluminum so that each allowed a transmission of about 10%. The plates were mounted (with their reflecting surfaces facing each other) on a metal jig provided with three tilting screws which could be adjusted
C I
985
to bring the plates into parallelism. The interferometer was held with the plates vertical and illuminated a t normal incidence by a parallel beam of white light from a tungsten filament lamp. A microscope objective combined with a projection eyepiece cast a magrufied image of the fiber, which was immersed in the liquid in the interferometer gap. The image was received on the slit of a prism spectrograph. The fiber was so mounted that the fiber axis was perpendicular to the length of the slit. The entire optical system was mounted on a precision optical bench. Strips of metal foil were placed between the interferometer plates to prevent any jamming of the fiber while adjusting the tilting screws. No auxiliary temperature control for the int,erferomet,er was incorporat>ed,as the purpose of the experiment was to det,ect local variat8ionsin the refractive index of the fiber rather than to det,ermine its absolute value. The sufficient requirement was the constancy of temperat,ure of the fiber and the ambient liquid (mixture of a-bromonaphthalene arid liquid paraffin) during the photography of the fringe pat,t,ern. This could be achieved by controlling the room temperature.
Preparation of Twisted Filaments Filaments were twisted individually on a yarn twisting machine. The number of turns per unit length N and the radius R of the twisted filament were measured on the machine. The nominal surface angle 8, was calculated from the well-known equation tane, = 2aNR
(1)
For refractometric measurements, the twisted filaments were wound on a thin metal frame, forming a uniform pad of parallel filaments. For Becke line measurements, the twisted filaments were held across a number of microscope slides arranged side by side. The filaments were fixed to the edges of each slide with a good cement. After the cement dried, the filaments were suitably cut and the slides separated. For interferometric work, the twisted filament was glued to the metal frame holding one of the silvered plates. Throughout the sample preparation, the twisted filaments were handled with meticulous care to ensure complete retention of the imparted twist.
RESULTS AND DISCUSSION Discrepancies in Refractive Index The refractive indices of a number of fibers, as measured by the fiber refractometer and by the Becke line method, are given in Table I. Both methods give the same results for viscose, nylon, and ramie. However, the refractometer gives higher values of n,ll and of birefringence for all cottons, and also high estimates of CV of refractive index. (The CV of the Becke line results on individual fibers is below 0.1% for all the samples.) We have
Bobshaw Acala P18C Watson Mebane Swollen cottons Jarila NaOH Swollen slack Jarila EI)A Swollen slack
Giza-45
Viscose Nylon Ramie Cottons Hopi Acala Jarila Deltapine
Sample
0.053 0.053 0.049 0,051
0.040 0,038
1,529
1.530 1.530 1.532 1.532 1.533 1.533
1 ,524
1 .52.i
1 .5x2 1 . .%3 1 -579 1 ,583 1 . .i77 1 .57.5 1 .,573
1.562
1 ,573 0.048
0.042
0.045
0.070
1 ,512 1 . ,527 1 .,729 0.040 0.0.i9
__ An
1 .d.i2 1 ..i86 1 . XI9
ni I
Becke line
1 ,377
1.564
1.582 1 ,584 1 ,581
1.588 1 .,585 1 ,586
1.588
1.S.il 1 ,586 1 . .509
-
1 ,523
1 ,522
1 .-5% 1 .529 1 ,530 1 . .532 1 ..5:30 1. ,533 I ,532
1 ..ill 1 . ,726 1 .329
Refractometer
TABLE I Results of Refractive Index Measurements (58'33 .k)
0.054
0.042
0.05'2 0.0.51 0,049
0 .0.2
0 ,031 0.0.59 0.055
0.070
0 060
0.040
4n
0.5
0.4
0 ..5 0.6 0.7 0.7 0.8
0.5
0.4
0.1 0.2 0.2
0.4
0.3
0.3 0.4 0.3 0.4 0.4 0.4 0.5
0.1 0.1 0 .1
CV, yo of n by refractometer
n
\D P
CET,LULOSIC FIBERS
987
attributed these differences to the pronounced and variable spiral structure of the cotton fiber.3 There may also be other possible contributions to optical variability, arising from convolutions, irregular size and shape of the fiber cross section, the lumen, and structural reversals. All effects but the last are known to decrease markedly when the fiber is highly swollen, yet the CV of lzl, shows only a slight decrease when cotton is swollen in alkali (Table I). Thus, these effects seem to exert only a marginal influence on optical variability. Reversals can also be dismissed since they account for so lithle of the fiber length.17 We are therefore left with the need for n deeper examination of the optical effects of spiral structure, which can be experimentally just, discerned in ramie, which has a spiral angle less than 60.18
