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The effect of temperature and humidity on the mechanical properties of textile fibres Price, Stanley James Whitworth 1955

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THE EFFECT OF TEMPERATURE AND HUMIDITY ON THE MECHANICAL PROPERTIES OF TEXTILE FIBRES STANLEY"* JAMES ¥HITWORTH PRICE A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of CHEMISTRY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE' Members of the Department of CHEMISTRY THE UNIVERSITY OF BRITISH COLUMBIA Apr i l , 1955 - i i -ABSTRACT Forced vibrational experiments and stress relaxation ex-periments have been performed on acetate rayon, viscose rayon, nylon, and polyethylene over a range of humidities at both 2°G and 25°G. Forced vibrational experiments have also been carried out on acetate rayon, viscose rayon, and raw silk over the tem-perature range -80°C to 0°C. Interpretation of previous experi-ments is discussed in terms of both Newtonian viscosity and Eyring viscosity* The apparatus employed is described and a method for calibrating the solenoid of the forced vibrator is outlined* An inverse relation has been found between I1** and the negative . slope of the stress relaxation curve, E°. Since the equation Y) to = T E° derived on the basis of Newtonian viscous units predicts a direct relation between *|UJ and the slope E°, i t is assumed that the flow in stress relaxation must be non-Newtonian* Preliminary cal-culations indicate that a more satisfactory relation between and E° may exist i f the flow units involved in stress relaxation follow the Eyring law of viscous flow* An outline for determin-ing such a relation is given* The experimental 1y observed increase with decreasing temperature of dynamic modulus, stress relaxation modulus, and energy loss, as measured by bcu, is interpreted in terms of increasing order of chain segments. A maximum found at -55°C in the *ju> vs. temperature curve for viscose rayon is - i i i -attributed to a "freezing in" of segment motions as the result of a second order transition* TABLE OF CONTENTS ACKNOWLEDGEMENTS 1 ABSTRACT. .' • i i TABLE OF NOMENCLATURE iv INTRODUCTION 1 A. General Introductory Remarks • .. 1 B. Interpretation of Previous Experiments.. 2 a. Mechanical Analogies •• 2 b. Distribution • • •••• 3 c. Eyring Approach....... • • k APPARATUS AND EXPERIMENTAL METHODS 7 A. Experiments at Various Relative Humidities........ 7 a. Temperature and Humidity Control. 7 b. Stress Relaxation Apparatus. • 7 c. Vibrational Apparatus. 8 B. Experiments at Low Temperatures.• 1 0 C. Calibration of the Solenoid and Determination of Parameters•••• • ••••• 1 2 EXPERIMENTS AND RESULTS..... l£ A. Relative Humidity Experiments 1$ a. Stress Relaxation....• • 1$ b. Forced Vibration..... • 1 6 B. Low Temperature Experiments 19 DISCUSSION 23 BIBLIOGRAPHY 27 - i -AGOOiffliiJIlGEMENTS The author wishes to express his sincere thanks to those •oho have contributed to this work: to the Shell Oil Company for the gift of a fellowship and to the National Research Council for a scholarship, to the Defence Research Board for the basic design of the liquid nitrogen pump and for providing funds for the pur-chase of equipment, to the Department of Mining and Metallurgy for the use of their Leitz projection microscope, and especially » to Dr. B.A. Dunell who, in addition to correcting the manuscript and suggesting a number of improvemsnts in i t , gave invaluable assistance in working up the theoretical discussion. o -iv-TABLE OF NOMENCLATURE Cross-sectional area Empirical constants describing a creep curve Extention modulus (dynamic or static) A constant: the value of a distribution function obtained from stress relaxation Distribution function for moduli of Maxwell units in a continuous array Modulus of "series spring*1 in the three-element model Modulus of "parallel spring" in the three-element model Force exerted by vibrator coil Force amplitude of vibrator Force amplitude at mechanical resonance Gravitational constant Height of vibrator unit suspension Current (milliamperes) Frequency with which an unstressed "flow unit" or seg-ment of a fibre jumps forward multiplied by the ratio of the. distance jumped to the distance between successive jumping segments A spring constant Boltzmann's constant Length of one vibrating filament Mass of the vibrating unit Coefficient of the dissipative force of the vibrator unit alone -V-Rc Electrical resistors used in calibrating the Statham strain gauges S, s Stress S [T) Distribution function for stress supported by Maxwell units in a continuous array t Time x Displacement of vibrator unit x Amplitude of vibration * XJU^ Displacement amplitude at mechanical resonance oc Volume of the Eyring flow unit divided by 23d? Constants which arise in solving a differential equation £ Strain 6, Strain in the dashpot of the three-element model 6' Strain in the "series spring" of the three-element model y\ Coefficient of Newtonian viscosity ~\f Frequency of vibration (cycles per second) **f Relaxation time "C X Upper and lower limits on relaxation time spectrum UOR Resonance value of (JJt£uf = ZTTl/] -1-•INTRQDUCTION A. General Introductory Remarks The physical properties of high polymers are among their most important attributes from the point of view of their practical utilization. Natural, a r t i f i c i a l , and synthetic polymers are used as lubricating oils, surface coatings, films, plastics, papers, and textiles, and i n a l l these cases some physical characteristics of the substance such as viscosity or elasticity are of import-ance. The research reported i n this thesis was undertaken to ex-tend the knowledge of certain of the mechanical properties of polymers over a wider range of temperature and humidity. • Among the most common methods for studying single filaments of textile fibres are stress relaxation, forced, vibra-tion, creep, and constant rate of elongation experiments. In the fi