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The influence of water sorption on the dynamic mechanical properties of nylon 6-6 and the plasticising… Quistwater, Jacques Marie Raymond 1958

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THE INFLUENCE OF WATER SORPTION OH THE DYNAMIC MECHANICAL PROPERTIES OF HYLOK 6-6 AND THE PLASTICISIKG EFFECT GF WATER by JACQUES MARIE RAXMOND QUISTWATER B. A . , University of Br i t ish Columbia, 1954 A THESIS SUBMITTED US PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science i s the Department of CHEMISTRY We accept th is thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1958 ABSEAGT Wuch work baa recently been done on studies of aechanical and e l a e t r l c s l dispersion phenoaana i n polymers* ^ay workers have been active studying the effect of p l a s t i e i s e r s , i r r a d i a t i o n * heat, and E s c h a n i c a l trea-teaat, copolyjaerisation, and c r o s s - l i n k i n g , such ae vulcanisation, on a large amber of high polyinsre. In spite of i t s great technological importance, ths effect of hiamidity on the isechanieal prop-e r t i e s of textile f i b r e s has not boon studied i n a systematic way. The present investigation l a an attempt at studying the influence of humidity on th© modulus and energy d i s s i p a t i o n of nylon 6-6 sionofilaBente. The modulus and energy l o s s were determined using a low-fTequeaoy vibyoaeter, ovor the f u l l range of r e l a t i v e humidities at 9, 35$ and 60 °Q., using 15 denier nylon zaonofHaiaents. Values of these empirical quantities were plotted as functions of &equency and hu-midity, and water content. The r e s u l t s were discussed taking i n t o account the fact that water sorted lay f i b r e s i s present predominantly i n the amorphous regions, and might be expected to break hydrogen bonds e x i s t i n g between adjacent peptide l i n k s , thereby reducing molecular i n t e r a c t i o n , and f a c i l i t a t i n g segmental motion. A mechanism was proposed i n order to explain the r e s u l t s . The values of the tangent of the l o s s angle vera compared with recent work by Saner at a l . Using espresssions derived by Ferry and coworkers, apparent a c t i v a t i o n energies f o r the flow processes were calculated at a number of f i s e d water contents, and were fiund to vary between 26.3 and 110 kcal./mole. I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Q\\KYY\X.A The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver S, Canada. - 1 -TABLE OF GG8TIS73 I. Theoretical and Experimental Introduction. . . .• . . . . . p. 1 . A. Historical Survey. p. 1 B. Recent Work on th© Mschanical Properties of Polymers, p. 1 1. Types of Experiiaents . . . , * . . . . . . . . . . p. 1 a. Experiments in which Stress* Strain, or Modulus i s Studied as a Function of Time or Frequency . p. 2 b. Stress-Strain Experiments p. 4 c. Espsriasnts in which Modulus end Energy Loss are studied as Functions of Temperature . . . . p. 4 2. Correlation of Tic©, and TeBg^rature Effects . . . p. 6 3. Influence of Humidity, Copolys&risatlon, and Irra-diation. . . . . . . . . . . . . . . . . . . . . . . p. 7 0. Dielectric Studies on High Polymers p. 9 D. Correlation between Mechanical and Dielectric disper-sions in Polymers.• • . . . . . . . . . . p. 10 E. Experimental Methods. p. 11 II. Apparatus and Experiments. . . . . . . . . . . p. 14 A. Description of the Apparatus. . • . . • . • • • • • • p. 14 B. Calibration of the Solenoids and Determination of Parameters. p. 21 III. Results. p. 26 17. discussion... . . . . . . . . . . . . . . . . . . . . . . p. 31 V. Appendix p. 39 VI. Bibliography . . . . . . . . . . . . . . p, 42 THEORETICAL AKD EXPERIMi^TAL IKTRODUCTIOH A. Historical Survey Studies of dynamic modulus, energy loss, and stress relaxation, and creep have been performed on a variety of materials, including wood, rubber, metals, and natural and synthetic fibres. These studies were i n i t i a t e d by Hooke who enunciated the lav of e l a s t i c i t y bearing his name. As a result of studies on the extension of metals under various loads. Young defined a tensile modulus E» = (FA) / ( A l / l ) , where F i s the force on a cross-sectional area A F and A 1 i s the elongation of a length 1. The studies of viscoelaeticity vera greatly extended by Voigt and Maxwell} who postulated various mechanical analogies, consisting of arrangements of springs and dashpots, to explain the 1 observed viscoelastic behaviour . The theoretical aspects were extended again by Eyring's application of his theory of rate 2 processes, leading to a non-Hewtonian viscocity , and by the concept of a distribution of relaxation and retardation times, as advanced 3 4 5 6 by Tobolsky , Kuhn . Becker , and Ferry and co-workers . A large number of workers have investigated the mechanical properties of polymers using various techniques, which w i l l be elaborated i n subsequent paragraphs. B. Recent Work on the Mechanical Properties of High Polymers.. 1. Types of experiments. Basically, three types of experiments can be performed. Th© f i r s t type, that i n which stress, strain, or modulus i s studied as a function of time or frequency, has been investigated most extensively. Experiments that f a l l in this class include stress relaxation, creep experiments, vibrational-torsional studies, and sound propagation. The second type of experiments, in which stress i s studied as a function of strain, i s a much smaller group. The third type of experiment involves studies of modulus as a function of temperature. 4 number of workers have carried out a large masher of investigations in this f ie ld, reporting results that show the following general trends: below the glass temperature, the modulus decreases slowly with increasing temperature, near the: glass tesiperature, the modulus decreases rapidly with increasing temperature, whereas above the glass temperature, i n the region of rubber-like elasticity, the modulus increases with increasing temperatare, Corresponding to each sharp modulus decrease in a transition temperature range, there i s a maximum in energy dissipation in vibrational experiments, a. Experiments in which Stress, Strain, or Modulus i s studied as a function of Tims or Frequency. 