# On-Line Measurement of Orientation Development in the High-Speed Melt Spinning Process.

TAKESHI KIKUTANI [*]

On-line measurement of birefringence was performed in the high-speed melt spinning process of poly(ethylene terephthalate) using an apparatus that incorporates a rotating polarizer for the measurement of the optical retardation of running filament. Particular attention was paid to the detailed measurements in the vicinity of neck-like deformation. Through the measurement at the take-up velocity of 5 km/min, development of birefringence under the strain rate up to about 1 [ms.sup.-1] was investigated. To analyze the relation between applied stress and birefringence, tension and temperature profiles of the spin-line were calculated based on the experimentally obtained diameter profiles. Even though the strain rate is extremely high, a linear relationship between birefringence and a parameter calculated by dividing stress by temperature was confirmed to hold up to birefringence and stress/temperature values of about 0.017 and 10 kPa/K, respectively.

INTRODUCTION

Anisotropy is one of the most important characteristics of polymeric materials. The main origin of the anisotropy is the orientation of molecular chain. Mechanical, optical and many other properties of polymeric products can be improved through the control of molecular orientation. Therefore it is important to analyze the mechanism of orientation development through experimental and theoretical investigations of the polymer processing behavior.

High-speed melt spinning is a process in which significant molecular orientation and orientation-induced crystallization occurs. The fiber structure development proceeds under extremely high tensile strain rate which usually is referred to as the neck-like deformation. There have been many attempts for the on-line measurements of the spinning behavior in high-speed melt spinning process [1]. We also have carried out diameter and temperature measurements of the spin-line paying particular attention to the region in the vicinity of neck-like deformation. Through the temperature measurement of the spin-line of poly(ethylene terephthalate) (PET), heat of crystallization was detected near the neck-like deformation [2]. The crystallization rate estimated from this result was [10.sup.4]-[10.sup.5] times larger than that for the isotropic state. The diameter profile of neck-like deformation was investigated in detail by analyzing the signals from multiple diameter monitors [3, 4] and by capturing the image using a sp ecially developed optical system with a CCD camera [5]. It was confirmed through these analyses that the maximum strain rate in the vicinity of neck-like deformation reaches a value higher than 20 [ms.sup.-1].

Similar results of temperature and diameter profiles for the high-speed spin-line of polyamide 6 and polyamide 66 were reported by Haberkorn et al. [6]. Development of fiber structure through the neck-like deformation was also investigated by taking wide-angle X-ray scattering patterns using a synchrotron radiation source [7]. Although there are some papers on the on-line measurement of birefringence in the melt spinning and solution spinning processes [8, 9], detailed investigation of birefringence development in the vicinity of the neck-like deformation has not been reported yet.

EXPERIMENTAL

Melt Spinning

Poly(ethylene terephthalate) [PET] pellet supplied by Toray Industries Inc. was used in this study. The intrinsic viscosity of the polymer was 0.949 dL/g. A polymer with high molecular weight was selected because the neck-like deformation starts to occur from relatively low take-up velocities although sharpness of the neck-like deformation is not so distinct [4].

The PET polymer was extruded from a single-hole spinneret of 0.5 mm diameter at 300[degrees]C. The throughput rate was controlled to 5.0 g/min. The quenching air was not applied to the spin-line. The extruded polymer was taken up by a high-speed winder placed at 330 cm below the spinneret. The take-up velocity was varied from 1 to 5 km/min. The spin-line tension was measured using a tension meter (Roschild, MiniTens R-046). The tension measurement was performed for the solidified region of the spin-line by changing the distance from the spinneret. The on-line measurements of diameter and birefringence were also conducted at various positions of the spin-line. The principle of the measurement is described in the following section.

Principle of Birefringence Measurement

A schematic diagram of the birefringence measurement system used in this work is shown in Fig. 1. The optical system consists of two blocks: a diameter measurement block and an optical retardation measurement block. For the diameter measurement, three diameter monitors (from the top, Zimmer OHG Model 460A/10, Keyence LX2-l00 and Zimmer OHG Model 460A/2) were used. All the diameter monitors are based on the back-illumination principle. The distance between each diameter monitor is 39 mm. The use of multiple diameter monitors enables us to monitor the movement of the position of neck-like deformation (3).

The optical system for the measurement of retardation, which is similar to the one reported in a patent [10], is composed of a He-Ne laser light source, polarizing filters, quarter-wave plates, a rotating polarizing filter, a beam splitter, a beam expander, and photo detectors. Time-course changes of the intensity of reference light [I.sub.ref] (t) and the intensity of light passed through the running filament [I.sub.meas] (t) can be expressed as follows (see Appendix for details):

[I.sub.ref](t) = A [1 - cos2[phi](t)] (1)

[I.sub.meas](t) = A {l - cos[2[phi](t) + [delta]} (2)

where A is the amplitude of light. [phi](t) the rotation angle of a polarizing filter, and [delta] the optical retardation of fiber sample. Birefringence of the spin-line [delta]n can be obtained from [delta] using the following equation.

[delta]n = [delta][lambda]/2[pi]L (3)

where [lambda] is the wave length of light and L the geometrical path for light in the filament cross-section. It is important to note here that only the phase shift a1 can be evaluated by comparing the signals of [I.sub.ref](t) and [I.sub.meas](t). The relation between [delta] and [a.sub.1] is

[delta] = 2[pi]N + [a.sub.1] (4)

where N is the order of interference which cannot be obtained directly through the measurement. In the data analysis, N near the spinneret was assumed to be zero and that at the end part of the spin-line was estimated from the birefringence of as-spun fibers. In some cases, a certain extent of ambiguity remains for the determination of N depending on how the birefringence develops in the spin-line.