r s t of these methods the rate of decay of stress is measured i n a filament held at constant strain. This decay may be followed by a beam balance system (1, 2 ) or by an electro-mechanical transducer such as a strain gauge (3) or an electronic tube (U). In forced vibration, the filaments may be vibrated longtitudin-ally by a solenoid centered in a radial magnetic field. The frequency of vibration is varied by changing the frequency of the alternating current supplied to the solenoid until the resonance condition of maximum amplitude for minimum current is. obtained. The amplitude of vibration, the current, the vibrator mass, the -2-length of the filaments, and the frequency are recorded and from these quantities the modulus and energy loss may be calculated. Creep experiments are i n a sense the converse of stress relaxation experiments. Here the strain produced by a constant stress i s measured as a function of time. The fourth method, constant rate of elongation, is largely self explanatory. By carrying out experiments at different rates of elongation, different tempera-tures, different humidities, etc.,information may be obtained about the relaxation times of the viscous mechanisms of the f i l a -ment. B. Interpretation of previous experiments a. Mechanical Analogies The mechanical properties of fibres are often represented by a system of springs and dasbpots. Representative of such systems are the Voigt unit for creep, the three-element model for stress-strain cycles j.'and the Maxwell unit for stress relaxation (Fig. 1). For a Maxwell element in stress relaxation the equation for the change of stress with time is S = Sa Ee" T /T , (1) i f i t is assumed that the dashpot operates according to the Newtonian law of viscosity, viz., stress = >f (rate of elongation). However, to f i t experimental data an array of Newtonian Maxwell units (Fig. 1) must be introduced. Such an array leads to the equation M S - j S (X ) d t (2) for the variation of stress with time, where S ( T ) d f i s the partial stress supported by the Maxwell element of the array whose relaxation time is T . For forced vibration experiments each of the filaments may be considered as a Voigt unit, and the equation of motion of the system, tfiich consists of a vibrator unit of mass M with a test filament of length JL and cross-sectional area A attached to each end, i s M dfx + YI £A dx + E 2A x =F0 cos u» t . (3) dt2 1 X d* I Solving this equation of motion for a condition of mechanical resonance and applying some simple corrections, which will be explained later, yields the equations (5) E = M [cju 2 - h g l I- (k) WM> = fFmax - R,u/| A. LXmax J 2A b. Distribution Functions (5) For substances which follow equation 2 'o S (t) = So j E ( T ) e ' ^ d t (6) Here the solution obviously depends on the nature of the distribution of relaxation time, E ( )• Kuhn (6) derived, by consideration of creep data, the distribution E ( T ) = b 1 T > 1 r CAu(cr-/; j t7T t c " ° o<T<c-or when applied under certain restricting conditions -k-E« ( T ) = b a T This distribution i s v a l i d only i n the region 0.01 second to 10,000 seconds since the expression used to evaluate the creep data i s v a l i d only i n this time interval. Another "step function" which has perhaps been more widely used i s E' (log T ) « 2.303 E 0 tJl< X « tm = o _T<.*i.. T > T m This function was used by Becker (7, 8) i n 1938 to represent the decay of magnetic polarization i n iron and more recently has been applied by Tobolsky, Dunell, and Andrews (9) to high polymer Systems. These workers have shown that i f the stress relaxation curve i s approximately linear over a wide range of logarithmic time, the height of the distribution function E 1 (log T ) at any time i n this range i s equal to the negative slope of the relaxa-t i o n curve plotted on a logarithmic time basis. These workers have also shown that i f the above line a r i t y exists, the value of Y\w should be related to the negative slope of the relaxation curve by the equation yj u» s TT (negative slope of the stress 4.6o6 relaxation curve) (7) c. Eyring Approach Eyring has discussed the use of elements similar to those shown i n Fig. 1, but employing mon-Newtonian dashpots, to describe the mechanical behavior of t e x t i l e fibres (10)• He assumes that change of shape i n fibres involves flow units exchanging old -5-neighbours for new and that even when no forces are acting such processes are going on* If stress is placed on a fibre these processes are unbalanced and accelerated in the direction of application of the stress. Consider a three-element model with Hookean springs but a non-Newtonian dashpot. Let the dashpot be defined by the two parameters 0 6 and K where oc is the volume of a flow unit divided by 2kT and K represents the frequency with which an unstrained segment jumps forward multiplied by the ratio of the distance jumped ( A ) to the distance between successive jumping segments ( A, )• If the cross-sectional area of a flow unit is Ax A3 and the stress acting on the unit is s, then in jumping forward through the distance A an amount of work S A t \ 3 A is done. The unit, in moving forward, presumably will go through an intermediate state of higher energy at the distance A/a # This assumes a symmetrical potential barrier. Thus the applied stress only contributes the work S ( A 2 A3 \ / z ) toward surmounting the barrier. If the flow unit moves against the applied force, i t will have to do this same amount of work against the applied stress. As a result, the flow unit moves in the forward direction (+) and in the backward direction (-) • times per second. The forward velocity of a flow unit i a the K _A, 2 X exp net number of times i t moves forward times the distance, A i t jumps - that is, -6-The resulting rate of strain is obtained by dividing the velocity by the distance i n the flow direction between point of flow ( A t )• Since the difference of exponentials in