Model of Spiral Structure That there is a spiral organization of fibrils in cotton has been known for a long t,ime.8a9 There are, however, two views as to the nature of the spiral angle. Duckett and TrippIg have recently tried to explain the azimuthal intensity distribution of the (002) x-ray diffraction from cotton on the basis that all fibrils are inclined to the fiber axis a t essentially the same angle, which is perturbed only by a random wander. This view is shared by earlier workers, such as Rebenfeld12 and Hearle.20 On the other hand, Warwicker13 sees in the (002) x-ray diffraction arc, evidence of a spiral angle which progressively decreases towards the core of the fiber. Strong confirmatory evidence is provided by x-ray work in this laboratory on the much more informative (040) profile.21 Berkley,22 Meredith,4 and Orr et al.9 also provide arguments in favor of a decrease in spiral angle towards the interior of the fiber. The optical data presented in Table I can be meaningfully interpreted in terms of a decrease in spiral angle from the periphery to the core of the fiber. It is assumed, following Preston et aL6J (and despite possible c r i t i ~ i s m ~that ~.~~ the ) Becke line value of nII represents a result which is weighted towards the surface of the fiber and is therefore low because the surface fibrils show maximum tilt to the fiber axis. On the other hand, the refractometer result depends on RayleighGans scattering of light24and would be affected by an integrated phase diference through the fiber cross section. If the spiral angle decreases towards the core of the fiber, the refractometer should give higher values of ?)11, as has been found only in the case of cotton. The high CV of refractive index would be due to variations in spiral arrangement among diff erent fibers or segments of the same fiber.
Results on Twisted Nylon Filaments The effects found in cotton can be simulated by twisted nylon filaments. The results are shown in Table 11. The refractive indices obtained with the refractomet,er and with the Becke line method are identical for the untwisted filaments. When enough twist is inserted to correspond to a surface helix angle of 37.5" [eq. (1)], there is a marked drop in nil and in birefrin-
n1 I
1.586 1.568
Surface refractive index hl)
1.586 1.564
Twist angle on the surface (02)
0 37.5
1.527 1.530
ni
Becke Line
0.059 0.038
An
1.586 1.577
nI I
1.526 1.527
ni
Refractometer
TABLE I1 Results of Observations on Untwisted and Twisted Nylon Filaments
0.060 0.050
An
0.4
0.2
C.V., yo of rill by refractometer
\D P P
CELLULOSIC FIRERS
989
gence as measured by both methods. However, the drop is greater by the Becke line technique. The difference in measurements by the two methods is of the same kind as in cotton, but greater in magnitude. These results can be understood in terms of a structural model consisting of a number of elements which are twisted together in accord with the “spinner’s rule” embodied in eq. (l),whereby the optical properties would become similar to those observed in cotton. A quantitative verification of the model is afforded by the Becke line value of nil for the twisted filament. Assuming that this is the value of rill a t the surface of the filament, the latter can be calculated from the refractive index ellipsoid of a uniaxial ~ r y s t a l : ~ , ~ ~ 1 nt l 2
-
cos2 6, nc2
sin2 BS
+n,Z
where the values of nr and n, are taken as nil and nl, respectively for the untwisted filament. This calculation yields a result which is in reasonable agreement with the Becke line value of nil for the twisted filament (Table 11). Therefore the Becke line result does seem to be weighted towards the surface of the fiber, as Preston et a1.6J originally postulated. The refractometric value of rill is considerably higher, in accord with the “equal pitch” model of spiral structure. The refractometric estimate of enhanced CV of nll on twisting the filament can be easily explained. When a long filament is held a t one end and twisted a t the other, it is difficult to achieve constancy of twist over all segments. These twist variations will in turn cause variability in the measured value of rill. It was verified that when filaments having different values of inserted twist were mixed together in the refractometer, the CV increased from 0.4 to 0.53%. There is an obvious similarity between this situation and the case of cotton fibers.