The analysis of the phase shift was conducted for [I.sub.ref](t) and [I.sub.meas](t) acquired using an A/D converter and a microcomputer. For the determination of the phase shift, the cross correlation function C ([tau]) of these intensity data was fitted to the sinusoidal function.

C (tau] = [[[integral of].sup.[t.sub.1]].sub.[t.sub.2]] [I.sub.meas] (t - [tau]) [I.sub.ref] (t) dt (5)

C ([tau]) = [a.sub.0] sin ([tau] + [a.sub.1]) + [a.sub.2] (6)

where [tau] is the lag. In each measurement, [I.sub.ref](t) and [I.sub.meas](t) were acquired for 1 second at the sampling frequency of 9 kHz. The rotation frequency of the linearly polarized light coming out from the rotating polarizing filter was 300 Hz, i.e. the rotation frequency of the polarizing filter was 150 Hz. Therefore, one cycle of the light intensity variation corresponds to thirty measurements which is large enough for the evaluation of phase shift. A typical example of [I.sub.ref](t) and [I.sub.meas](t) and the analyzed cross correlation function are shown in Fig. 2.

The measuring apparatus has some other unique features which are worth noting. The laser light for the measurement was expanded only in the horizontal direction using a beam expander consisting of cylindrical lenses. This is to increase the efficiency of data acquisition because the position of spin-line fluctuates in the direction perpendicular to the filament axis. The photo detector was offset 26[degrees] from the primary laser beam to allow the direct measurement of [I.sub.meas](t). In this case, the geometrical path for the light L can be expressed as follows (8):

L = D ([n.sub.f] - cos [theta]/2)/[square root of][sin.sup.2][theta]/2 + [([n.sub.f] - cos[theta]/2).sup.2] (7)

where [theta] is the offset angle, and D and [n.sub.f] (=1.57) are the diameter and refractive index of the spin-line. Although the measurement of retardation was performed at the same position as the second diameter monitor, there was no optical disturbance between these two apparatuses because the wave lengths of incident light and corresponding band-path filter are different, i.e. 730 and 633 nm for the diameter and retardation measurements, respectively.

Measurement of Birefringence in the Vicinity of Neck-Like Deformation

A method developed for the measurement of detailed diameter profile in the vicinity of neck-like deformation (3) was utilized for the evaluation of detailed birefringence profile. The principle of this method is as follows. If diameter measurement is conducted near the position of neck-like deformation using three diameter monitors, the neck-like deformation occasionally passes through the three diameter monitors because of up-and-down fluctuation of its position. In such a case, time-course signals of diameter shown schematically in Fig. 3 may be obtained. From the time difference of the passage of neck-like deformation, which can be evaluated from Fig. 3, and the distance between the diameter monitors, the moving velocity of the position of neck-like deformation [v.sub.n] can be estimated. This moving velocity is applicable for the conversion of time-axis to distance-axis. In other words, the diameter profile of neck-like deformation, i.e. diameter versus axial distance curve, can be obtained by multiplying the abscissa in Fig. 3 by [v.sub.n].

Therefore, if the measurement of phase shift is performed simultaneously with the diameter measurements at the position of the second diameter monitor and with a similiar time resolution, birefringence profile in the vicinity of the neck-like deformation can be obtained. A schematic diagram explaining the condition for the data analysis of the phase shift adopted in this work is shown in Fig. 4. Because of the quick movement and steep diameter change of the neck-like deformation, the phase shift is expected to change rapidly with time. Therefore, data only for 3.3 ms (30 points of measurements), which corresponds to one cycle of intensity variation generated by the rotation of polarizing filter, was used for the phase shift analysis. It was difficult to obtain the phase shift if the time for analysis is shorter than 3 ms because of high noise level of the signal from measurement light. By moving the 3.3 ms time-frame with the step of one data point, change of the phase shift was obtained at the data acquisiti on frequency of 9 kHz. Therefore, the analyzed curve corresponds to the smoothed curve of the 9 kHz data after the moving average operation over thirty data points.

RESULTS AND DISCUSSION

Overall Diameter and Birefringence Profiles

Changes of the phase shift, diameter and birefringence along the spin-line measured in the high-speed melt spinning process of PET at take-up velocities of 2 and 5 km/min are shown in Figs. 5 and 6. In case of 2 km/min, it can be understood easily that the order of interference changed from 0 to 1 at around 200 cm where the phase shift changed from 360[degrees] to 0[degrees]. The birefringence showed a sigmoidal increase and the value obtained at the end part of the spin-line was close to that for as-spun fibers. In case of 5 km/min, neck-like deformation was observed at around 100 cm. Immediately before the neck-like deformation, phase shift started to increase steeply. It is difficult to judge how the phase shift varies in the steepest part of neck-like deformation, however, from the knowledge of the birefringence of as-spun fibers, the order of interference just below the neck-like deformation was estimated to be 3. Below the neck-like deformation, birefringence kept increasing gradually suggesting that t here still is a certain degree of structural change in the spin-line after the neck-like deformation.

Diameter and birefringence profiles for the take-up velocities of 1 to 5 km/min are summarized in Fig. 7. The neck-like deformation was found for the 4 and 5 km/min spinnings, and the birefringence increased steeply at the neck-like deformation. It can be noticed here that even at 3 km/min, there was a concentration of birefringence development at around 160-180 cm where relatively steep diameter reduction occurred.