the velocity relation i s twice the hyperbolic sine of the argument, the hyperbolic sine law for rate of strain d€ K sinh ©< s (8) dt i s arrived at. Now, i f 6,' is the strain in the spring of a Maxwell element and 6, is the strain on the dashpot of this element then S = E ^ ' (9) and d6, = d_£ - _1 ds ( 1 0 ) dt dt Ej^  dt By the hyperbolic' sine law d6 , = K sinhotS ( 1 1 ) dt Substituting ( 1 0 ) into ( 1 1 ) and considering the special case where o_€ is zero that arises in a stress relaxation experi-dt ment, we get _i as = K sinh eC s ( 1 2 ) \ dt If the Maxwell unit under discussion i s now considered as the i th element of an array, the equation for stress i n the element i s , , - 1 r *<i KE • t n $ . « _ 2 _ tanh [ e 4 Tanh ~ i 1 ° * * 2. . ( 1 3 ) and the total stress on the array i s s « 21 s i (Hi) ( -7-APPAKATUS AMD EXPERIMENTAL METHODS t A. Experiments at Various Relative Humiciities a. Temperature and Humidity Control The experiments -were performed i n a constant tempera-ture room, controlled to within * 0.5°C by thermal regulators which govern the operation of. a Bush unit cooler and two 1000 watt heaters. A blower fan maintained good a i r circulation throughout the room. Control of humidity was accomplished by s p l i t t i n g an a i r stream and passing one portion through s i l i c a gel and the other through a water saturating column packed with porcelain saddles. The dried and the saturated a i r were then mixed i n appropriate proportions to give the desired relative humidity and the mixed stream circulated through jackets surrounding the test apparatus. In the f i r s t experimental run following regeneration of the s i l i c a gel i t i s possible to obtain humidi-ties of 15% at 25°C Examination of the available methods, with their limitations, for measuring relative humidity had led i n previous work (U) to the use of a wet - and dry - junction thermo-couple. This method proved satisfactory and has continued i n use. b. Stress Relaxation Apparatus The experimental c i r c u i t for stress relaxation i s shown i n Fig. 2. While only one Statham strain gauge i s shown, -8-the apparatus actually employs three such gauges, thus allowing three filaments to he tested i n any one experiment. The cathode-ray oscillograph i s connected only long enough to obtain a photographic record of the f i r s t second of stress decay, after which time i t i s replaced i n the c i r c u i t by the Rhodes potentio-meter. The release mechanism to trigger the filament clamp i s identical to that used i n previous work (li). Calibration was carried out by means of the calibrating resistors R c (Fig. 2 ) . By the use of seven such resistors, a complete calibration curve could be obtained i n only a few seconds. Such a calibration was made after each experiment and was checked periodically by comparing the response of the gauge i n this resistor calibration to the response to standard weights applied to the gauge, c. Vibrational Apparatus The vibrator used for the observation of dynamic modulus and viscosity i s of the forced resonance type i n which tne test filaments are vibrated longbitudinaliy by a solenoid of Formex magnet wire wound on a paper core cemented to an aluminium disc and spindle and centered i n a radial magnetic f i e l d . This transducer i s supplied with current from a Hewlett-Packard low frequency oscillator and i s thus made to vibrate longtitudinally ( i . e . i n the direction of the filament length) with a sinusoidal motion at the frequency set by the osc i l l a t o r . This apparatus i s essentially the same as that used by Dunell and Dillon (j?) and by Mclntyre (11). Ihe test -9-filaments, together with the solenoid and i t s mounting (trans-ducer) may be "tuned" to mechanical resonance by adjusting the frequency of the vibration* At such a condition of resonance the ratio of amplitude of vibration to current i n the solenoid i s a maximum. The resonant frequency can be varied by changing the vibrating length of the filaments and the mass of the trans-ducer. At resonance the current i n the solenoid i s measured by a Weston thermocouple milliammeter. The amplitude of vibra-ti o n i s measured by observing the apparent increase i n the length of a recessed portion of the transducer spindle with a travelling microscope which measures to within 0.0001 cm. The length of the filaments, the mass of the transducer, and the frequency of vib-ration are also determined. From these measured quantities the dynamic modulus and viscosity can easily be calculated (equations During the course of a vibrational experiment with any one pair of filaments, the vibrating length of the filaments i s changed several times by clamping them at different points along their length. Since the whole apparatus must b e enclosed i n a box to control the humidity of the system, this clamping ana un-clamping must be done by remote control from outside the enclosing box. It has been found convenient to accomplish this by using the mutual attraction and repulsion of l i t t l e Alnico horseshoe magnets. To the upper verti c a l l y movable portion of the filament clamp two horseshoe magnets are fixed side by side with tneir -10-like poles adjacent to each other. Immediately above these, and on tne outside of the brass top of the box which encloses the filament, two other norseshoe magnets are mounted. -When the filaments are to be i'imuy clamped at a certain point along their length the top pair of magnets are placed with their- noi-oh poles opposite the north poles of the lower pair and their south poles opposite the south poles of the lower pair. When the position of the clamps is to be altered, the lop pair of magnets is turned about so that north poles are above souths and souths above norths; the upper clamp is thus lifted clear of the filament, and the clamp can be moved along the length of the filament to a new position* Cork liners are used on the clamping surfaces to