7 Ferry initiated comprehensive studies on the 8 rheology of polymer solutions; Ledderman studied the creep 9 10 11 behaviour of various fibres. Harris, Speakman , and Meredith , examined the stress-strain properties of wool and other fibres. 3,12 Tobolsky and associates have made extensive studies of rubber, polyethylene, polytetrafluoroethylene, methacrylates, and urethanes 13 H 15 by stress relaxation. Nolle , Ferry , and Guth have investigated -3 -high-frequency vibrational properties of rubbers. Ballon 20 21 and Smith and Fujino and coworkers have studied the 22 vibrational properties over a vide frequency range. Hamburger has attempted to correlate sonic techniques and stress-strain fests at normal speed on filaments and yarns. More recently, 23 6-6 Bammerle and Montgommery > working with nylon ... have verified the feet that the shear modulus and energy loss can be predicted from the relaxation of torque, as predicted by Alfrey. 24 Ferry and coworkers have carried out wide investigations on rheological properties of polymer solutions, and, more recently, on solid polymers such as polystyrene, polyvinyl acetate, various methacrylates, and others. By reducing results obtained at a number of temperatures to one arbitrarily chosen temperature, they have succeeded in super-imposing all results for any one polymer onto one master curve. They have calculated activation energies for viscous flow from the graphs of the temperature reduction factor against temperature. 6,24 Ferry, Grandine, and Fitzgerald have derived methods of obtaining the distribution functions of relaxation and retardation times for rubber-like polymers Including polystyrene, polyiso-butylene, and various methacrylates. 21 Fujino and coworkers have studied the properties of rayons, silks, and nylon 6 over a very wide frequency range, at 20°C. and 6$% relative humidity. Applying the method of Ferry to calculate the distribution functions, they found them to 9 10 2 be, In almost all cases, between 10 and 10 dynes / cm , within o -7 the time-3eele 10 - 10 see. They also investigated the effect of crystallisation and molecular orientation upon the relaxation spectra of terylane, nylon 6, polyvinyl chloride, and polyvinyl alcobri, using some physical treatments, such as heat treatment. and cold drawing. b b. Stress-Strain Esperiments. In this type of experiment, the stress developed by a given extension in a constant rate of load or constant rate of elongation experiment Is determined. Fibrous materials display histeretlc behaviour in loading-unloading cycles. It has been found that the stress is dependent not only on the strain, but also on the rate of strain, and also, as 25 would be expected, on temperature and humidity as well. 2,26 Halsey and Eyring applied the theory of rate processes to these phenomena, and derived the hyperbolie sine law of viscous flow. By using this lav, they were able to interpret visco-elastic experiments with only one, two, or three relaxation mechanisms, rather than with an infinite (or at least a very large) number of relaxation times required i f Hewtonian viscosity Is presupposed. In addition to applying i t to stress-strain experiments, they also applied this law to the creep data obtained 3 by Leaderman for viscose, cellulose acetate, and silk, and obtained good fit s . They calculated free energies of activation of the order of 25 klloealories per mole for these materials. c. Experiments in which Modulus and Energy Loss are studied as Functions of Temperature. 13 Nolle has studied the mechanical properties of synthetic and natural rubber, both unvulcanlged and vulcanised, over a vide frequency and temperature range. In addition, he performed some experiments 6n the e f f e c t of added carbon black, as a " f i l l e r * , on the properties of the rubbers. I t has been postulated that the carbon black e x i s t s i n the rubber as a separate phase, and may therefore be expected to exert a marked e f f e c t on the dynamic properties of the rubber. His experiments have, i n f a c t , confirmed t h i s viev. 27 Saner, K l i n e , and others have examined the dynamic properties of both c r y s t a l l i n e and non-crystalline polymers. They report that polyethylene and polytetrafluoroethylene, both c r y s t a l l i n e materials, e x h i b i t maxima i n the energy l o s s versus temperature curve, at temperatures w e l l below room temperature. On the other hand, polystyrenej which i s amorphous, does not e x h i b i t any maxima. One should, however, not generalise from these observations, f o r energy l o s s maxima have been observed at temperatures w e l l below room temperature f o r various methacrylates, \ which are amorphous. They have also examined the e f f e c t of branching 28? on the mechanical properties of polyethylene •* In addition, they have also investigated the e f f e c t of i r r a d i a t i o n on the dynamic properties o f nylon 6 - 6 , nylon 6 - 1 0 * and a copolymer of nylon 6 - 6 , 29,30 nylon 6 - 1 0 , and nylon 6 , as we l l as the e f f e c t of humidity on the value and temperature of the^energy"loss maximum f o r nylon 6 - 6 , 29 .31 , i n a very q u a l i t a t i v e fashion . Fitzg e r a l d has studied the mechanical resonance dispersion i n t e f l o n , and reports a satisfactory - 6 -agreement between experimental results and the behaviour predicted from the simple mechanical model he postulates. He obtains an activation energy of 13.2 fecal./mole. 3 2 In addition, Wolf and his school have examined the influence of temperature on the dynamic tensile modulus and energy loss for a large number of polymers, 33 both crystalline and non-crystalline. Price and Dunell have reported the modulus and loss faetor for viscose rayon within o the temperature range 0 to - 80 C. A number of workers at the Imperial Chemical Industries laboratories in Great Britain have studied the modulus and energy loss factor of various acrylic polymers, and polyethylene over a temperature range of about o 4 3 * 4 4 * 4 5 3 0 0 C . 