Diameter and Birefringence Profiles in the Vicinity of Neck-Like Deformation

Changes of diameter, phase shift and birefringence in the vicinity of neck-like deformation obtained from the 5 km/min spin-line are shown in Figs. 8a and 8b. The moving velocity of the position of neck-like deformation analyzed from this data is 0.50 m/s. As can be seen in Fig. 8a, analyzed phase shift increased with the reduction of fiber diameter, and near the end part of the neck-like deformation, a vigorous change of phase shift was observed. As described previously, the order of interference immediately below the neck-like deformation is known to be 3. Considering this, the order of interference was estimated as shown in the figure. Change of the order from 0 to 1 can be found clearly at around 0.22 s. There is another jump in the phase shift at around 0.27 s; however, it is difficult to determine the position of the third jump which is supposed to exist. We assume at present that the phase shift at around 0.27 s is too rapid to detect clearly because the change of order from 2 to 3 occurs soon after t he 1 to 2 change. Variations of phase shift, diameter and birefringence are plotted in Fig. 8b. In this Figure, phase shift after the consideration of the order of interference is shown. Also, the abscissa is converted to the distance along fiber axis by multiplying time-axis by the moving velocity of neck-like deformation. At the early stage of neck-like deformation, birefringence increases gradually with the decrease of fiber diameter. Increase of birefringence accelerates with the reduction of fiber diameter and stabilizes suddenly when the steep deformation finishes. As indicated in Fig. 7, there still remains a gradual increase of birefringence after the neck-like deformation.

Analyses on Temperature and Tension Profiles of the Spin-Line

From the measured diameter at a certain position, filament velocity can be evaluated using the equation of continuity.

W = [pi][D.sup.2]/4 [[rho].sup.v] (8)

Then, the temperature and tension profiles of the spin-line can be analyzed from the diameter and velocity profiles based on the heat balance and momentum balance equations [11].

dT/dx = - [pi]Dh/[WC.sup.p] (T - [T.sup.a]) (9)

dF/dx = W (dV/dx - g/V) + [pi]D[[tau].sub.f] (10)

where F, V, D and T denote the spin-line tension, velocity, diameter and temperature at a distance x from the spinneret, W is the extrusion mass flow rate, h and [[tau].sub.f] are the heat transfer coefficient and the air friction stress, [rho] and [C.sup.p] are the density and heat capacity of polymer, g the acceleration of gravity, and [T.sub.a] the ambient temperature. Parameters and empirical equations adopted for the calculation, which are described in detail elsewhere [2, 12], are shown below.

[rho] = 1.356 - 5.0 X [10.sup.-4]T (g/[cm.sup.3]) (11)

[C.sup.p] = 1.26 + 2.5 X [10.sup.-3]T (J/(g K)) (12)

h = [K.sub.a]/D (0.28 [[R.sup.-0.334].sub.e]) (13)

[[tau].sub.f] = 1/2 [[rho].sub.a] [V.sub.2] (0.66 [R.sup.-0.61].sub.e]) (14)

The temperature and tension profiles of the spin-line were estimated based on these equations consulting measured spin-line tension. The analyzed temperature and tension profiles along with the experimental data are shown in Fig. 9. It can be seen from this Figure that the neck-like deformation at 5 km/min occurs at about 170[degrees]C.

Relation Between Stress, Temperature and Birefringence

The stress-optical law can be derived by comparing the stress tensor [sigma] and the anisotropic part of the index of refraction n for Gaussian chains [13].

n = C[sigma] (15)

Here, the stress-optical coefficient C can be expressed as follows.

C = 2[pi]/45kT [(n + 2).sup.2]/n ([[alpha].sub.1] - ([[alpha].sub.2]) (16)

where n is the isotropic part of the index of refraction, [[alpha].sub.1]-[[alpha].sub.2] the difference between the axial and transverse polarizabilities of the link, T the absolute temperature and k the Boltzmann constant.

Relation between birefringence and tensile stress calculated from tension and diameter profiles of the 1 km/min spin-line is shown in Fig. 10a. Considering the temperature dependence of the stress-optical coefficient, a plot between birefringence and a parameter calculated by dividing the tensile stress by the spin-line temperature is also prepared as shown in Fig. 10b. There is a slight downward concaveness of the curve in Fig. 10a. On the other hand, Fig. 10b gives a fairly good linear line which passes through the origin. Therefore, a log-log plot of the latter type was prepared from the overall diameter and birefringence profiles of various take-up velocities as shown in Fig. 11. It can be seen from this figure that the birefringence and the stress/temperature shows a good linear relationship with a slope of unity up to those values of about 0.017 and 10 kPa/K, respectively. If intrinsic amorphous birefringence of 0.275 is adopted [14], this critical birefringence corresponds to the orientation factor of about 0.06. From the intercept of the straight line, C X T value of 1.66 K/MPa is obtained. This value corresponds to the stress-optical coefficient of 4.8 [GPa.sup.-1] at the glass transition temperature, which agrees well with the reported value [15]. Above this region, there is a steeper increase of birefringence followed by a tendency of saturation at different levels depending on the take-up velocity.