prevent slippage* B. Experiments at Low Temperatures Only forced vibrational experiments were done at low temperatures, and for this phase of the research new vibrational apparatus was constructed. The transducer unit and the measur-ing instruments are identical to those used in the relative humidity experiments. The enclosing boxes and clamping system are however quite different. The boxes consist of double lucite cases with the 3/k inch gap between the inner and outer cases filled with rock wool insulation. Instead of one movable clamp, as in the vibrational apparatus used for the relative humidity experiments, five separate clamps were so placed as to enable filaments of 61 cm., 31 cm., 16 cm., 11 cm., and 8.f> cm. to be vibrated* Starting at the 6 l cm. position, the height of the -11-bottam half of the clamps diminishes by one sixteenth of an inch per clamp, so that when the fibre is clamped down in any position the clamps at the shorter lengths do not interfere with the vibration of the filament. The upper portion of each clamp is attached to two lucite rods so that i t may be raised when i t is not in use* The faces of the clamps are tapered so that the area of contact between the upper and lower halves is only 0*1+ cm • When a particular clamp is in use i t is held firmly down by a flaSk containing 6 0 0 grams of mercury set upon a platform which fits the tops of the lucite clamp rods* All openings through the boxes are lined with lucite tubing to prevent moisture from entering the insulation* The enclosing boxes and the clamps were built completely of lucite and an acetone solution of lucite shavings was used as a cement* The desired low temperatures were obtained by use of liquid nitrogen vapour* A "liquid nitrogen pump", which consists in essence of a heater immersed in the liquid nitrogen, was used to force the cold vapours through tygon tubes insulated with glass wool into the boxes enclosing the filaments* At first a Cenco bimetallic thermoregulator was used to control the tempera-ture* However, this gave control only within 1 2*5°C and was soon discarded when i t was found that control within - 0*1°G could be obtained even at -80°C by regulating the current supplied to the heater and hence the flow rate of the cold nitrogen -12-vapours• The tables of Roeser and Dahl (12) were used to determine the temperature from the emf generated by iro n -const ant an thermocouples* Two sets of couples were employed* The measuring couple of the f i r s t set was fixed i n position at the £0 cm* fibre position of the l e f t hand box* The measuring couple of the second set was loose and could be placed at any position i n either box* An insulated ice-water bath was used to keep the reference junctions of both sets of thermocouples at 0°G. G* Calibration of the Solenoid and Determination of Parameters* The solenoid, or vibrator unit, was calibrated so that the force i t exerts can be determined from the current that i s put through i t . To do this the whole apparatus was set up with i t s axis v e r t i c a l , and the vibrator unit was suspended i n the mag-netic f i e l d from a linear calibrated spring* The vibrator and spring were then loaded with a succession of analytical weights and after each addition, the vibrator unit was brought back to approximately i t s unloaded position by passing a direct current through the solenoid c o i l . The current, I, and the distance, A x, between the loaded and unloaded positions of the vibrator unit were measured and the force was calculated from the equation F » Mg + k» A x (15) where g = gravitational constant k' • the modulus of the spring. The plot of F against I (Fig. 3) gives a straight l i n e of slope y dynes per milliampere. An alternating current whose root-mean-square value, read off the a-c. milliammeter, i s I exerts - 1 3 -a maximum force Fe = sfT V I. It is this maximum force which is used in the calculation of ^ u> . Once the solenoid has been calibrated the effective mass M of the transducer system may be calculated from the equation of motion M d* x + R dx + Px » F 0 cos u> t ( 1 6 ) "cTF dt where R - 2A ^ + ^ (17) and P » 2A E + PT (18) X P^  m Mg/h is a correction for the vertical displacement of the vibrator unit during horizontal vibration while is a correction for dissipative forces other than those present in the filaments. The steady state solution of equation 1 6 is x B oL1 cos cu t + /^'sin tw t ( 1 9 ) where ot'. F. (H^.p) (20) and P m F° B u ' (21) Differentiation of (19) with respect to time and use of (20) and (21) shows that the displacement amplitude is x c - F. [ (M u,x -P) 2 + R 2 W * J -V2 ( 2 2 ) In equation 22, Rw is negligible compared to M to3" - P for values of IP which are not too close to ur, • Hence a plot of t (v r c * max against U > x should give a curve which deviates from a straight line only near resonance, the slope of the straight line portion being M, the effective mass of the vibrating system. This curve is shown in Fig. U. For the freely vibrating system the equation of motion is M d * * + * * + p i x = 0 (23) dt*" 1 dt x Examination of the solution of this equation yields the relation R a M UJ in T (x max) m ] 1 n TT L (x max) m + n J (2k) from which can be calculated by measuring the decrease in amplitudes during "n" vibrations which occur in time t. -15-EXPERIMENTS AND RESULTS A. Relative Humidity Experiments a* Stress Relaxation Filaments of acetate rayon, viscose rayon, nylon, and polyethylene have been tested at various relative humidities at both 2°G and 25°G, The upper end of the filament to be tested was attached to a movable clamp which was held against the action of a spring by an iron bar. The bottom of the filament was then wrapped several times between two clamping nuts on the arm of the strain gauge. The temperature and humidity units were turned on and adjusted to produce the desired atmospheric conditions. After four hours the filament was placed under just