Results of Interferometry As described earlier, transmission interference fringes of equal chromatic order14were obtained by passing collimated, polarized white light through slightly transmitting glass plates between which the fiber and a matching liquid were sandwiched. Photographs of these fringes are shown in Figures 1 and 2 . I n the case of glass and nylon, t,he fringes are exactly similar to those described by earlier w ~ r k e r s . ~ The ~ J ~ fringes inside the fiber are straight and continuous with those inside the liquid in the region of the matching wavelength (marked B). Thus the refractive index is homogeneous across the fiber. On either side of this wavelength, the fringes bulge towards the middle of the fiber on account of increased path length. The situation changes slightly with ramie and markedly with cotton and twisted nylon. The shape of the fringe can be explained in terms of optical heterogeneity of the fiber from the surface to the core. Figure 3 shows a heterogeneous fiber with a n idealized circular cross section. It is assumed that the refractive index of a fiber element increases progressively from the edge to the center. Different segments of the fiber, such as K , L, M in
99 0
KRISHNA. IYER. NEELAKAhTAN. RADHAKRISHNAN
Fig. 1. Fringes of equal chromatic order formed by ( a ) glass, ( b ) nylon, and ( c ) ramie, for light vibrating parallel to the fiber axis (positive print).
Fig. 2 . Fringes of equal chromatic order formed by ( a ) twisted nylon and ( b ) and cotton, for light vibrating parallel to the fiber axis (negative print).
(c)
CELLULOSIC FIBERS
4
+Red
cb-b
Fibre region
991
(b)
Violet-
Fig. 3. Schematic diagrams of ( a ) an idealized circrilar C I ’ U S ~section of an optically heterogeneous fiber and ( b ) fringes of equal chromatic order i i i such a fiber having refractive index increasing towards the axis.
Figure 3, will introduce a total path retardation (or advance) given by J[n(z,y) - 1211dz for each y, where n.(z,y) is the refractive index of the fiber a t the point (ZJ) on the cross section, and nl that of the liquid, for the same wavelength. Since the liquid has a steeper dispersion curve than the fiber,1.3 the fiber will show a lower refractive index than the liquid on the ‘blue’ or low wavelength side of matching. The decrement in refractive index is greatest a t the edges of the fiber, in segments such as K . However, there is little path retardation because the fiber thickness is small a t the edges. At interior segments such as, L and ill, the geometrical path difference increases, but the average value of decrement in refractive index drops. Thus the fringes in the fiber show a displacement which rapidly increases to a maximum as one goes away from the edge and then falls back towards the middle. Figures 1 and 2 show that this is the shape of the fringes obtained in cotton, twisted nylon and, to a just discernible extent, in ramie. Such fringe shapes are not obtained on the higher or “red” side of matching, because the changes in geometric path and in refractive index do not oppose each other. The resulting fringes are similar to those obtained with optically homogeneous fibers. The foregoing explanation is very sinipliiied and does not, take into account the complicated tilt of the index ellipsoid in different regions of the fiber. However, it appears unlikely that a more sophisticated theory mill alter the nature of the argument. One coriditioii of the argument is that there should be a steep fall in the path through the fiber from the middle
992
KHISHNA, IYEH, NEELAKANTAN, HADHAKHISHNAN
towards the edges. This condition will not be fulfilled by typical cotton cross sections, which approximate to hollow fiattened ellipses. A mature and nearly circular fiber from a coarse species, such as Bengals, shows the effect best.
CONCLUSIONS The difference between Becke line measurements and refractometric measurements of the extraordinary refractive index of cotton can be explained on the basis that the fibrils in cotton are more inclined towards the fiber axis as one goes away from the core of the fiber. Interferometric studies of the fiber are also in full agreement with this hypothesis. The optical effects of spiral structure in cotton can be well simulated by a twisted nylon filament. The authors thank the Director of ATIltA for permission to publish this paper.