2 . Correlation of Time and Temperature Effects. The time-temperature superposition 3 6 principle has been applied by workers such as Tobolsky and Ferry * Ferry has Investigated a large number of acrylie polymers, and has }6 been successful in superposing results obtained at various temperatures on one master curve, at an arbitrarily chosen temperature. Generally speaking, the time-temperature superposition principle can be applied to amorphous polymers. Very l i t t l e Information on i t s application to semicrystalline polymers i s presently available. 17 Dunell correlated stress relaxation and vibrational properties for a number of rubbers and textile fires, and reported an order of magnitude agreement between observed values of the dynamic energy loss and values calculated from Becker's distribution function. In most eases, i t vas found that the losses predicted from stress relaxation data are smaller than the 39 observed dynamic losses* F. M. Bueche has investigated and discussed the Young's modulus of semi crystalline substances and the mechanical properties of various rubbers. Making certain assumptions, he derives an equation for Young's modulus, for semi-crystalline polymers, and reports quite good agreement between values of the modulus obtained from It, and empirical values, for polyethylene, but not for natural rubber. 35 Yoehitomi et al. have investigated the stress relaxation of polycaproamide (Nylon 6} of low crystallinity. They applied Ferry's reduction method to reduce the results at 0 and 75$ relative humidity at a number of temperatures to respective master curves. These two curves were further reduced to one curve by taking into account a molecular theory of crystalline polymers. Using a first order approximation method, they obtained 21 the relaxation spectrum over a very wide time scale range — 10 2 1 sec, in good agreement with the more limited data obtained by Fujino 36 and by Tokita. 3. Influence of Humidity, Gopolymerisation, and Irradiation. 38 Ifeyer and Lotmar haw examined qualitatively the effect of moisture content on the dynamic Young's modulus of a number of rayons, and on ramie and hemp. For all fibres, they reported a very considerable decrease in the modulus as the moisture content was increased, Anderson reported similar results for viscose rayon, In the frequency range 25 - 40 c.p.s. de Vries reported a decrease in dynamic modulus, determined at 9 kc./s, with increasing moisture content, which amounted to about A.3% decrease in modulus per 1% increase in moisture regain over the 38 range 40 to 85$ relative humidity, for Fortisan. In very recent publications, Tokita 39 and Kanamaru discuss the viscoelasticity of viscose and acetate rayons crosslinked to various degrees by tetramethylene bisethylene urea and tetramethylene-diisocyenate urea. They report that, as crosslinking increase a, a minimum in the modulus and the apparent 10 activation energy occurs, the lowest values being 9 x 10 dynes / 2 em. , and 95 kcal./mole respectively. They report a strong relative humidity dependence of these values, attributable to a solvating, or plastieising effect of water. In this laboratory, Price, Pattison, 37 Mclntyre and Dunell have carried out rather limited studies on the effect of temperature and humidity changes on the dynamic mechanical properties of nylon 6-6, viseose, and acetate rayon, and polyethylene. The polyethylene, as might be expected, was found to be quite insensitive to humidity changes. The properties of the other materials, however, were found to be strongly influenced by humidity changes. Woodward, Sauer, Deeley and Kline have studied the change of modulus and energy loss versus temperature for a copolymer of nylon 6, 6-6, and 6-10, over a wide temperature range, © 29 from about 80 to 430 E. They have also examined the effect of 9 irradiation dn the dynamic mechanical properties of nylon 6-6 27,29 and polyethylene. The predominant effect of neutron and be gamma irradiation apperas to that of introducing cross-linking 30 and destroying cryatalllnity. G. Dielectric Studies on High Polymers. m Fuocs has carried out very extensive investigations on the electrical properties of a number of polymers, but primarily on polyvinyl chloride. He found that the electrical properties of poiyvinyl-chloride depend on i t s thermal history — as a result of pyrolysis, which leads to formation of hydrogen chloride, which i s released very slowly within the polymer. The dielectric constant changes with time in a way which suggests a relaxation mechanism. Examining the system polyvinyl chloride-tri-o 4 cresyl phosphate at 40 C , and 20 to 1© e.p.s., and a variety of compositions, he observed maximum change in the electrical properties in the range 50-70$ polyvinyl chloride, and postulated a hindrance of freedom of orientation of dipoles in polymeric materials in applied electric fields. He also investigated the effect of a large number of plasticisers, and found that the d i -electric constant and the dielectric loss factor were dependent upon the size and strength of the polar groups of both the polymers and the plasticisers, and the f lexibil ity of the bond of the polar group to the polymer chain. He also observed that In the system polyvinyl ehloride-2©% diphenyl, the electrical properties are most markedly affected in the low concentration (0 to 2$) range of compositions, and concluded that this represented a viscosity phenomenon. He - 1 0 discussed these dipole moments onjia theoretical basis, and showed that the results for the polyvinyl chlorlde-diphenyl system were in agreement vith theoretical deductions. 