sufficient tension to hold i t straight, the clamping nuts were tightened together, and a spot of glue was applied to glue the fibre to the nuts. The filament was allowed to condition for a further 16 hours before the experiment was carried out. After this conditioning period the filament was elongated to a predetermined strain by removing the iron "trigger" by means of an electromagnet. A record of the decay of stress in the first second was obtained by photographing the screen of the cathode-ray oscillograph. Subsequent readings were taken from the Rhodes pot-entiometer until two hours and forty-six minutes (10,000 sec.) had elapsed. Readings were thus obtained over six cycles of log-arithmic time. Actually three filaments were tested in any one experiment. The second filament was stretched forty minutes after the first, and the third, fifty minutes after the second. This overlap of running times was made possible by a k-bank-3-position switch which allows rapid change from one circuit to another. The -16-calibration was checked at the end of each experiment but showed practically no variation daring the course of this work* The stress relaxation curves for the four fibres are given in Figs. $9 6, 7, and 8* The negative slope of these curves is shown as a function of relative humidity in Figs* 9, 10, 11, and 12 and for three of these filaments as a function of moisture regain in Figs. 13, It;, and 15>* Several well defined trends have been found. First, for any one temperature the Slope of the stress relaxation curves increases with decreasing relative humidity. This change of slope is gen-erally greatest for viscose rayon although i t is also very rapid for acetate rayon at 2f>°C in the region below h0% relative hum-idity* The initial modulus at a given temperature was also found to increase with decreasing relative humidity* For a given rel-ative humidity and probably also for a given moisture regain, the slopes of the stress relaxation curves for nylon and the two rayons increased with decreasing temperature* Polyethylene appears to be an exception to this pattern but the variation of slope with relative humidity and temperature for this fibre is probably within the limits of experimental error, b. Forced Vibration Filaments of nylon, polyethylene, viscose rayon, and acetate rayon have been tested at various humidities at both 2°C and 2£°C. The filaments to be tested were mounted loosely in the apparatus and the temperature and humidity control units were turned on. After a minimum period of 16 hours at the desired at-mospheric conditions to allow the filament to come to equilibrium with its surroundings, a tension of 0.5 gram per 1 (10 c m2. ft -17-cross-sectional area was applied and the fibres were allowed to creep for 18 to 20 hours. It has been shown, that after such a period' under constant tension the dynamic parameters are sufficiently con-stant with time that no appreciable change occurs during the time required to complete the experiments on the fibre (J>). The hum-idity was checked periodically during the conditioning period and was under constant observation during the run. In all runs the initial vibrating length of each filament was 60 cm. and the initial mass of the transducer 57.16 grams. Increasing resonance frequencies were obtained by reducing this mass in several steps to $.kk grams and then by shortening the vibrating length of the fibre. The cross-sectional areas of the filaments were calculated from the denier and the tabulated density values of l.lU gm/cc. for nylon. l.£0 gm/cc. for viscose rayon, and 1.33 gm/cc. for acetate rayon (13), and a measured value of 1.01 gm/cc. for po]yethylene. In these experiments, a new specimen from the Same continuous-filament sam-ple was taken for each run at each hundditjy. The experimentally determined values of dynamic modulus as cal-culated from equation k are shown in Figs. 16, 17, 18, and 19. With the possible exception of polyethylene, which shows very l i t t l e change in its properties with variation of relative humidity, dynamic modulus was found to increase with decreasing relative hum-idity at both 2°G and 25°G. This effect was greatest for viscose rayon. For a given relative humidity the dynamic modulus increased with decreasing temperature for acetate rayon, viscose rayon, and polyethylene. Nylon does not appear to follow this pattern but since -18-filaments from an entirely different source to that of the nylon used in the remainder of the research was used for the vibrational ex-periments at 25° C, no definite conclusion can be reached (lli). The values of dynamic modulus at 2f>°C for acetate rayon, viscose rayon, and polyethylene show excellent agreement with those of Dunell and Dillon (£)• The values for nylon are in good agreement in the region of 10 cycles per second but show a decrease with increasing frequency not found by these workers* In view of the agreement obtained with the results of Dunell and Dillon for the other fibres this difference is difficult to explain* Since the results of Dunell and Dillon cover a much wider range of frequencies and are not as scattered i t must be assumed that i f any error exists, i t is in the present work* The values of )jw shown in Figs. 9, 10, 11, and 12 as a func-tion of relative humidity and in Figs. 13, Ik, and 15 as a function of moisture region were calculated using equation 5* For any one temperature all four types of fibre tested showed as increase in >|W with increasing relative humidity • For a given relative humidity vis-cose rayon and polyethylene show an increase in )} «*/ with a decrease in temperature. Although the variation of l\u> with relative hum-idity is small for polyethylene the change with temperature is quite large. Undoubtedly the most suprising fact, however, is the small change in with variation of humidity found for viscose rayon, a fibre in which the other properties tested were extremely sensitive to humidity variations. Within