A similar analysis was applied for the data obtained in the vicinity of the neck-like deformation as shown in Fig. 12. In the Figure, the data from the overall spin-line are also plotted. Both data showed good continuity each other. The linearity in the relation between birefringence and stress/temperature is also found to hold up to the birefringence of about 0.02. Smoothed profiles of diameter, strain rate and stress/temperature in the vicinity of the neck-like deformation are shown in Fig. 13. A position in the neck-like deformation corresponding to the critical stress/temperature value is indicated in the Figure. It is important to note that the stress-optical law is applicable up to the critical birefringence even though the strain rate is as high as ca. 0.5 [ms.sup.-1] at the temperature of about 170[degrees]C.

CONCLUSION

An optical system for the simultaneous measurements of fiber diameter and retardation was developed. Using this system, on-line measurement of birefringence in the high-speed melt spinning process was accomplished. It was also possible to measure the detailed birefringence profile in the vicinity of neck-like deformation, and the measurement at the take-up velocity of 5 km/min provided the data on birefringence development under the strain rate up to about 1 [ms.sup.-1]. Temperature and tension profiles of the spin-line were calculated based on the experimentally obtained diameter profiles. These profiles were used for the analysis of the relation between applied tensile stress and birefringence. Even though the strain rate is extremely high, a linear relationship between birefringence and stress/temperature was confirmed to hold up to those values of about 0.017 and 10 kPa/K, respectively.

APPENDIX

Detailed arrangement of the optical system for the measurement of retardation (phase shift) is shown in Fig. 14. Linearly polarized laser light becomes circularly polarized light after passing through a quarter-wave plate, and then changes to rotating linearly polarized light after passing through a rotating polarizing filter. The components of electric vector in x and y directions, [E.sub.x] and [E.sub.y], for this light are

[E.sub.x] = Asin[phi](t)sin[omega]t (17)

[E.sub.y] = Acos[phi](t)sin[omega]t (18)

where A is the amplitude, [omega] the angular frequency, and [omega](t) the rotation angle of a polarizing filter. The time average intensity of the reference light [I.sub.ref](t) can be expressed as follows.

[I.sub.ref](t) = [[E.sup.2].sub.x] = ([A.sup.2]/2)[sin.sup.2][phi](t) = ([A.sup.2]/4)[1-cos2[phi](t)] (19)

On the other hand, the measurement light after passing through the quarter-wave plate is

[E.sub.x] = Asin[phi]sin ([omega]t + [pi]/2) = Asin[pi]cos[omega]t (20)

[E.sub.y] = Asin[phi]sin[omega]t (21)

Therefore, the electric vector components in the directions parallel and perpendicular to the fiber axis, [E.sub.[alpha]] and [E.sub.[beta]], are

[E.sub.[alpha]] = [(E.sub.x] - [E.sub.y])/[square root of]2 = - (A/[square root of]2)sin[[omega]t - [phi](t)] (22)

[E.sub.[beta]] = [(E.sub.x] + [E.sub.y])/[square root of]2 = (A/[square root of]2)sin[[omega]t + [phi](t)] (23)

Since the oriented PET fiber has higher refractive index in the direction parallel to the fiber axis, the light after passing through the fiber can be expressed as follows.

[E.sub.[alpha]] = -(A/[square root of]2) sin [[omega]t - [phi](t) - [delta]] (24)

[E.sub.[beta] = (A/[square root of]2) sin [[omega]t + [phi](t)] (25)

where [delta] is the optical retardation. Therefore, [E.sub.x] component at the photo detector is

[E.sub.x] ([E.sub.[alpha]] + [E.sub.[beta]])/[square root of]2 = - Acos ([omega]t - [delta]/2)sin

[- [phi](t) - [delta]/2] (26)

and consequently the time average intensity of the measurement light [I.sub.meas](t) is

[I.sub.meas](t) = [[E.sup.2].sub.x] = ([A.sup.2]/2) [sin.sup.2] [[phi](t) + [delta]/2] = ([A.sup.2]/4) {1 - cos [2[phi](t) + [delta]]} (27)

ACKNOWLEDGMENT

The authors wish to thank Mr. M. Fukuhara and Mr. Y. Maeda of Toray Industries Inc. for their helpful assistance and discussion during this work.

(*.) To whom correspondence should be addressed.

REFERENCES

(1.) A. Ziabicki and H. Kawai, eds., High-Speed Fiber Spinning, John Wiley & Sons (1985).

(2.) T. Kikutani, Y. Kawahara, T. Matsui, A. Takaku, and J. Shimizu, Seikei-Kakou, 1, 333 (1989).

(3.) T. Kikutani, T. Matsui, A. Takaku, and J. Shixnizu, Sen'i Gakkaishi, 45, 441 (1989).

(4.) T. Kikutani, N. Ogawa, and N. Okui, Polymer Thocessing Society 12th Annual Meeting, p. 315, Sorrento. Italy (May 27-31, 1996).

(5.) T. Kikutani, Y. kawahara, N. Ogawa, and N. Okui, Sen'i Gakkaishi. 50, 561 (1994).

(6.) H. Haberkorn, K. Hahn, H. Breuer, H.-D. Dorrer, and P. Matthles, J. Appl. Polym. Sci., 47, 1551 (1993).

(7.) H. Hirahata, S. Seifert, and H. G. Zachmann, Polymer, 37, 5131 (1996).

(8.) S. A. Mortimer and A. A. Peguy, Textile Res. J., 64, 544 (1994).

(9.) F.-M. Lu and J. Spruiell, J. Appl. Polym. Sci., 34, 1541 (1987).