41 Davies, Miller and Busse carried out investigations parallel to Fuoss*, on polyvinyl chloride plastioised with dimathylthianthrene, t r i to ly l phosphate, and dioctyl phthalete. They also separated the dielectric loss into a loss due to dipole rotation and a loss due to ionic conduction. Observing that the apparent energy of activation for mechanical deformation and dipole rotation are of about the same magnitude for these various plasties, they suggest that the chain units that move in mechanical deformations are of the same order of magnitude as the size of the chain units that move vith dipole rotations. D . Correlation Between Mechanical and Dielectric Dispersions in Polymers. Several papers published in Kolloid 32,42 Zeitschrift point out the parallelism between meohanical dispersion and dielectric relaxation phenomena in high polymers. 42 Beyboer reports observing two peaks in both the mechanical and the electrical energy loss versus temperature curves for polymethyl methacrylate. The high temperature mechanicl energy loss maximum corresponds to an activation energy of approximately 100 kcal./mole; the low temperature one, to approximately IB kcal./mole. The magnitudes of the loss peaks for dielectric relaxation exhibit the -11 -reverse behaviour, with the high temperature peak being the smaller. Examining the structure of methacrylate polymers, he ascribes the high temperature transitions, with large relaxation time, to the motion of the paraffin-backbone of the polymer, and the low temperature transition, with small relaxation time, to motions of the strongly polar methacrylate part of the polymer. A series of papers published by workers at Imperial Chemical Industries laboratories in Great Britain discussed the relation between the structure of polymers and their dynamic mechanical and electrical properties. They report activation energies varying from about 2d to 139 keal./mole for polymethyl methacrylate and polymethyl o<-chloroacrylate, depending on the 43 method used to evaluate them. They examined the mechanical properties of a large number of methacrylates over a temperature range o of - 200 to about 130 C, and reported activation energies for lov-44 temperature processes between 3 and 11 keal./mole. Cakes and 45 Robinson report the dynamic mechanical and electrical properties of polyethylene over a wide temperature range, and report peaks in the o mechanical energy dissipation faetor at about -100, 0 and 60 C, for which they calculate activation energies of 6, 30 and 40 keal./mole respectively. £. Experimental Methods. Various methods are available for studying the mechanical properties of high polymers, enabling one to choose between experiments on single filaments, on yarns, on films, 12 -or on rods of blocks of the polymers. The most common types of mechanical experiments performed on fibres, however, are creep extensions, stress relaxation, vibrational, and torsional experiments. Methods involving sound propagation through rods of the polymer are similar to vibrational experiments inasmuch as both involve the application of strains of very short duration. Most experimental methods depend upon one or more of the following conditionss constant strain, constant stress, constant rate of strain, constant rate of stress, or sinusoidal variation of stress and strain. Such experiments therefore give information concerning stress-strain-time behaviour. Vibrational experiments enable this study to be extended over strains of very short duration, and provide a set of data which complements results obtainable from other experiments, such as creep and stress-strain studies, for which the time base i s much longer. Two types of vibrational experiments can be made - one in which a mass l a attached to the fibre and the free vibrations of the system are measured, and the other in which the fibre i s subjected to forced vibrations by applying a dis-placement varying einueoidally with time. The resonant frequency of the system can be altered by changing either the length of the vibrating filament, or the mass of the transducer. As mentioned previously, a third method consists in propagating a sound wave through the polymer sample, and measuring i t s velocity and attenuation. In most vibration experiments, the - 13 -strain amplitude is kept small, so that the stress may be treated as linearly related to the strain, and linear differential equations relating stress, strain, and time may be used, the periodic strain resulting from the sinusoidal stress i s generally out of phase with the stress, and i s described by an expression of the form a s a 0sin(2irft - 8) where 9 i s the phase angle between the stress and Hie strain. The strain can also be thoughtof as consisting of two components, one of which i s in phase with the. applied stress, and the other of which i s 9 0 ° out of phase with the applied stress. The stress divided by the component of the strain in phase with the stress i s termed the energy loss JE* * . This relationship may conveniently be described by the complex dynamic modulust E * * B» 4 IE* • s £« 4 i^uo (l) where E * i s ; the complex dynamic modulus, E* i s a measure of the elastic energy stored and recovered during each cycle of deformation, (tta Hootoan part of nsc^XaeUc teha4iour) « * * E " i e proportional to the energy dissipated during each cycle, (resulting from those elements of the structure that do not respond Instantaneously to a given deformation) B M can be equated to ^uj in which ^ represents the resultant viscosity of a set of Newtonian dashpots giving rise to the energy dissipation. Characterisation of the dynamic mechanical properties of any material then requires the evaluation of both E' and as functions of frequency, temperature, and moisture content. 