the range of humidities used in the experiments, l\w at a given relative humidity was also found to in-crease with decreasing temperature for acetate rayon. It would appesr, -19-however, that extrapolation of the curve for 2°C would reverse this pattern for relative humidities below k$%» This reversal would not occur i f the curve for acetate were drawn through the points at $h% R.H. and 62% R.H., and allowed to curve up sharply in the region .above 90% R.H. Nylon, because of the previously mentioned differ-ence of source, cannot be compared quantitatively with regard to temperature variation of the properties tested. However, the mois-ture regain curve for this fibre does show an increase in ^ UJ with decreasing temperature for a given moisture content of the fibre. The variation of Y\ with frequency is shown in Figs. 2 0 , 2 1 , 2 2 , and 2 3 . The straight lines drawn with a slope of - 1 indicate constant >?<0 and are included for comparison with the experimental results. B. Low Temperature Experiments Filaments of acetate rayon, viscose rayon, and raw silk have been tested over the temperature range -80°C to 0°C. The filaments to be tested were mounted in the apparatus and for viscose rayon 6 2 and acetate rayon a tension of 0.5 gram per 1 ( 1 0 ) can • cross-sectional area was applied. In the case of raw silk a tension of 0 . 1 3 gram per 1 ( 1 0 ~6) CB^t cross-sectional was used. The fibres were allowed to creep for 18 to 2 0 hours at room temperature (5). The filaments were then cooled to the desired temperature at a rate of approximately one degree per minute. The filaments were allowed to condition for thirty minutes at this temperature. The temperature was checked periodically during cooling and was under constant observation during the run. In all runs the initial length of each filament was 6l cm. and the initial mass of the transducer U 7 . 06 grams. Increasing resonant frequencies were obtained by reducing this mass in several steps to U . 2 3 grams and then by shortening the vibrating length of the fibres. -20-The cross-sectional areas of the acetate rayon and the viscose rayon had previously been calculated for use in the relative humidity experiments. The diameter of the raw silk was determined by three independent observers using a Leitz projection microscope* In these experiments a new specimen from the same continuous filament sample was taken for each run at each temperature* The values of dynamic modulus which are shown in Figs* 2k, 25* and 26 were calculated using equation k. For a l l three materials the modulus was found to increase with decreasing temperature* The modulus of acetate rayon at -80°C was found to be .about 2$% greater than the modulus of this fibreat 0°G* Both viscose rayon and raw silk showed approximately a h0% increase in this parameter over the same temperature range* The moduli" of the three fibres tested failed to show any marked dependence on frequency* Comparison of the values of modulus for acetate rayon and viscose rayon observed in this low temperature work at 2°C with moduli observed in the previous varying humidity experiments at 2°C indicate that the moisture content of these fibres must be very low* Since these fibres can always be regarded as in equilibrium with.the air immediately surrounding them (15) and since the vapour from liquid nitrogen is presumably free of moisture, this apparent conditions of the fibres seems quite reasonable* The values of modulus and, as will be mentioned later, the values of V\ «A> found for silk are nearly an order of magnitude less than the values of Dunell and Dillon at 21°C and 65% B.H* (5)* . Since decreasing the humidity and decreasing the temperature should both increase the modulus, i t can only be assumed that the silk used in these experiments is of an entirely different type to that used by these workers* -21-The values of >\u> calculated from equation 5 are shown in Figs* 27, 28, and 29* For acetate rayon these values increase linearly with decreasing temperature* The values for raw silk and viscose rayon, however, exhibit a very interesting pattern* As can be seen from figure 28 the value of ^ tu for viscose rayon increases linearly until a value of 8*9 x 10 dynes per cm.2 is reached at -U0°C. The curve then becomes slightly concave - up until i t levels off be-tween -J>0°C and -5&°C, below which temperature i t falls off sharply finally levelling out in the region of -65° C at a value of t{ ut approximately the same as that found at -10°G. The number beside each experimental point on the curve of Fig. 28 indicates the number of reproducible runs the point represents. The letter n s n indicates that the point does not represent a complete run but only a single determination of >jio made as part of a "spot run" covering a range of temperatures. A pattern of )|u» values similar to that found for viscose rayon seems to have been found for raw silk. However the author does not feel that the results for silk are at all conclusive. Only six of the points represent a complete experiment. The values at -30°G and -k0°C are single determinations made as part of a "spot run". Also since the current needed to produce a convenient vibration was small compared to the current required in the case cf the rayon, slight disalignment of the vibrator would introduce serious errors into the value of >fu» for raw silk. In view of these facts acceptance of the curve shown in Fig. 29 should be very tentative. The variation of ^  vibh frequency is shown in Figs. 30, 31, and 32. As in the relative humidity experiments, the experinent al results are compared with the straight line of slope -1 that would result i f TJu> were independent of frequency* The variation of >f W with amplitude for viscose rayon and raw silk is shown in Figs* 33 and 3h» Apparently a smaller force per unit of strain is needed as the amplitude of vibration is increased although for strains greater than 0*0015 this change