(10.) Japanese Patent Application 79-1076, P. H. Harris, I. C. I. (1979].

(11.) S. Kase, and T. Matsuo, J. Polym Set., Part-A, 3, 2541 (1965).

(12.) J. Shimizu, N. Okui, and T. Kikutani, High-Speed Fiber Spinning, p. 179, A. Ziabicki and H. Kawai, eds., John Wiley & Sons, (1985).

(13.) R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, p. 95, Buttherworth Publishers, Stoneham, (1988).

(14.) J. H. Dumbleton, J. Polym. Sci., A-2, 6, 795 (1968].

(15.) K. Oda, J. L. White, and E. S. Clark, Polym. Eng. Set, 18, 53 (1978).

On-line measurement of birefringence was performed in the high-speed melt spinning process of poly(ethylene terephthalate) using an apparatus that incorporates a rotating polarizer for the measurement of the optical retardation of running filament. Particular attention was paid to the detailed measurements in the vicinity of neck-like deformation. Through the measurement at the take-up velocity of 5 km/min, development of birefringence under the strain rate up to about 1 [ms.sup.-1] was investigated. To analyze the relation between applied stress and birefringence, tension and temperature profiles of the spin-line were calculated based on the experimentally obtained diameter profiles. Even though the strain rate is extremely high, a linear relationship between birefringence and a parameter calculated by dividing stress by temperature was confirmed to hold up to birefringence and stress/temperature values of about 0.017 and 10 kPa/K, respectively.

INTRODUCTION

Anisotropy is one of the most important characteristics of polymeric materials. The main origin of the anisotropy is the orientation of molecular chain. Mechanical, optical and many other properties of polymeric products can be improved through the control of molecular orientation. Therefore it is important to analyze the mechanism of orientation development through experimental and theoretical investigations of the polymer processing behavior.

High-speed melt spinning is a process in which significant molecular orientation and orientation-induced crystallization occurs. The fiber structure development proceeds under extremely high tensile strain rate which usually is referred to as the neck-like deformation. There have been many attempts for the on-line measurements of the spinning behavior in high-speed melt spinning process [1]. We also have carried out diameter and temperature measurements of the spin-line paying particular attention to the region in the vicinity of neck-like deformation. Through the temperature measurement of the spin-line of poly(ethylene terephthalate) (PET), heat of crystallization was detected near the neck-like deformation [2]. The crystallization rate estimated from this result was [10.sup.4]-[10.sup.5] times larger than that for the isotropic state. The diameter profile of neck-like deformation was investigated in detail by analyzing the signals from multiple diameter monitors [3, 4] and by capturing the image using a sp ecially developed optical system with a CCD camera [5]. It was confirmed through these analyses that the maximum strain rate in the vicinity of neck-like deformation reaches a value higher than 20 [ms.sup.-1].

Similar results of temperature and diameter profiles for the high-speed spin-line of polyamide 6 and polyamide 66 were reported by Haberkorn et al. [6]. Development of fiber structure through the neck-like deformation was also investigated by taking wide-angle X-ray scattering patterns using a synchrotron radiation source [7]. Although there are some papers on the on-line measurement of birefringence in the melt spinning and solution spinning processes [8, 9], detailed investigation of birefringence development in the vicinity of the neck-like deformation has not been reported yet.

EXPERIMENTAL

Melt Spinning

Poly(ethylene terephthalate) [PET] pellet supplied by Toray Industries Inc. was used in this study. The intrinsic viscosity of the polymer was 0.949 dL/g. A polymer with high molecular weight was selected because the neck-like deformation starts to occur from relatively low take-up velocities although sharpness of the neck-like deformation is not so distinct [4].

The PET polymer was extruded from a single-hole spinneret of 0.5 mm diameter at 300[degrees]C. The throughput rate was controlled to 5.0 g/min. The quenching air was not applied to the spin-line. The extruded polymer was taken up by a high-speed winder placed at 330 cm below the spinneret. The take-up velocity was varied from 1 to 5 km/min. The spin-line tension was measured using a tension meter (Roschild, MiniTens R-046). The tension measurement was performed for the solidified region of the spin-line by changing the distance from the spinneret. The on-line measurements of diameter and birefringence were also conducted at various positions of the spin-line. The principle of the measurement is described in the following section.

Principle of Birefringence Measurement

A schematic diagram of the birefringence measurement system used in this work is shown in Fig. 1. The optical system consists of two blocks: a diameter measurement block and an optical retardation measurement block. For the diameter measurement, three diameter monitors (from the top, Zimmer OHG Model 460A/10, Keyence LX2-l00 and Zimmer OHG Model 460A/2) were used. All the diameter monitors are based on the back-illumination principle. The distance between each diameter monitor is 39 mm. The use of multiple diameter monitors enables us to monitor the movement of the position of neck-like deformation (3).

The optical system for the measurement of retardation, which is similar to the one reported in a patent [10], is composed of a He-Ne laser light source, polarizing filters, quarter-wave plates, a rotating polarizing filter, a beam splitter, a beam expander, and photo detectors. Time-course changes of the intensity of reference light [I.sub.ref] (t) and the intensity of light passed through the running filament [I.sub.meas] (t) can be expressed as follows (see Appendix for details):

[I.sub.ref](t) = A [1 - cos2[phi](t)] (1)

[I.sub.meas](t) = A {l - cos[2[phi](t) + [delta]} (2)

where A is the amplitude of light. [phi](t) the rotation angle of a polarizing filter, and [delta] the optical retardation of fiber sample. Birefringence of the spin-line [delta]n can be obtained from [delta] using the following equation.