4s in most cases one i s dealing with a set of viscosities or relaxation times, the resultant viscosity wil l be frequency dependent. - u -APPARATU3 AMD EXPERIMENTS The dynamic Young's modulus E 1 and the energy lose factor E ' 1 for 1 5 denier nylon monofilaments were determined at various conditions of temperature and humidity, using a 17 technique similar to that of Bunell and Dillon. The latter 19 apparatus was very similar to that of Lyons and Prettyman and also to the Firestone resonance vibrator for rubber samnles in 16 shear, as described by Dillon, Prettyman and. Hal l . Descriptions of the Apparatus. The apparatus used i s sketched schematically in Figures 1 to 3. The driving mechanism consists of a solenoid of fine wire W wound on a paper core C which i s cemented to a disc and a spindle D constructed from aluminum tubing, the solenoid coi l lying in a radial magnetic field which traverses the annular space E in the magnetic circuit shown in Figure 3. The unit i s suspended at each end by nylon filaments F which can be lengthened or shortened and moved back and forth at right angles to the axis of the vibrator unit to centre i t in the magnetic field and insure that there i s no contact between the coll and the sides of the angular gap in which i t i s located. The permanent magnetic field i s maintained by th© two powerful permanent magnets N of Figure 2, two similar poles H, facing one another on one side of the radial gap, and a cylinder S forming the opposite pole on the other side of the gap. The filaments G which are to be tested are each cemented at one end to small thin pieces of aluminum each of which i s in turn inserted 15 -into a s lot at each end of the abaft of the vibrator uni t and made fast there v i t h a small pin H. The other end of the filaments pass, through a relat ive humidity and temperature adjusting boxes J , to pulleys K at the end of the apparatus, and are tensioned by the weights L. The filaments may be clamped at various positions by screwing together fixed clamps, operable from without the chambers. The transducer assemblies used i n these experiments consisted of three solenoid c o l l s wound coaxial ly on a horizontal spindle and ly ing i n a rad ia l magnetic f i e l d . The solenoid c o l l s consisted respectively of about 2, 25, and 90 turns of no. AO copper magnet wire. These three c o i l s were so wound i n order that one could always obtain a reading somewhere on the scale of a Leeds and Northrup thermomilliammeter whose f u l l scale reading could be adjusted to 2, 10, or 50 milliamperes. The frequency of vibrat ion of the transducer assembly could be changed continuously by alter ing the frequency of the applied electromotive force, which Is , i n fact , the frequency of v ibrat ion. The apparatus could be tuned to mechanical resonance by adjusting the frequency of the Hewlett-Packard low frequency osc i l la tor used. The exact resonant frequency could be determined by determining the frequency at which the amplitude of vibrat ion was a maximum for a given current value, or , for frequencies i n excess of 10*- e . p . s . , by that frequency at which the peak to peak amplitude of the voltage across the solenoid c o i l was a maximum as displayed on an osci l loscope. The l a t t e r method was used as much as possible, inasmuch as stray mechanical vibrations of the system as a whole seemed to have a l ess pronounced effect;. - 16 -As neither high humidities nor very low humidities could be readily achieved within the constant temperature room available, i t was decided to enclose the fibres within constant humidity chambers, using the constant temperature room in order to o o control the temperature at 35 C. within plus or minus 0.1 to 0.3 C . The chambers were constructed of lucite and were provided with clamps operable from without the boxes, located at 5, 10, 15, 30, and 60 cm. from the end nearest the transducer assembly. Provision was also made for measuring the relative humidity at eight points 4 6 within the boxes, using wet and dry junction thermocouples . Air of controlled relative humidity was admitted vitktx; Jbe chambers by means of an air manifold running the length of the boxes, the air being Introduced into the manifold at the centre of the box. During the course of the experiments, the humidity within the boxes was checked periodically, and was found to be reasonably homogeneous -in all cases, the variation did not exceed 2%. Later, the average humidity of the air was measured by passing i t over aminco-Dunmor© Electric Hydrometer vide range humidity sensing elements. The elements were coupled to a Bristol recorder, and the humidity reported for any particular experiment is the average obtained from the recorder trace. ^ The humidity of the air was adjusted by splitting the stream of compressed air, and passing one portion of i t through drying towers of silica gel, and the other, through gas dispersion tubes into vessels filled with water, and immersed in an oil-filled constant temperature bath controlled by a Zeitfuchs-Doty thermoregulator to o o plus or minus 0.01 C. at 35 C. The two streams of air were then re-17 -combined, and passed over the humidity sensing unit, just before entering the Incite boxes enclosing the test filaments. The relative humidity of the air could be altered to practically any desired value by adjusting the volume of air passing through the drying columns and saturating vessels. When no air was passed through the saturating vessels, a low relative humidity of 11% could be achieved, using freshly regenerated s i l i c a gel; when the entire stream was passed through the saturating vessels, a maximum relative humidity of 96$6 could be obtained. Essentially the same experimental set-up was used to determine the mechanical properties at 9 v , #' with the following modifications. In order to condense out as much water as possible, the compressed air stream was passed through cooling colls located immediately in front of the cooling fan used to cool the room. Then It was passed through a glass water trap to remove condensed water, and, finally, through two columns, one packed with glass wool, tVo remove small spray droplets, and another packed with anhydrous calcium chloride. Part of this air stream was then passed through saturating vessels; these were, however, not held in constant temperature baths. The humidity of the air stream was adjusted as in o the 35 G. work. During the course of any particular experiment, the temperature