of force is quite small* -23-DISCUSSION From consideration of mechanical models employing Newtonian dashpots Dunell, Tobolsky, and Andrews (?) derived the relation W U J » 7T E° (25) where E°, a "step" distribution function of relaxation times, is equal to the negative slope of the straight line portion of the stress relaxation curve between a minimum and a maximum relaxation time, TT^  and T„, and is zero outside these limits. Since the experimental results of this thesis as well as the results of previous work done in this laboratory (U, 11> 16) show an inverse relation between Wu; and the slope E° as relative humidity is varied, equation 25, which predicts a direct relation between H ^  and E°, not only fails to give better than order of magnitude agreement between these quantities but even fails to give qualitative agreement. The viscous units involved in stress relaxation may therefore be non-Newtonian. Preliminary calculations have shown that the use of Eyring viscous units may lead to a more satisfactory relation between the slope of the relaxation curve and tyu) • Consider the following procedure for determining the stress relaxation curve corresponding to an experi-mental value of when i t is assumed that the viscous units involved in a stress relaxation experiment are Eyring units. From this experimental value of for a given relative humidity, pre-dict from equation 25 a slope, -E°, for a stress relaxation curve based on Newtonian elements. It is assumed that since Eyring viscosity reduces to Newtonian viscosity for the case of small stresses, - 2 U -such as are involved in the vibrational experiments, that the ob-served fu> values should be predictable from Newtonian parameters* Extrapolate the experimental stress relaxation curve for the same humidity to zero stress to obtain a value of T n . From the curve of va. E°, for the appropriate constructed from sets of curves similar to those shown in Fig* 3 5 , obtain a value of tyi • Since the curves of Fig* 3 5 are drawn for a constant Yf{ , the value of r\(°*i obtained from the relation rii- _i ( 2 6 ) K ocL (which may be derived by making °C s in equation 1 1 small) will also be constant* Now since, from the definition of the relaxation time in these systems, values of E^ can be calculated for values of f4- between ^  and , From the theoretical data used to plot Fig* 3 6 i t is estimated that ^ should be less than . 0 0 0 2 seconds* Assuming that the strain on a segment of the fibre is the same as the overall strain we write • * i - * (28) and (s 0). may be determined from the relation (s«). » ( 6 •£•• = £ E'-• ( 2 9 ) Now, by choosing a value for ©C , a theoretical stress relaxation curve may be plotted by calculating values of stress from equations 1 3 and lJU* From a number of trials the value of oC which gives the best theoretical agreement with the experimental results can be deter-mined* If the above procedure is now repeated for the same fibre at a different relative humidity i t is possible that the calculated slope of the stress relaxation curve will be found to decrease as y^U) increases* -25-The decrease of modulus with increasing temperature and in-creasing humidity can be interpreted in terms of the work of Freund and Mark (17 )• These workers found that for nylon, polyethylene, and acetate rayon the extent of ordered arrangement of the chain molecules was decreased with swelling at constant temperature or by heating at constant stress* The small variation of the modulus of polyethylene with relative humidity is possibly due to too short a conditioning period* From the data of Deeg and Frosch (18) i t has been estimated that i f the acetate rayon samples used required one minute to reach moisture equilibrium with their surroundings, the polyethylene used would have required I4.8 hours* Previous discussion has shown that increasing values' of the resonant frequency can be expected as the temperature is decreased* Since the viscosity coefficient would also be expected to increase with decreasing temperature, i t seems quite reasonable that 7£ UJ should increase with decreasing temperature* That this decrease of tyu» with increasing temperature should be linear for acetate rayon over the experimental range of temperature and for viscose . rayon- from -1*0°C to 0°6 is somewhat surprising since ^  is an exponential function of temperature* That is, Yf.- i (e B / k T ) (30:) where 8 is an energy terra* It must be considered, however, that as the temperature decreases the extent of order of the chain molecules increases, thus allowing the distance between some of the groups con-tributing to secondary interchain forces to decrease* The increase in magnitude of these secondary forces resulting from this decrease of distance may be sufficient to cause some of the viscous flow elements -26-to become fixed and hence in terms of a mechanical model, change from dashpobs to springs. The resulting decrease in the number of units contributing to ^  as the temperature is decreased might give rise to the linear relation found experimentally. However, on the basis of this reasoning alone the maximum in bu> found at quite low tempera-ture for viscose rayon and possibly also for raw silk would certainly not be expected. Nolle (19) has found a similar maximum in the curve of #u> for Buna-N gum vulcanite at -5>°C. Here V is a coefficient of viscosity closely related to • Furthermore his curve for modulus versus temperature is of identical: form to that shown in Fig. 37 for viscose rayon. Sack et al. (20) have found a maximum in the mechanical loss curve for butadiene-styrene copolymers at or below -20°C. For the various copolymers tested the temperature at which the maximum in the energy loss curve occurred was approximately the same as the temperature of the second order transition of the mater-i a l • It is assumed by these workers that below this temperature the segments of the chain molecules "freeze in" and are no longer able to orient as freely as they can above this temperature. They conclude from this that the relaxation phenomena responsible for energy loss are linked to this segment mobility. The observed variation of ^u> with amplitude does not agree with the results of Dunell and Dillon (9). Since the shape of the >| ui versus amplitude curves change only slightly over the experi-mental range of temperature i t appears quite probable that the dissipative forces other than those occurring in the fibre must be slightly larger than the measured value of would indicate. -27-BIBLIOGRAPHY ANDREWS, R.D., HOFMAN-BANG, N. AND TOBOLSKT, A.V. J. Polymer Sci. 3*669. 