References 1. K. Freeman and J. NI. Preston, J . TextileZnst., 34, T-19 (1943). 2. P. Neelakantan, K. R. Krishna Iyer, and T. Radhakrishnan, J . Teztile Inst., 57, T-490 (1966). 3. K. R. Krishna Iyer, P. Neelakantan, and T. Radhakrishnan, J . Polym. Sci. 8-2, 6 , 1747 (1968). 4. R. Meredith, J . Textile Znst., 37, T-205 (1946). 5. S. M. Betrabet, K. P. R. Pillay, and R. L. N. Iyengar, Text. Res. J., 33, 720 (1963). 6. J. M. Preston and R. V. Bhat, J . Textile Znst., 39, T-211 (1948). 7. J. M. Preston and K. I. Narasimhan, J . TeztileInst., 40, T-327 (1949). 8. G. G. Osborne, Text. Res. J., 5,275 (1935). 9. R. S. Orr, A. W. Burgis, L. B. DeLuca, and J. N. Grant, Text. Res. J., 31, 302 (1961). 10. R. C. Faust, Proc. Phys. SOC.Ser. B, 68,1081 (1955). 11. J. H. McLean, Tezt. Res. J., 35,242 (1965). 12. L. Rebenfeld, in Morphological Foundations of Fiber Properties, J . Polym. Sci. C, 9, A. V. Tobolsky, Ed., Interscience, New York, 1965, p. 91. 13. J. 0.Warwicker, J . Polym. Sci. A-d,4,571 (1966). 14. S. Tolansky, “Multiple Beam Interferometry,” Oxford Univ. Press, 1948. 15. R. C. Faust, Proc. Phys. SOC.Ser. B 65,48 (1952). 16. N. S. Kapany, J . 0pt.Soc. Amer., 47,413 (1957). 17. T. Radhakrishnan, B. It. Shelat, and G. S. Viswanathan, Proceedings of The Joint Technological Conference, ATIRA, Ahmedabad, 1959, A-36. 18. P. H. Hermans, Physics and Chemistry of Cellulose Fibres, Elsevier, New York, 1949, p. 171. 19. K. E. Duckett and V. W. Tripp, Test. Res. J., 37,517 (1967). 20. J. W. S. Hearle, J . A p p l . Polym. Sci., 7,1207 (1963). 21. T. Radhakrishnan, N. E. Dweltz, and N. B. Patil, Text. Res. J.,in press. 22. E. E. Berkley, Text. Res. J., 9,355 (1939). 23. H. de Vries, On the Elastic arid Optical Properties of Cellulosic Fibres, Doctoral Thesis, Technische Hogeschool, Delft, 1953, p. 81. 24. H. C. Van de Ilulst, Light Scdtering by Small Particles, John Wiley & Sons, 1957, pp. 93-96. 25. J. M. Preston, Trans. Faraday SOC.,29,65 (1933).
Received November 18, 1968
VOL. 7, 983-992 (1969)
Birefringence of Native Cellulosic Fibers. Spiral Structure of Cotton
Part 11.
li. R. IiRISHNA IYER, P. NEELATiAKTAS, and T. R ADH A N
Synopsis Interferometric studies have been made on cotton fibers as well as on twisted nylon filaments. The results so obtained provide strong evidence that the fibrils in the cotton fiber become less inclined to the fiber axis as one proceeds from the surface to the core. Also, studies on twisted nylon filaments by the fiber refractometer and Becke line techniques indicate that the latter, as practiced in this laboratory, does give values of refractive index which are heavily weighted towards the fiber periphery.
INTRODUCTION The well-known fiber refractometer of Freeman and Preston' has been improved in the authors' laboratory so that its scope can be extended to cover variable natural fibers such as cotton.2 By using this improved instrument, i t becomes possible to measure the mean value of each refractive index in a parallel pad of fibers. An estimate can also be made of the variability in the refractive index among fibers or length elements within fibre^.^ The results obtained on cotton differed in two respects from those obtained by earlier workers who used the Becke line m e t h ~ d . ~ . ~ The extraordinary refractive index n and consequently the birefringence A n were higher; the variability in refractive index also appeared to be more than could be surmised from B e c k line results which indicate next to no variability. By following the a r g ~ m e n t ~ofs Preston et al.,6J these differences were tentatively attributed to the differences between the surface and the interior of the fiber. The Beckr line method gives an estimate of the refractive index near the fiber surface, while the refractometer result represents some sort of average through all the layers of the fiber. Since cotton has a spiral s t r u c t ~ r eand ~ * ~the fibrils in the inner layers may be more oriented than those along the surface, the refractometer value for the extraordinary refractive index could be higher than the Becke line result. The higher variability of refractive index could likewise be due to variations among individual fibers in the spiral arrangement of fibrils from the surface to the core, to which the refractometer is sensitive. However, these explanations are questionable in the light of other earlier work. li'aust1° has adduced reasons to believe that the Becke line refractive indices are 983
984
KRISHNA, IYER, NEELAKANTAN, RADHAKRISHNAN
not superficial. This belief is strengthened by certain interferometric observations of McLean." There is also a view that the fibrils in different layers of cotton may be deposited in spirals of equal angle12 rather than equal pitch.13 I n the present paper, a critical analysis of the situation is attempted with the help of data gathered in three ways: (1) with the improved fiber refractometer, (2) by the Becke line method, and (S) by interferometry of single fibers.
