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Thermodynamics of Processing Synthetic Fibers S. K. MUKHOPADHYAY Department of TextileIndustries University of Leeds Leeds, Ls2 %IT, United Kingdom This paper deals with a new approach to nonlinear and nonequilibrium thermodynamics. The new concept, developed by P. H. Lindenmeyer, states that in a heat-setting process, with the same average processing temperature, the addition of a sinusoidal fluctuation (approximately) can produce two opposite changes depending upon the frequency and amplitude of the temperature fluctuation. Preliminary experimental results obtained on nylon 6 monofilaments using a flexible thermomechanical analyzer have clearly shown that the physical properties (in this case torque-twist modulus) depend not only upon the average temperature but also upon its time rate of change. INTRODUCTION

ost industrial operations in fibers are carried out under conditions of constant or monotonically changing temperature, stress, and other variables. In the industrial heat-setting process, temperature has a crucial role to play on ultimate fiber properties (1). Both mechanical and structural prop erties change on changing the temperature. However, according to Lindenmeyer (2-5), such changes in fiber properties can be significant if a controlled fluctuation of dynamic power (e.g., temperature) is used during processing without changing the average value. Lindenmeyer’s approach, which is based on nonlinear and nonequilibrium thermodynamics, involves a reformulation of the second law, in which entropy production is replaced by a concept of excess energy (4-8). The principal advantage of this reformulation is that the change in excess energy can be measured experimentallyin real time, by the application of dynamic power and the use of modem microprocessor technology (9). This paper introduces an experimental approach and some preliminary results to test Lindenmeyer’shypothesis involving polymeric fibers in a heat-setting process. A torque-twist experimental mode using a method of oscillating specimen temperature at different frequencies and amplitudes was chosen with nylon 6 monofilaments.

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LMDENMEYER’S THERMODYNAMIC APPROACH FOR MATERIALS

Background Survey Basic fiber formation is clearly a steady-state irre versible process (6, 7).which occurs under conditions far from equilibrium. This can be called a nonequilibrium process, and the solidified morphology is known as nonequilibrium structure. From the concept of the second law of thermodynamics, it is

clear that entropy production is very important and can be useful even in a nonequilibrium state. However, the theories are found to be valid only in the linear approximation or near a time independent steady state. Lindenmeyer(5)outlined that in an isolated system the energy dissipation and entropy production are synonymous. When a system can exchange energy, work, or matter with its environment, it is quite likely that energy may be dissipated within the system as a consequence of entropy produced outside the system or vice versa. But if energy dissipation is considered with respect to time evolution of a nonisolated thermodynamic system, the concept of entropy produc tion does not work because it is functionally dependent upon an equilibrium state where it assumes some maximum value. Now if fiber formation or any other high-speed heat-setting process (viz. texturing) is considered, one has to go beyond a linear appro& mation to the time evolution of a nonlinear and nonequilibrium system. Excess Energy

The excess energy of a thermodynamic system is the total Legendre transform of energy with respect to all the extensive variables (8, 10).The concept requires a new kind of free energy function. The excess energy is composed of gradients in the intensive variables along with surface energies, cracks, defects, and any other kind of inhomogeneitiesthat can store more energy than the equilibrium structure. Excess energy can reach a critical level (e.g. by increasing the external forces of the system)where the motion within the system can dissipate less energy to form F’rigogine’s nonequilibrium or dissipative structure. (Note -Dissipative structure is inhomogenous, contains gradients with characteristic sizes. It is formed by

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irreversible processes far from equilibrium and depends upon the history or path by which it reached its present state.) The change in excess energy averaging over the interval of time and over a given volume can be experimentally measured (qualitatively). Fiber Structure and Excess Energy

The fiber structure that results from the solidification of polymer is strongly dependent upon the rate of energy transfer. In return, such structure depends upon the path a polymer follows between quasi-static molten state to equilibrium crystalline room temperature state. According to Lindenmeyer, the nature of such a path, followed by the time evolution, is determined by the minimization of the unaccompanied dissipation of energy. This minimization of energy results from an interaction between flow of energy (e.g. heat) and motion of matter (e.g. work), which gives order from disorder through fluctuations. I t is well known that the strength and moduli of present commercial fibers are well below the theoretical limits. Therefore, it is possible to improve physical properties of such polymers by changing the molecular morphology.