of the air stream was measured periodically. Although the o ' room temperature was maintained at 2 plus or minus 0 .2 C., i t was found that the temperature of the air stream could not be lowered to o this temperature, but remained quite constant at 9 plus or minus 0 .3 C. Using freshly peeked drying towers, i t was possible to attain relative humidities below 5% - the limit of the sensing elements - nominally - 13 -listed in the results as *0* relative humidity, because the recorder indicated a reading of 0. The maximum humidity attained was 96$. Entirely new apparatus was designed and constructed o for the work at 60 Cs because such an elevated temperature could not be achieved within the constant temperature room, i t was decided that those portions of the apparatus enclosing the air stream and the fibre should be surrounded by thermostating jackets. The chambers enclosing the fibres were constructed from brass. Provision was made for clamping the fibres at 10,13 and 40,25 cms. from either end of the solenoid spindle. At these positions, windows were inserted so that the damps* operable from without, could be screwed tightly together without causing any lateral displacement of the fibre. In order to have approximately the same number of determinations of the mechanical properties per experiment a number of additional weights to alter the mass of the vibrator assembly were constructed. As some of the lower humidity range Aminco-Dunmore ELeetric Hydrometer elements in the wide range humidity sensing 47 o apparatus could not be exposed to air whose dew point exceeds U0 F., the Aminco-Dunmore narrow range high sensitivity humidity sensing elements . Each high sensitivity element responds to humidities within a particular humidity ranges so that, with some overlap between t-& elements, one can measure any humidity desired. As no calibrations for 140 C. were provided, the elements were calibrated b o by extrapolating data provided within the temperature range 40 - 120 F., 49 as advised by the Aminco-Dunmore engineering department. As In previous experiments, the humidity of the air stream was adjusted by combining a dried and a wet stream of a ir in appropriate proportions. The wet air was obtained by passing compressed air through the saturating vessels as before, but this time the o i l bath temperature was maintained at 75 ° C . The two air streams were comb-ined in an air manifold immersed in the water circulating bath maintained at 60.0 plus or minus 0.05 ° C . After passing through a heat exchanger also immersed in the water bath, the a ir was sent by means of water? jacketed rubber conduits to the humidity measuring chamber, whence It was led, again by means of water-jacketed rubber conduit, into the chambers surrounding the filaments.. Water was circulated throughout the system by means of an Eastern Industries pump of 8 gallons per minute capacity. The •temperature drop throughout the system was less than one degree. It was found that at higher humidities — above 55 % — water irons tils a i r stream leaving the chambers surrounding the f i l a -ments condensed on the mcuh cooler transducer assembly, altering i t s mass. In order to overcome this difficulty, a stream of compressed air was made to flow at each end of the tranducer assembly, in such a way as to deflect the moist air emanating from the chambers, thereby preventing condensation of water on the transducer. As this air flow interfered in the determination of the mechanical /properties, i t was shut off whenever a reading was taken. Any small amount of water that condensed on the transducer during the course of a determination was wiped off with cotton wool. Two filaments, of the same material, each about 75 cm long, were attached one to each end of the vibrator spindle, making a sym-metrical arrangement of two test pieces lying horizontally one on each side - 20 -of the transducer and coaxial with i t . Each filament was tansioned at i t s end remote from the vibrating spindle by gram weights approximately equal to half the denier value of the fi laments, e . g . , S g for 15 denier nylon, and allowed to creep under this applied load for sixteen to twenty hours before he experiment, and was kept under th is tension during the? experiment. During the tensioning and conditioning period «~- usual ly over night — control of the humidity was usually within 5 $ of the required humidity. Just preceding, and during the actual vibrat ional experiment, the humidity was manually adjusted, i f necessary, to the required humidity. Overall variat ion i n the humidity during the actual experiment was 1 to 2 %, depending on the temperature. In a l l experiments, the v ibrat ional amplitude was approximately 0.15 % s t ra in , i n most cases, several determinations of the mechanical properties, on dif ferent fi laments, were made. When suf f ic ient data, usually three runs, had been gathered at a given humidity, the humid-i t y was increased by about 10 $. The entire humidity range was scanned i n th is way, the results were plotted i n rough fashion In order to keep track of the changes i n the properties with humidity, and, i f conditions warranted, experiments were performed at intermediate humidities.