EXPERIMENTAL Samples The fibers studied were ramie, cotton, and filaments of viscose and nylon. Eight varieties of cotton were chosen on the basis of x-ray angle to represent a large spread in orientation. The viscose and nylon filaments were included since they were fibers with no spiral structure, lumen, etc. However, certain experiments were conducted with nylon filaments twisted so as to simulate a spiral structure. Full particulars of the method and the extent of twisting will be given later.
Measurements by the Refractometer The details of measurement are fully described in earlier papers2s3 and will not be repeated here. It will only be remarked that the samples were in the form of a pad of highly parallelized fibers immersed in a "matching" liquid and illuminated by polarized, collimated white light. The irradiated portion consisted of about 1 cm length of the pad consisting of a few thousand fibers. Prior to immersion, the samples were conditioned a t 65% R H and during measurement, the temperature was controlled within 30 f 0.1"C.
Measurements by the Becke Line Method Contrary to the usual practice, as many as a hundred fibers were examined by this method. A somewhat elaborate procedure3 was used to estimate not only the mean, but the coefficient of variation (CV) of the refractive index. Fibers used for this measurement were also conditioned a t 65% R H and tested a t 30°C.
Measurements by the Interferometer Multiple-beam interferometry, employing fringes of equal chromatic order,14was adopted in the present investigation. Since earlier ~ o r k e r s ~ ~ ~ ~ ~ have fully described the method, only a few aspects will be mentioned here. The interferometer plates were thin glass pieces, each about 2 cm in diameter and cut from a good photographic plate. These plates were coated with aluminum so that each allowed a transmission of about 10%. The plates were mounted (with their reflecting surfaces facing each other) on a metal jig provided with three tilting screws which could be adjusted
C I
985
to bring the plates into parallelism. The interferometer was held with the plates vertical and illuminated a t normal incidence by a parallel beam of white light from a tungsten filament lamp. A microscope objective combined with a projection eyepiece cast a magrufied image of the fiber, which was immersed in the liquid in the interferometer gap. The image was received on the slit of a prism spectrograph. The fiber was so mounted that the fiber axis was perpendicular to the length of the slit. The entire optical system was mounted on a precision optical bench. Strips of metal foil were placed between the interferometer plates to prevent any jamming of the fiber while adjusting the tilting screws. No auxiliary temperature control for the int,erferomet,er was incorporat>ed,as the purpose of the experiment was to det,ect local variat8ionsin the refractive index of the fiber rather than to det,ermine its absolute value. The sufficient requirement was the constancy of temperat,ure of the fiber and the ambient liquid (mixture of a-bromonaphthalene arid liquid paraffin) during the photography of the fringe pat,t,ern. This could be achieved by controlling the room temperature.
Preparation of Twisted Filaments Filaments were twisted individually on a yarn twisting machine. The number of turns per unit length N and the radius R of the twisted filament were measured on the machine. The nominal surface angle 8, was calculated from the well-known equation tane, = 2aNR
(1)
For refractometric measurements, the twisted filaments were wound on a thin metal frame, forming a uniform pad of parallel filaments. For Becke line measurements, the twisted filaments were held across a number of microscope slides arranged side by side. The filaments were fixed to the edges of each slide with a good cement. After the cement dried, the filaments were suitably cut and the slides separated. For interferometric work, the twisted filament was glued to the metal frame holding one of the silvered plates. Throughout the sample preparation, the twisted filaments were handled with meticulous care to ensure complete retention of the imparted twist.