shows the torque-twist hysteresis behavior at 50°C 100°C. and 150°C. A drop in modulus with increasing temperature is characteristic of viscoelastic material. Figure 2 shows the variation between individual cycles at 50°C. This indicates negligible difference in torque-twist behavior after the second cycle (i.e. 3rd and 4th traverse). From unfluctuated results, 100°C was chosen as average temperature and fluctuation in temperature was made on either side of 100°C, changing the ama = 5OoC,

b = 100OC.

c = 150'C

EXPERIMENTAL EVIDENCE TO LINDENMEYER'S APPROACH New Flexible Thermomechanical Analyzer

i

A high-speed flexible thermomechanical analyzer

("FTMA")was successfully used to oscillate specimen temperature at different frequencies and amplitudes. The instrument had flexible control of temperature, allowing rapid heating and cooling ( > lOOO"C/s) with a flexible control of extension and twist. The arrangement of specimen temperature oscillation was made possible by a rapid movement of specially designed hot and cold valves, which in turn changed the proportion of hot and cold air in the heat enclosure. A detailed description of the FTMA and the various methods of its use are published elsewhere (12- 14).

Fig, 1 . Torque-twist hystersis behavior at dizerent ternperature. c y c l e s . a = lst, b = 2 n d , c = 3rd

Materials Used Commercial nylon 6 monofilament of 100-pm diameter was used for experimental purposes. To avoid any influence arising from material's variability, detailed experimental work was carried out on specimens that were preset at 180°C at constant length for 3 h in a ventilated air oven. Experimental Arrangements and Results

The experiment consisted of measuring the torquetwist modulus by twisting the monofilament 5 turns/ cm on either side of zero twist and measuring the difference between the extreme values of torque. A complete traverse between extremes required 10 s, and 10 traverses were made and averaged. Initially, measurements were performed at a constant temperature of 50"C, 100"C, and 150°C. The heating rate was 150"C/s, and gage length was 2 cm. m u r e 1 372

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F Q . 2. Torqut-twist hystersis cycling at 50°C.

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7 h e d y n a m i c s of Processing SyntheticFibers

plitude from f8"C to f48"C using the frequency range of 0.2 Hz to 5.0 Hz. Figure 3 illustrates the torque-twist behavior of the 5th and 6th traverse at an unfluctuated (maximum variation > f 1°C) temperature of 100°C. Figures 4 and 5 show torque-twist curves at the third cycle with temperature fluctuations of f 18°C and f40"C, respectively, at 1 Hz frequency response. Figure 6 shows the torque-twist response of a specimen at the third cycle, changing an amplitude of f30°C at 2 Hz frequency. Details of the results given in Table I indicate a change in torque-twist moduli with changing amplitude at a fKed frequency (phase lag was not considered). A change in frequency also indicates a change in property (Table2).However, at higher frequency ranges (e.g. 5.0 Hz), a wider selection of amplitude could not be achieved because of technical dficulties. Detailed work on an un-preset specimen showed behavior similar to that mentioned above. Figure 7 highlights the behavior of an un-preset specimen at the third cycle, changing f40"C amplitude 1 Hz fre quency response. However, for the sake of clarity, only results of preset specimens have been considered for this paper. DISCUSSIONS

The excess energy averaged over an interval of time and over a given volume can be measured experimentally by fluctuating one or more environmental vari-

ables with controlled frequency and amplitude. A measurable change in excess energy is caused by temperature fluctuations without a change in average environment. The preliminary results (Tables I and 2) in temperature fluctuation have shown the evidence of excess energy. It demonstrated that at the same average temperature, the addition of a sinusoidal fluctuation (approximately) can provide two opposite changes in the properties, depending upon the frequency and amplitude of the temperature fluctuation. From the evidence of this experimental work, it can be concluded that:

(a) the response of a system to fluctuations about the average value of environmental thermodynamic and pseudothermodynamic variables is dependent upon both the amplitude and the frequency of the fluctuations: (b) increasing the amplitude at a constant frequency increases the deviation of the response from that of the response of the unfluctuated variable: and (C) responses similar to (b) may be observed by changing the frequency (owing to technical difficulties, experiments over a wide range of frequencies at constant amplitude could not be conducted). Thus, it appears that the concept of a nonequilib rium free energy function in the form of the excess energy functional, along with its measurement and control by the application of dynamic power, can lead

Flg. 3. Torque-twist cyclic loading at a constant temperature of 100°C. POLYMHl E M W € E R I f f i AND SCIWCE, FEBRUARY 1994, Vol. 34,No. 4

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Fg. 4. Torque-twist cyclic loading (third cycle) at an average temperature of 100°C with a change in amplitude of f 18°C at 1 H z jiequency response.