-Dozing the actual experiment, the resonant frequency of the system, the vibrat ional amplitude, and the current required for that amplitude were recorded. At 35 °C , the temperature and humidity were recorded as wel l ; at 9 °C , re lat ive humidity only. At these two temperatures, the humidity during the course of the experiment was determined as the? average of these readings. At 60 °G, the average relat ive humidity was obtained by in teg-rat ing the area under the' recorder t race. • ~ 21 -the resonant frequency of the system was altered by changing the length of the filament clamped, and by Increasing the mass on the vibrating spindle. The l a t t e r method merely required placing small weights; from 2 to 100 g on the v i rat ing spindle. Using these methods, i t was possible to obtain readings over somewhat more than one cycle of l o g -arithmic frequency. B. Cal ibrat ion of the Solenoids and Determination of Parameters. The solenoids, or vibrator un i ts , were calibrated so that the fiorce they exerted could be determined from the current floowing through them1. To do t h i s , the magnet-vibfator assembly was set up ve r t i ca l l y i n such a way that the vibrator unit could be suspended f reely In the mag-netic gap> by a l inear calibrated spring, f^ae vibrator was centered v i ^ l u ^ the magnetic gap, and was then loaded with a succession of analyt ical weights The vibrator was brought back to I ts unloaded posit ion by passing direcct current through the solenoid c o l l . The force could be calculated from the -equation W « Mg • KAx, where M i s the added mass, g , the gravitat ional constant! K, the modulus of the spring, and A x i s the distance between .loaded end unloaded positions of the vibrator un i t . Ixperiaentation allowed, however, that the corrections result ing from differences i n the exact p o s i -tions of the vibrator uni t between the loaded and unloaded positions could be neglected, as these corrections amounted to only a few tenths of one percent, at the » r y most. Accordingly, F s Mg was considered to give a value suf f ic ient ly close to the actual value. A plot of F against i , the current i n milliamperes, w i l l give a straight l ine of slope Tdynes per milliampere. &n alternating current whose root mean square value, read o f f the alternating current milliampere, i s i exerts a maximum force Fmax=</2H7 I t i s th is maximum force which Is used In the calculat ion of l w . - 22 -Two different vibrator assemblies were constructed during the course of this work. The first assembly's main coil was accident-ally burned out midway in the 9 °C work. Both consisted of three solenoid coilss one large* of about 90 to 95 turns, a smaller coi l of 25 to 30 turns, and another, smaller yet, of 1 to 2 turns. In the calibration of the large coils, 1 to 8 g weights were usedf for the medium cois ;, 0.1 to 1.0 g weights;, and for the small coils, 10 to 100 mg weights. Data concerning the number of turns and the calibration factor i n dynes per mllliampere are reported in Table I. Table I. Coil Calibrations. First Assembly Second Assembly lumber of turns Calibration Faetor Mumber of turns Calibration Factor dyne/ma. dyne/ma. 93 50.0 90 25 12.09 30 %en the solenoid had been calibrated, the effective mass M of the transducer could be calculated from the equation of motions M dje * R da; • Px * F ^ ^ coscot (2) dt* dt where R s „ • % (3) 1 v . and P - 2 | E ' * P, (4) 1 A P^ i s a correction factor for the ^r t ica l displacement of the vibrator unit during, horizontal vibration, and i s given by 2^ *• Mg/h, where M Is the mass of the system, g i s the gravitational acceleration, and h i s the suspension height. Rj Is a correction factor for dlsslpative forces other than those present in the filaments. It i s given by » F/to,x, at resonance, 60.2 20.3 1.40 where F i s the force required to produce x, the vibrational amplitude, at the resonant frequency c o r . T h e steady state solution of the equation i s x a °X costot ' • . p'-eiiaoit (5) where , - F ^ * ( Mu)2 - P ) « = — (©) ( M c u 2 - p )2 4, i2u>2 and a' = Unax Differentiation with respect to time, and use of equations (6) and (7) shows that x ^ = F 0/-[(Mu) 2 -P) 2 * B 2cu 2} i (8) g2 w 2 ia uegligible compared to {Mui2 - ff for values of u> which are not too close to cu r. Hence a plot of ±F/'x against u>* should give a curve which deviates from a straight line only near resonance, the slope of the line being M, the effective mass of the vibrating system* lesults of effective mass determinations are reported in fable I I . Table I I . Mass Sali^r^tions. First Assembly Second Assembly Effective Mass leighed Mass Effective Mass Weighed Mass M, in grams. gram M>. in g. g; 4.69 4.08 4.51 4.40 24.64 . .. 25.04 16.6 16.1 Several mass ealibfations were performed on each of the two vibrator assemblies. %ffleal ties were encountered in obtaining results' that agreed reasonably well with the known, or ^weighed* weights of the vibrator assemblies* A glance at Table II reveals that the effective mass i s not necessarily identical to the weighed mass of the system. Effective mass i s the mass determined by the method just elaborated, and weighed mass i s the mass of the vibrator assembly obtained by adding a l l the weights of the components of the assembly. The correction factor P^ was evaluated simply by measuring M and h, and using g equal to 981 dynes /sec.^ The Rj factors were determined by a forced vibration method. Values obtained are reported in Tables III and I?.. The values reported for in the; f i rs t column In Table III were obtained by plotting x/F versus tu and drawing smooth curves through the po int sThi s met hod was not deemed satisfactory, as the uncer-tainty In the exact position of the inflection point was very great} some-times this uncertainty amounted to 20 Accordingly, subsequent values Table III. Ri Correction Factors for First Transducer Assembly. Total weight of transducer R} factor. In dyne-sec./cm, assembly and added mass. evaluated for experiments at gram 35 °G 60 °C 4.09 3.10 1.98 9.81 2.38 2.04 15.53; 2.44 1.90 29.38 2.15 2.29 40.83 2.63 1.97 54.50 2.77 2.0© (est.) 79.79 3.64 reported in Tables III and IV were determined by tuning directly to resonance, and measuring F and x directly at resonance. This method was found to be entirely satisfactory. %e high values reported in the f irst column of Table IV were; obtained; for the assembly with colled leads going - 25 -from the solenoid coils to fixed terminals placed on top of the magnet, the lower values reported in the second column were obtained for straight leads simply curved upwards from the solenoid terminals to the fixed ter-minals on the magnet. Table 17. Correction Factors for Second Transducer Assembly.. Total weight of transducer Rj_ factor, In dyne-sec/cm, assembly and added mass. evaluated for experiments at gram 9 ° C 60 °C . 