19U8. 2. TOBOLSK!, A.V., PRBTTYMAN, I.B. AND DILLON, J.H. J. Applied Physics 15:380* 19^. 3. BURLEIGH, E.G. AND WAKEHAM, H. Textile Research J. 17*2U5. 19U7. U. PRICE, S.J. B. A. Thesis. University of British Columbia. 1953. 5 . DUNELL, B.A. AND DILLON, J.H. Textile Research J. 21:393* 1951. 6 . KUHN, W., KUNZLE, 0 . AND PREISSMAN, A. Helv. Chim. Acta. 30:307, U6U, 839. 19U7. 7. BECKER, R. Problems der technischen Magnetisierungskurve. Springer, Berlin. 1938. p. 103. 8. BECKER, R. AND DORING, W. Ferromagnetismus. Springer, Berlin. 1939. p. 25U. 9 . DUNELL, B.A., TOBOLSK!, A.7. AND ANDREWS, R.D. Textile Research J. 21:l*0tu 1951. 10. HALSET, G«, WHITE; H.J. Jr. AND STRING, H. Textile Research J. 15:295. 19U5. 11. McINTXRE, A.D. M.A. Thesis. University of British Columbia. 1952. 12. ROESER, Wn. F. AND DAHL, A.I. J. Research Natl. Bur. Standards. r 20:337. 1938. -28-13. MA.UERSBERGER, H.R. Textile Fibres. John Wiley and Sons. Inc., New York. p. 17. lU. FULLER, G.S., BAKER, W.D. AND PAPE, N.R. J. Am. Chem. Soc. 62:3275- 19U0. 15. CASSIE, A.B.D. Trans. Faraday Soc.-Discussions. 3:239. 19U8. 16. PATTISON, J.P. M.A. Thesis. University of British Columbia. 1952. 17. FREUND, E.H. AND HARK, H. Rayon Textile Monthly. 23:515, 605. 19U2. 18. DEEG, G. AND FROSCH, C.J. ASTM Symposium On Plastics. 191*U. p. U7. 19. NOLLE, A.W. J. Polymer Sci. 5:1* 1950. 20. SACK, H.S. IAUB, H.L. AND WORK, R.N. J. Applied Physics. I8:k50. 19U7. Figure 1. Models used i n describing the mechanical properties of high polymers Parallel array of Maxwell units ± zero < L d : adjust; Rhodes potentiometer transducer 1*1 D» C 0 preamplifier 1 K £_ J i ^ — » I M — i -U-U 9T1000K 90V Figure 20 Electrical c i r c u i t for measurement of stress relaxation Current (milliamperes) o r H I o e 1 < 3 w CO Figure 6. Stress relaxation for single filaments of acetate rayon 2"C, 30$ R.H. 2°C, $0$ R.H. 25°C, 20$ R.Ho 25°C, U6$ R.H. 2°C, 97$ R.H. 97$ R.H. 1 ,01 .10 loO 10 100 1000 10000 0.1 1.0 Time (sec 10 Figure 7» Stress relaxation for single filaments of nylon 16$ R.H., 2$°C h0% R.H. 2°C 65$ RoHc, 2°C 53$ R.H., 25°C 8k$ R.H., 2°C 100 J 1000 I 10000 i  97$ R.H., 25°C 0% 20% hO% 60% 00% 100% Figure 9« Variation of T\IV and the slope of the stress relaxation with relative humidity for acetate rayon fielative humidity 0% 20% hO% 60% 80% 1 0 0 Figure 1 0 » , Variation of Y\OJ and the slope of the stress relaxation curve with humidity for viscose rayon_ °% 20$ k0% 60% Q0% 100% Figure 11. Variation of Y\CU and the slope of the stress relaxation curve with humidity for nylon i 1 1 r 0% 20% U0% 60% 80% 100% Relative humidity Figure 12 0 Variation of r t^u and the slope of the stress relaxation curve with humidity for polyethylene 0% h% % 12% 16% 20% Figure 13. Variation of and the slope of the stress relaxation curve with moisture regain for acetate rayon Moisture regain ( % dry weight) I I I I : I 0% 10% 20% 30% k0% 50% Figure l k o Variation of and the slope of the stress relaxation curve with moisture regain for viscose rayon Figure l6o Dynamic modulus vs» frequency for acetate rayon X Co X x # • • x x Sh% RoHo, 2 C O • _ 6.0 |~~ § . • O • # 62$ R.H., 2°C 5.0 U.5 o o o • <? a o D CI U5$ R.H., 25°C S A 0 Q 15$ R.H., 25°C 5»5 f"~ | A 79$ R.H., 25°C T 3 + 97$ R.H., 2°C J L ~^ Cycles/sec. 10 20 30 50 70 100 16 e o a -a o 12 T3 10 Figure 17. Dynamic modulus vsofrequency for viscose rayon X O o X o X o X o X 65% R.Ho, 2°C ° k6% R .H. , 2$°C » 73$ R.H. , 2°C + 97$ R.H. , 2°C 81$ R.H., 25C J L ~^ (cycles/seco) 10 20 50 100 Figure 180 Dynamic modulus vs. frequency for nylon X X a A X • + 0 A O 28$ R.H., 2£°C X X ii8$ R.K., 2°C + l & R . H . , 2°C 98$ R.H., 2°C Q O R.H e , 25 C A A 83$ RoH., 25°C (cvcles/seco) _ l L 10 20 30 50 2,2 1.8 r Figure 19° Dynamic modulus vs» frequency for polyethylene X < eg 0 s X + x + 03 • g. O _. J 35$ R.H», 2°C ' X x + X + + 98$ R.H., 2°C i o rH O J -*n E X! w p o o ° -— 36$ & 72$ R.H., 25°C — 1 1 ~^ (cycles/sec <,) 1 I I 1 1 10 20 30 50 70 ioo 200 u Frequency secT-1-J M i l l , i i I i I i i i 10 20 30 50 70 Frequency sec. I I I I I 1 1 I I 1 I I I 7 10 20 30 $0 70 100 10 — Figure 2k. Dynamic modulus vs. frequency for acetate rayon 9 ego • 0 ° a * • a _ 7 7 o c 8 — O <D rH i o • • • • X • X -66 °C • • -ko°c + -22°C 7 I—1 o •H e o o o +2°C 6 "V' Frequency sec 1 1 1 1 1 I I 1 1 | 1 I 1 1 1 1 1 3 5 • 7 10 20 30 50 70 100 Figure 25o Dynamic modulus vs.. frequency for 29 — viscose rayon 28 — • a • a 0 0 D -80'C 27 26 e u | O x X X * X X * -55°c 25 o rH 2h — ynamic • • • • • • # -l*o°c 23 •u W 22 21 + + + > - 2 2' c 20 ° o o o o o • -2°C 19 Frequency secl^-1 1 1 1 I i 1 i 1 1 1 1 1 1 1 1 5 7 10 20 30 50 70 100 5 — Figure 26o Dynamic modulus vs 0 frequency for ((/ — raw s i l k k — o o rH t o o o 0 o o 0 o-60°C rH O •H e & X x x X ^ • • • • x x • • x x -5o°c 3 + * + + ° ° o o 0 • + + -20°C "V' Frequency secT^ 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 2 5 7 10 20 30 50 70 100 cycles/sec. I I I I 1 1 l _ 1 1 1 I 1 5 7 10 20 30 50 70 Figure 32. YJ vs. V for raw s i l k 10' O W I (0 <p & T3 O -60~C X -$0°C + - 5°c i o 6 cycles/sec. 1 I I I I I 1 I 1 1 1 1 1 5 7 10 2 0 - 3 0 $0 70 8 26 2k 22 20 18 -80 CM o e O Figure 37° Dynamic modulus vs. temperature for viscose rayon Temperature °C -50 -ho -30 -20 -10 0 


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