RESULTS AND DISCUSSION Discrepancies in Refractive Index The refractive indices of a number of fibers, as measured by the fiber refractometer and by the Becke line method, are given in Table I. Both methods give the same results for viscose, nylon, and ramie. However, the refractometer gives higher values of n,ll and of birefringence for all cottons, and also high estimates of CV of refractive index. (The CV of the Becke line results on individual fibers is below 0.1% for all the samples.) We have
Bobshaw Acala P18C Watson Mebane Swollen cottons Jarila NaOH Swollen slack Jarila EI)A Swollen slack
Giza-45
Viscose Nylon Ramie Cottons Hopi Acala Jarila Deltapine
Sample
0.053 0.053 0.049 0,051
0.040 0,038
1,529
1.530 1.530 1.532 1.532 1.533 1.533
1 ,524
1 .52.i
1 .5x2 1 . .%3 1 -579 1 ,583 1 . .i77 1 .57.5 1 .,573
1.562
1 ,573 0.048
0.042
0.045
0.070
1 ,512 1 . ,527 1 .,729 0.040 0.0.i9
__ An
1 .d.i2 1 ..i86 1 . XI9
ni I
Becke line
1 ,377
1.564
1.582 1 ,584 1 ,581
1.588 1 .,585 1 ,586
1.588
1.S.il 1 ,586 1 . .509
-
1 ,523
1 ,522
1 .-5% 1 .529 1 ,530 1 . .532 1 ..5:30 1. ,533 I ,532
1 ..ill 1 . ,726 1 .329
Refractometer
TABLE I Results of Refractive Index Measurements (58'33 .k)
0.054
0.042
0.05'2 0.0.51 0,049
0 .0.2
0 ,031 0.0.59 0.055
0.070
0 060
0.040
4n
0.5
0.4
0 ..5 0.6 0.7 0.7 0.8
0.5
0.4
0.1 0.2 0.2
0.4
0.3
0.3 0.4 0.3 0.4 0.4 0.4 0.5
0.1 0.1 0 .1
CV, yo of n by refractometer
n
\D P
CET,LULOSIC FIBERS
987
attributed these differences to the pronounced and variable spiral structure of the cotton fiber.3 There may also be other possible contributions to optical variability, arising from convolutions, irregular size and shape of the fiber cross section, the lumen, and structural reversals. All effects but the last are known to decrease markedly when the fiber is highly swollen, yet the CV of lzl, shows only a slight decrease when cotton is swollen in alkali (Table I). Thus, these effects seem to exert only a marginal influence on optical variability. Reversals can also be dismissed since they account for so lithle of the fiber length.17 We are therefore left with the need for n deeper examination of the optical effects of spiral structure, which can be experimentally just, discerned in ramie, which has a spiral angle less than 60.18
Model of Spiral Structure That there is a spiral organization of fibrils in cotton has been known for a long t,ime.8a9 There are, however, two views as to the nature of the spiral angle. Duckett and TrippIg have recently tried to explain the azimuthal intensity distribution of the (002) x-ray diffraction from cotton on the basis that all fibrils are inclined to the fiber axis a t essentially the same angle, which is perturbed only by a random wander. This view is shared by earlier workers, such as Rebenfeld12 and Hearle.20 On the other hand, Warwicker13 sees in the (002) x-ray diffraction arc, evidence of a spiral angle which progressively decreases towards the core of the fiber. Strong confirmatory evidence is provided by x-ray work in this laboratory on the much more informative (040) profile.21 Berkley,22 Meredith,4 and Orr et al.9 also provide arguments in favor of a decrease in spiral angle towards the interior of the fiber. The optical data presented in Table I can be meaningfully interpreted in terms of a decrease in spiral angle from the periphery to the core of the fiber. It is assumed, following Preston et aL6J (and despite possible c r i t i ~ i s m ~that ~.~~ the ) Becke line value of nII represents a result which is weighted towards the surface of the fiber and is therefore low because the surface fibrils show maximum tilt to the fiber axis. On the other hand, the refractometer result depends on RayleighGans scattering of light24and would be affected by an integrated phase diference through the fiber cross section. If the spiral angle decreases towards the core of the fiber, the refractometer should give higher values of ?)11, as has been found only in the case of cotton. The high CV of refractive index would be due to variations in spiral arrangement among diff erent fibers or segments of the same fiber.