[delta]n = [delta][lambda]/2[pi]L (3)

where [lambda] is the wave length of light and L the geometrical path for light in the filament cross-section. It is important to note here that only the phase shift a1 can be evaluated by comparing the signals of [I.sub.ref](t) and [I.sub.meas](t). The relation between [delta] and [a.sub.1] is

[delta] = 2[pi]N + [a.sub.1] (4)

where N is the order of interference which cannot be obtained directly through the measurement. In the data analysis, N near the spinneret was assumed to be zero and that at the end part of the spin-line was estimated from the birefringence of as-spun fibers. In some cases, a certain extent of ambiguity remains for the determination of N depending on how the birefringence develops in the spin-line.

The analysis of the phase shift was conducted for [I.sub.ref](t) and [I.sub.meas](t) acquired using an A/D converter and a microcomputer. For the determination of the phase shift, the cross correlation function C ([tau]) of these intensity data was fitted to the sinusoidal function.

C (tau] = [[[integral of].sup.[t.sub.1]].sub.[t.sub.2]] [I.sub.meas] (t - [tau]) [I.sub.ref] (t) dt (5)

C ([tau]) = [a.sub.0] sin ([tau] + [a.sub.1]) + [a.sub.2] (6)

where [tau] is the lag. In each measurement, [I.sub.ref](t) and [I.sub.meas](t) were acquired for 1 second at the sampling frequency of 9 kHz. The rotation frequency of the linearly polarized light coming out from the rotating polarizing filter was 300 Hz, i.e. the rotation frequency of the polarizing filter was 150 Hz. Therefore, one cycle of the light intensity variation corresponds to thirty measurements which is large enough for the evaluation of phase shift. A typical example of [I.sub.ref](t) and [I.sub.meas](t) and the analyzed cross correlation function are shown in Fig. 2.

The measuring apparatus has some other unique features which are worth noting. The laser light for the measurement was expanded only in the horizontal direction using a beam expander consisting of cylindrical lenses. This is to increase the efficiency of data acquisition because the position of spin-line fluctuates in the direction perpendicular to the filament axis. The photo detector was offset 26[degrees] from the primary laser beam to allow the direct measurement of [I.sub.meas](t). In this case, the geometrical path for the light L can be expressed as follows (8):

L = D ([n.sub.f] - cos [theta]/2)/[square root of][sin.sup.2][theta]/2 + [([n.sub.f] - cos[theta]/2).sup.2] (7)

where [theta] is the offset angle, and D and [n.sub.f] (=1.57) are the diameter and refractive index of the spin-line. Although the measurement of retardation was performed at the same position as the second diameter monitor, there was no optical disturbance between these two apparatuses because the wave lengths of incident light and corresponding band-path filter are different, i.e. 730 and 633 nm for the diameter and retardation measurements, respectively.

Measurement of Birefringence in the Vicinity of Neck-Like Deformation

A method developed for the measurement of detailed diameter profile in the vicinity of neck-like deformation (3) was utilized for the evaluation of detailed birefringence profile. The principle of this method is as follows. If diameter measurement is conducted near the position of neck-like deformation using three diameter monitors, the neck-like deformation occasionally passes through the three diameter monitors because of up-and-down fluctuation of its position. In such a case, time-course signals of diameter shown schematically in Fig. 3 may be obtained. From the time difference of the passage of neck-like deformation, which can be evaluated from Fig. 3, and the distance between the diameter monitors, the moving velocity of the position of neck-like deformation [v.sub.n] can be estimated. This moving velocity is applicable for the conversion of time-axis to distance-axis. In other words, the diameter profile of neck-like deformation, i.e. diameter versus axial distance curve, can be obtained by multiplying the abscissa in Fig. 3 by [v.sub.n].

Therefore, if the measurement of phase shift is performed simultaneously with the diameter measurements at the position of the second diameter monitor and with a similiar time resolution, birefringence profile in the vicinity of the neck-like deformation can be obtained. A schematic diagram explaining the condition for the data analysis of the phase shift adopted in this work is shown in Fig. 4. Because of the quick movement and steep diameter change of the neck-like deformation, the phase shift is expected to change rapidly with time. Therefore, data only for 3.3 ms (30 points of measurements), which corresponds to one cycle of intensity variation generated by the rotation of polarizing filter, was used for the phase shift analysis. It was difficult to obtain the phase shift if the time for analysis is shorter than 3 ms because of high noise level of the signal from measurement light. By moving the 3.3 ms time-frame with the step of one data point, change of the phase shift was obtained at the data acquisiti on frequency of 9 kHz. Therefore, the analyzed curve corresponds to the smoothed curve of the 9 kHz data after the moving average operation over thirty data points.

RESULTS AND DISCUSSION

Overall Diameter and Birefringence Profiles

Changes of the phase shift, diameter and birefringence along the spin-line measured in the high-speed melt spinning process of PET at take-up velocities of 2 and 5 km/min are shown in Figs. 5 and 6. In case of 2 km/min, it can be understood easily that the order of interference changed from 0 to 1 at around 200 cm where the phase shift changed from 360[degrees] to 0[degrees]. The birefringence showed a sigmoidal increase and the value obtained at the end part of the spin-line was close to that for as-spun fibers. In case of 5 km/min, neck-like deformation was observed at around 100 cm. Immediately before the neck-like deformation, phase shift started to increase steeply. It is difficult to judge how the phase shift varies in the steepest part of neck-like deformation, however, from the knowledge of the birefringence of as-spun fibers, the order of interference just below the neck-like deformation was estimated to be 3. Below the neck-like deformation, birefringence kept increasing gradually suggesting that t here still is a certain degree of structural change in the spin-line after the neck-like deformation.