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Flg. 6. Torque-twist cyclic loading (third cycle) at an auerage temperature of 100°C with a change in amplitude of f30°C at 2 Hz frequency response. Table 1. Torque-Twist Moduli of 100-um-Diameter Nylon 6 Monofilament at an Average Temperature of 100°C: Effect of Change in Amplitude at a Constant Frequency of 1 Hr. Average temp. eC) Amplitude of temp. change PC) Av. torquevalue (N.m.x No. of readings

100

100 k18 3.692 2

Nil

3.785 12

100 22 3.621 2

100 f25 3.534 2

*

100 30 3.488 2

+

100 f40 3.458 2

100 *I45

3.510 2

Table 2. Torque-Twist Moduli of 100-um-Diameter Nylon 6 Monofilamentat an Average Temperature of 100°C: Effect of Change in Frequency at a Constant Amplitude of f22%. Average temp. PC) Frequency of temperature change (H3 Av. torque value (N.m.x 10 No. of readings

100

100

Nil

0.2 3.485 2

3.785 12

100 1 .o 3.621 2

100 2.0 3.704 2

100 3.0 3.781 2

100

5.0 3.82 2

to a method of providing improved properties in the fibrous material.

(15)or constant bulk nonisothermal false twist texturing ( 16).

FINAL REMARK

REmRENCES

The method of oscillating temperature and its intluence on fiber property have been successfully examined. This method predicts that the minimum dissipation of excess energy may improve the fiber spinning or fundamental flber forming processes (e.g., it can increase the maximum draw ratio by fluctuating the straining rate). It is likely that the idea may And application in the texturing process and may improve the heat-setting behavior of fibers. The new t h e m e dynamic concept has also shown more evidence in the form of twist asymmetry in the synthetic fiber

1. S.K. Mukhopadhyay,in Advances in Fibre Science,S . K . Mukhopadhyay, ed., The Textile Institute, U.K.(1992). 2. P.H.Lindenmeyer, Text Res. J.,50. 395 (1980). 3. P. H. Lindenmeyer, private communications (in 1983 and 1984). 4.P.H.Lindenmeyer,Text Res. J.,54. 131 (1984). 5. P. H. Lindenmeyer, A report submitted to the Royal Society, U.K.(1984). 6.P. H. Lindenmeyer, J. Polyrn Sci, Physics, 17, 1965 ( 1979). 7.P.H.Lindenmeyer. Polyrn J.,11. 677 (1979). 8.P.H.Lindenmeyer, Polyrn Eng. Sci. 21. 958 (1981).

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FYg. 7. Torque-twistcyclic loading (third cycle) at an average temperature of 100°C with a change in amplitude of f 40°C at 1 H z frequency response. 9. J. W. S. Hearle, S. K. Mukhopadhyay, a n d P. H. Lindenmeyer, Conference Proceedings, International Sympo sium on Fibre Science and Technology, Hakone, J a p a n ( 1985). 10. E. A. Debloge, Holt R n e h a r t & Winston Inc., New York (1966). 11. I. Prigogine, Introduction to the Thermodynamicsof lrre versible Processes, 3rd Ed., Wiley Interscience, New York ( 1967). 12. S. K. Mukhopadhyay, PhD thesis, University of Manchester, U.K. (1985).

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13. C. P. Buckley, J. W. S. Hearle, S. K. Mukhopadhyay. and M. E. Sikorski, Conference Proceedings, International Conference on Deformation, Yield, and Fracture of Po@ mers, Cambridge, U.K. (April 1985). 14. S. K. Mukhopadhyay a n d J. W. S. Hearle. J. Text InstC tute, 81,No. 2, 156 (1990). 15. S. K. Mukhopadhyay a n d J. W. S. Hearle, to be p u b lished. 16. P. W. Foster, S. K. Mukhopadhyay, R. Jeetah, I. Porat, a n d K. Greenwood, J. Text. Institute, 83, No. 3, 414 (1992).

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