Results on Twisted Nylon Filaments The effects found in cotton can be simulated by twisted nylon filaments. The results are shown in Table 11. The refractive indices obtained with the refractomet,er and with the Becke line method are identical for the untwisted filaments. When enough twist is inserted to correspond to a surface helix angle of 37.5" [eq. (1)], there is a marked drop in nil and in birefrin-
n1 I
1.586 1.568
Surface refractive index hl)
1.586 1.564
Twist angle on the surface (02)
0 37.5
1.527 1.530
ni
Becke Line
0.059 0.038
An
1.586 1.577
nI I
1.526 1.527
ni
Refractometer
TABLE I1 Results of Observations on Untwisted and Twisted Nylon Filaments
0.060 0.050
An
0.4
0.2
C.V., yo of rill by refractometer
\D P P
CELLULOSIC FIRERS
989
gence as measured by both methods. However, the drop is greater by the Becke line technique. The difference in measurements by the two methods is of the same kind as in cotton, but greater in magnitude. These results can be understood in terms of a structural model consisting of a number of elements which are twisted together in accord with the “spinner’s rule” embodied in eq. (l),whereby the optical properties would become similar to those observed in cotton. A quantitative verification of the model is afforded by the Becke line value of nil for the twisted filament. Assuming that this is the value of rill a t the surface of the filament, the latter can be calculated from the refractive index ellipsoid of a uniaxial ~ r y s t a l : ~ , ~ ~ 1 nt l 2
-
cos2 6, nc2
sin2 BS
+n,Z
where the values of nr and n, are taken as nil and nl, respectively for the untwisted filament. This calculation yields a result which is in reasonable agreement with the Becke line value of nil for the twisted filament (Table 11). Therefore the Becke line result does seem to be weighted towards the surface of the fiber, as Preston et a1.6J originally postulated. The refractometric value of rill is considerably higher, in accord with the “equal pitch” model of spiral structure. The refractometric estimate of enhanced CV of nll on twisting the filament can be easily explained. When a long filament is held a t one end and twisted a t the other, it is difficult to achieve constancy of twist over all segments. These twist variations will in turn cause variability in the measured value of rill. It was verified that when filaments having different values of inserted twist were mixed together in the refractometer, the CV increased from 0.4 to 0.53%. There is an obvious similarity between this situation and the case of cotton fibers.
Results of Interferometry As described earlier, transmission interference fringes of equal chromatic order14were obtained by passing collimated, polarized white light through slightly transmitting glass plates between which the fiber and a matching liquid were sandwiched. Photographs of these fringes are shown in Figures 1 and 2 . I n the case of glass and nylon, t,he fringes are exactly similar to those described by earlier w ~ r k e r s . ~ The ~ J ~ fringes inside the fiber are straight and continuous with those inside the liquid in the region of the matching wavelength (marked B). Thus the refractive index is homogeneous across the fiber. On either side of this wavelength, the fringes bulge towards the middle of the fiber on account of increased path length. The situation changes slightly with ramie and markedly with cotton and twisted nylon. The shape of the fringe can be explained in terms of optical heterogeneity of the fiber from the surface to the core. Figure 3 shows a heterogeneous fiber with a n idealized circular cross section. It is assumed that the refractive index of a fiber element increases progressively from the edge to the center. Different segments of the fiber, such as K , L, M in
99 0
KRISHNA. IYER. NEELAKAhTAN. RADHAKRISHNAN
Fig. 1. Fringes of equal chromatic order formed by ( a ) glass, ( b ) nylon, and ( c ) ramie, for light vibrating parallel to the fiber axis (positive print).
Fig. 2 . Fringes of equal chromatic order formed by ( a ) twisted nylon and ( b ) and cotton, for light vibrating parallel to the fiber axis (negative print).
(c)
CELLULOSIC FIBERS
4
+Red
cb-b
Fibre region
991
(b)
Violet-
Fig. 3. Schematic diagrams of ( a ) an idealized circrilar C I ’ U S ~section of an optically heterogeneous fiber and ( b ) fringes of equal chromatic order i i i such a fiber having refractive index increasing towards the axis.