Diameter and birefringence profiles for the take-up velocities of 1 to 5 km/min are summarized in Fig. 7. The neck-like deformation was found for the 4 and 5 km/min spinnings, and the birefringence increased steeply at the neck-like deformation. It can be noticed here that even at 3 km/min, there was a concentration of birefringence development at around 160-180 cm where relatively steep diameter reduction occurred.

Diameter and Birefringence Profiles in the Vicinity of Neck-Like Deformation

Changes of diameter, phase shift and birefringence in the vicinity of neck-like deformation obtained from the 5 km/min spin-line are shown in Figs. 8a and 8b. The moving velocity of the position of neck-like deformation analyzed from this data is 0.50 m/s. As can be seen in Fig. 8a, analyzed phase shift increased with the reduction of fiber diameter, and near the end part of the neck-like deformation, a vigorous change of phase shift was observed. As described previously, the order of interference immediately below the neck-like deformation is known to be 3. Considering this, the order of interference was estimated as shown in the figure. Change of the order from 0 to 1 can be found clearly at around 0.22 s. There is another jump in the phase shift at around 0.27 s; however, it is difficult to determine the position of the third jump which is supposed to exist. We assume at present that the phase shift at around 0.27 s is too rapid to detect clearly because the change of order from 2 to 3 occurs soon after t he 1 to 2 change. Variations of phase shift, diameter and birefringence are plotted in Fig. 8b. In this Figure, phase shift after the consideration of the order of interference is shown. Also, the abscissa is converted to the distance along fiber axis by multiplying time-axis by the moving velocity of neck-like deformation. At the early stage of neck-like deformation, birefringence increases gradually with the decrease of fiber diameter. Increase of birefringence accelerates with the reduction of fiber diameter and stabilizes suddenly when the steep deformation finishes. As indicated in Fig. 7, there still remains a gradual increase of birefringence after the neck-like deformation.

Analyses on Temperature and Tension Profiles of the Spin-Line

From the measured diameter at a certain position, filament velocity can be evaluated using the equation of continuity.

W = [pi][D.sup.2]/4 [[rho].sup.v] (8)

Then, the temperature and tension profiles of the spin-line can be analyzed from the diameter and velocity profiles based on the heat balance and momentum balance equations [11].

dT/dx = - [pi]Dh/[WC.sup.p] (T - [T.sup.a]) (9)

dF/dx = W (dV/dx - g/V) + [pi]D[[tau].sub.f] (10)

where F, V, D and T denote the spin-line tension, velocity, diameter and temperature at a distance x from the spinneret, W is the extrusion mass flow rate, h and [[tau].sub.f] are the heat transfer coefficient and the air friction stress, [rho] and [C.sup.p] are the density and heat capacity of polymer, g the acceleration of gravity, and [T.sub.a] the ambient temperature. Parameters and empirical equations adopted for the calculation, which are described in detail elsewhere [2, 12], are shown below.

[rho] = 1.356 - 5.0 X [10.sup.-4]T (g/[cm.sup.3]) (11)

[C.sup.p] = 1.26 + 2.5 X [10.sup.-3]T (J/(g K)) (12)

h = [K.sub.a]/D (0.28 [[R.sup.-0.334].sub.e]) (13)

[[tau].sub.f] = 1/2 [[rho].sub.a] [V.sub.2] (0.66 [R.sup.-0.61].sub.e]) (14)

The temperature and tension profiles of the spin-line were estimated based on these equations consulting measured spin-line tension. The analyzed temperature and tension profiles along with the experimental data are shown in Fig. 9. It can be seen from this Figure that the neck-like deformation at 5 km/min occurs at about 170[degrees]C.

Relation Between Stress, Temperature and Birefringence

The stress-optical law can be derived by comparing the stress tensor [sigma] and the anisotropic part of the index of refraction n for Gaussian chains [13].

n = C[sigma] (15)

Here, the stress-optical coefficient C can be expressed as follows.

C = 2[pi]/45kT [(n + 2).sup.2]/n ([[alpha].sub.1] - ([[alpha].sub.2]) (16)

where n is the isotropic part of the index of refraction, [[alpha].sub.1]-[[alpha].sub.2] the difference between the axial and transverse polarizabilities of the link, T the absolute temperature and k the Boltzmann constant.

Relation between birefringence and tensile stress calculated from tension and diameter profiles of the 1 km/min spin-line is shown in Fig. 10a. Considering the temperature dependence of the stress-optical coefficient, a plot between birefringence and a parameter calculated by dividing the tensile stress by the spin-line temperature is also prepared as shown in Fig. 10b. There is a slight downward concaveness of the curve in Fig. 10a. On the other hand, Fig. 10b gives a fairly good linear line which passes through the origin. Therefore, a log-log plot of the latter type was prepared from the overall diameter and birefringence profiles of various take-up velocities as shown in Fig. 11. It can be seen from this figure that the birefringence and the stress/temperature shows a good linear relationship with a slope of unity up to those values of about 0.017 and 10 kPa/K, respectively. If intrinsic amorphous birefringence of 0.275 is adopted [14], this critical birefringence corresponds to the orientation factor of about 0.06. From the intercept of the straight line, C X T value of 1.66 K/MPa is obtained. This value corresponds to the stress-optical coefficient of 4.8 [GPa.sup.-1] at the glass transition temperature, which agrees well with the reported value [15]. Above this region, there is a steeper increase of birefringence followed by a tendency of saturation at different levels depending on the take-up velocity.

A similar analysis was applied for the data obtained in the vicinity of the neck-like deformation as shown in Fig. 12. In the Figure, the data from the overall spin-line are also plotted. Both data showed good continuity each other. The linearity in the relation between birefringence and stress/temperature is also found to hold up to the birefringence of about 0.02. Smoothed profiles of diameter, strain rate and stress/temperature in the vicinity of the neck-like deformation are shown in Fig. 13. A position in the neck-like deformation corresponding to the critical stress/temperature value is indicated in the Figure. It is important to note that the stress-optical law is applicable up to the critical birefringence even though the strain rate is as high as ca. 0.5 [ms.sup.-1] at the temperature of about 170[degrees]C.

CONCLUSION

An optical system for the simultaneous measurements of fiber diameter and retardation was developed. Using this system, on-line measurement of birefringence in the high-speed melt spinning process was accomplished. It was also possible to measure the detailed birefringence profile in the vicinity of neck-like deformation, and the measurement at the take-up velocity of 5 km/min provided the data on birefringence development under the strain rate up to about 1 [ms.sup.-1]. Temperature and tension profiles of the spin-line were calculated based on the experimentally obtained diameter profiles. These profiles were used for the analysis of the relation between applied tensile stress and birefringence. Even though the strain rate is extremely high, a linear relationship between birefringence and stress/temperature was confirmed to hold up to those values of about 0.017 and 10 kPa/K, respectively.

APPENDIX

Detailed arrangement of the optical system for the measurement of retardation (phase shift) is shown in Fig. 14. Linearly polarized laser light becomes circularly polarized light after passing through a quarter-wave plate, and then changes to rotating linearly polarized light after passing through a rotating polarizing filter. The components of electric vector in x and y directions, [E.sub.x] and [E.sub.y], for this light are

[E.sub.x] = Asin[phi](t)sin[omega]t (17)

[E.sub.y] = Acos[phi](t)sin[omega]t (18)

where A is the amplitude, [omega] the angular frequency, and [omega](t) the rotation angle of a polarizing filter. The time average intensity of the reference light [I.sub.ref](t) can be expressed as follows.

[I.sub.ref](t) = [[E.sup.2].sub.x] = ([A.sup.2]/2)[sin.sup.2][phi](t) = ([A.sup.2]/4)[1-cos2[phi](t)] (19)

On the other hand, the measurement light after passing through the quarter-wave plate is

[E.sub.x] = Asin[phi]sin ([omega]t + [pi]/2) = Asin[pi]cos[omega]t (20)

[E.sub.y] = Asin[phi]sin[omega]t (21)

Therefore, the electric vector components in the directions parallel and perpendicular to the fiber axis, [E.sub.[alpha]] and [E.sub.[beta]], are

[E.sub.[alpha]] = [(E.sub.x] - [E.sub.y])/[square root of]2 = - (A/[square root of]2)sin[[omega]t - [phi](t)] (22)

[E.sub.[beta]] = [(E.sub.x] + [E.sub.y])/[square root of]2 = (A/[square root of]2)sin[[omega]t + [phi](t)] (23)

Since the oriented PET fiber has higher refractive index in the direction parallel to the fiber axis, the light after passing through the fiber can be expressed as follows.

[E.sub.[alpha]] = -(A/[square root of]2) sin [[omega]t - [phi](t) - [delta]] (24)

[E.sub.[beta] = (A/[square root of]2) sin [[omega]t + [phi](t)] (25)

where [delta] is the optical retardation. Therefore, [E.sub.x] component at the photo detector is

[E.sub.x] ([E.sub.[alpha]] + [E.sub.[beta]])/[square root of]2 = - Acos ([omega]t - [delta]/2)sin

[- [phi](t) - [delta]/2] (26)

and consequently the time average intensity of the measurement light [I.sub.meas](t) is

[I.sub.meas](t) = [[E.sup.2].sub.x] = ([A.sup.2]/2) [sin.sup.2] [[phi](t) + [delta]/2] = ([A.sup.2]/4) {1 - cos [2[phi](t) + [delta]]} (27)

ACKNOWLEDGMENT

The authors wish to thank Mr. M. Fukuhara and Mr. Y. Maeda of Toray Industries Inc. for their helpful assistance and discussion during this work.

(*.) To whom correspondence should be addressed.

REFERENCES

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(10.) Japanese Patent Application 79-1076, P. H. Harris, I. C. I. (1979].

(11.) S. Kase, and T. Matsuo, J. Polym Set., Part-A, 3, 2541 (1965).

(12.) J. Shimizu, N. Okui, and T. Kikutani, High-Speed Fiber Spinning, p. 179, A. Ziabicki and H. Kawai, eds., John Wiley & Sons, (1985).

(13.) R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, p. 95, Buttherworth Publishers, Stoneham, (1988).

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Author: | KIKUTANI, TAKESHI; NAKAO, KAZUHITQ; TAKARADA, WATARU; ITO, HIROSHI |
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Publication: | Polymer Engineering and Science |

Geographic Code: | 1USA |

Date: | Dec 1, 1999 |

Words: | 3954 |

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