Figure 3, will introduce a total path retardation (or advance) given by J[n(z,y) - 1211dz for each y, where n.(z,y) is the refractive index of the fiber a t the point (ZJ) on the cross section, and nl that of the liquid, for the same wavelength. Since the liquid has a steeper dispersion curve than the fiber,1.3 the fiber will show a lower refractive index than the liquid on the ‘blue’ or low wavelength side of matching. The decrement in refractive index is greatest a t the edges of the fiber, in segments such as K . However, there is little path retardation because the fiber thickness is small a t the edges. At interior segments such as, L and ill, the geometrical path difference increases, but the average value of decrement in refractive index drops. Thus the fringes in the fiber show a displacement which rapidly increases to a maximum as one goes away from the edge and then falls back towards the middle. Figures 1 and 2 show that this is the shape of the fringes obtained in cotton, twisted nylon and, to a just discernible extent, in ramie. Such fringe shapes are not obtained on the higher or “red” side of matching, because the changes in geometric path and in refractive index do not oppose each other. The resulting fringes are similar to those obtained with optically homogeneous fibers. The foregoing explanation is very sinipliiied and does not, take into account the complicated tilt of the index ellipsoid in different regions of the fiber. However, it appears unlikely that a more sophisticated theory mill alter the nature of the argument. One coriditioii of the argument is that there should be a steep fall in the path through the fiber from the middle
992
KHISHNA, IYEH, NEELAKANTAN, HADHAKHISHNAN
towards the edges. This condition will not be fulfilled by typical cotton cross sections, which approximate to hollow fiattened ellipses. A mature and nearly circular fiber from a coarse species, such as Bengals, shows the effect best.
CONCLUSIONS The difference between Becke line measurements and refractometric measurements of the extraordinary refractive index of cotton can be explained on the basis that the fibrils in cotton are more inclined towards the fiber axis as one goes away from the core of the fiber. Interferometric studies of the fiber are also in full agreement with this hypothesis. The optical effects of spiral structure in cotton can be well simulated by a twisted nylon filament. The authors thank the Director of ATIltA for permission to publish this paper.
References 1. K. Freeman and J. NI. Preston, J . TextileZnst., 34, T-19 (1943). 2. P. Neelakantan, K. R. Krishna Iyer, and T. Radhakrishnan, J . Teztile Inst., 57, T-490 (1966). 3. K. R. Krishna Iyer, P. Neelakantan, and T. Radhakrishnan, J . Polym. Sci. 8-2, 6 , 1747 (1968). 4. R. Meredith, J . Textile Znst., 37, T-205 (1946). 5. S. M. Betrabet, K. P. R. Pillay, and R. L. N. Iyengar, Text. Res. J., 33, 720 (1963). 6. J. M. Preston and R. V. Bhat, J . Textile Znst., 39, T-211 (1948). 7. J. M. Preston and K. I. Narasimhan, J . TeztileInst., 40, T-327 (1949). 8. G. G. Osborne, Text. Res. J., 5,275 (1935). 9. R. S. Orr, A. W. Burgis, L. B. DeLuca, and J. N. Grant, Text. Res. J., 31, 302 (1961). 10. R. C. Faust, Proc. Phys. SOC.Ser. B, 68,1081 (1955). 11. J. H. McLean, Tezt. Res. J., 35,242 (1965). 12. L. Rebenfeld, in Morphological Foundations of Fiber Properties, J . Polym. Sci. C, 9, A. V. Tobolsky, Ed., Interscience, New York, 1965, p. 91. 13. J. 0.Warwicker, J . Polym. Sci. A-d,4,571 (1966). 14. S. Tolansky, “Multiple Beam Interferometry,” Oxford Univ. Press, 1948. 15. R. C. Faust, Proc. Phys. SOC.Ser. B 65,48 (1952). 16. N. S. Kapany, J . 0pt.Soc. Amer., 47,413 (1957). 17. T. Radhakrishnan, B. It. Shelat, and G. S. Viswanathan, Proceedings of The Joint Technological Conference, ATIRA, Ahmedabad, 1959, A-36. 18. P. H. Hermans, Physics and Chemistry of Cellulose Fibres, Elsevier, New York, 1949, p. 171. 19. K. E. Duckett and V. W. Tripp, Test. Res. J., 37,517 (1967). 20. J. W. S. Hearle, J . A p p l . Polym. Sci., 7,1207 (1963). 21. T. Radhakrishnan, N. E. Dweltz, and N. B. Patil, Text. Res. J.,in press. 22. E. E. Berkley, Text. Res. J., 9,355 (1939). 23. H. de Vries, On the Elastic arid Optical Properties of Cellulosic Fibres, Doctoral Thesis, Technische Hogeschool, Delft, 1953, p. 81. 24. H. C. Van de Ilulst, Light Scdtering by Small Particles, John Wiley & Sons, 1957, pp. 93-96. 25. J. M. Preston, Trans. Faraday SOC.,29,65 (1933).
Received November 18, 1968