4.51 5.35 1.82 6.77 — 2.00 8.40 — 2.02 10.23 3.84 1.73 13.63 1.91 14.12 3.58 1.91 15.96 ... 1.63 19.35 — 1.65 25.1 1.88 29.8 3.55 1*59 41.2 4.82 1.96 55.1 4.44 2.72 80.2 2.37 105.3 — 3.49 RESULTS The dynamic modulus E* of nylon i s plotted as s> function of logar.tlthmlc frequency at a number of relat ive humidities at 9» 35 and 60 °C . i n Figures 3» U and 5 respectively. Inspection of the 9 oC. resul ts shows that , i n most eases, the dynamic modulus Increases with increasing frequency. This increase Is not so great as ttiat reported by 21 Fujino et a l . for Nylon 6., I t i s not at a l l clear why the modulus decreases with increasing frequency i n the region 19 to 60 % r . h . A closer examination of the results at any humidity within the range- shows that some experiments exhibit an Increase; i n E» vit3i increasingrfrequency*. The foremeationed affect may be? spurious, fo r the slopes observed at?higher humidities might lead one to believe that only a decrease in elope to zero, followed by an increase, to rather large values, with increasing relat ive humidity may occur. The results are not suf f ic ient ly precis©, however, to permit detailed analysis. ?&e 35 and 60 o&. results for the dynamic modulus show more regular i ty , the modulus increases with increasing frequency at a l l humidities. The change i n slope with increasing humidity does not appear to follow a regular pattern,, as may be seen by Inspection of Table ? . It was found that, although individual runs were f a i r l y consistent within themselves,, showing only small deviations from l inear i ty , , d i f f i c u l t y was experienced i n reproducing these values, at the same humidity.. Examination of the results 5 at 35 °C . and 63 % r . b . shows that the two runs do not superimpose at a l l . Results for each run were plotted against logarithmic frequency; and the best straight l ine drawn through them. These; straight l ines were averaged to give the l ines reported on the graphs. - 27 _ Table Slopes of E* against log graphs, in dynes/em2 x 1 0 " ^ # 9 G C . 35 ° C 6 0 °G. r .h . Slope r .h . Slope r . h . Slope 0 0 11.0 - 0.30 10.5 - 0.39 5.4 - 0.11 12.3 • 0.21 18.3 - 0.62 9.5 -0.05 22.5 - 0.30 20.5 - 0.63 16.3 - 0.04 31.1 - 0.24 25.1 - 0.55 19.0 - 0.09 39.4 - 0.31 28.2 - 0.47 30,0 - © a s 44.1 - 0.23 35.4 - 0.44 38.3 - 0.05 50.7 - 0.38 37.9 - 0.44 48*2 - 0.02 51.8 - 0.23 41.0 - 0.48 51.0 0 56.2 - 0.54 51.2 - 0.54 58.4 - 0.05, 63.0 - 0.42 57.2 - 0.32 67.6 - 0.44 67.7 - 0.35 59.8 - 0.19 76.0 - 0.28 69.7 - 0.46 63.4 - 0.18 86.0 - 0.66 80.5 - 0.26 70.7 - 0.32 88.3 - 0.66 82.7 - 0.46 76.0 - 0.18 93.5 - 0.50 89.2 - 0.17 85.0 - 0.16 96.0 - 0.18 93.8 - 0.34 These straight lines may, in some eases:,, not appear to be the best straight lines that could be drawn: i t must be remembered nevertheless that a number of experimental points could not be reported in the: graphs, as they over-lapped one another•• This situation Is especially true with respect to those determinations in which three or more runs were made. The energy loss E* i s plotted as a function of log-- 28 -arithmic frequency at a number of relative humidities at % 35* ana 60 on Figures 6, % and 8 respeotively.. I t would appear that at 9 ° C increases with frequency at low; humidities.. Within the range 40 to 60 $ r . h . , the energy loss appears to be constant with frequency, and then, at higher, humidities, decreases with increasing frequency. At 35 ° 0 . » the energy loss decreases with increasing frequency at low humidities, appears to be constant with increasing frequency within the rang© 50 - 70 % P.P.* and increases £ t h increasing frequencies at higher humidities. The same type of behaviour i s shown by the 60 °G, experiments. At humidities below 40 %» tho energy loss decreases i£th increasing frequency} in the range 40 to 65 % r . h . , i t appears to b « i n s e n s i t i v e to frequency,: whereas at humidities in excess of 65 %* i t appears to increase gain with increasing frequency. These conclusions may fe* checked by examining the; values fir ne slope of the graphs of E a against logcu in Table VI. The. slopes of the energy loss; versus logarithmic frequency curves do not appear to increase wit© increase in relative humid-i ty . This behaviour may o due to tbe scatter within iSs* experiments. The lines drawn throughout the data; for E t t ware obtained by plotting the data as log versus log co m plotting a l l results at one temperature and humidity on one graph, and drawling the best straight line through the points. %©se plots give rather better straight lines (See Figures 9 to 1 7 . ) than would appear from Figures 6 to 8 . Values of (E®) were evaluated at arbitrarily chosen values of oo and were plotted an toe I B versus: log W J graphs, to give the straight line reported in the B su i t s . Th© f u l l lines drawn into Figures 9 to 1 7 represent the best straight lines that can be drawn through the points} the dotted lines represent S 8 =• constant lines, included for purposes of comparison. Table VI. Slopes of E* against log graphs. In dynes/cm2 x 10-9. 9 °C 35 0C. 60 °C, r.h. Slope r.h. Slope rJh. Slope - 0.35 11.0 - 0.23 10*5 - 0.54 5.4 -0.31 12.3 - 0.22 18.3 - 0.53 9.5 - 0.30 22.5 - 0.18 20.5 - 0.36 16.3 - 0.17 31.1 - 0.30 25.1 - 0.32 19.0 - 0.22 39.4 - 0.24 28.2 - 0.36 30.0 -•0.11 44.1 - 0.21 35.4 - 0.16 38.3 - 0.24 50.7 -0.02 37.9 - 0.22 48.2 - 0.09 51.8 - 0.02 41.0 - 0.05 51.0 © 0 51.2 - 0.29 58.4 - 0.08 63.0 - 0.02 57.2 - 0.14 67.6 - 0.12 67.7 - 0.24 59.8 - 0.48 76.0 - o»04 69.7 - 0.14 63.4 - 0.05 86.0 0 80.$ - 0.27 70.7 - 0.44 88.3 82.7 -0.32 76.0 - 0.29 93.5 - 0.65 89.2 - 0,21 85.0 - 0.13 96,0 - 0.30 93.8 - 0.19 Figures 18 and 19 report the dynamic modulus as a function of relative humidity at two arbitrarily chosen frequencies, to s 20, and <*> - 150, respectively. The firmer represents the lover frequency extremity; the latter,, the upper frequency extremity. Comparison of these tvo figures shows that, for 35 and 60 °C, the modulus increases with increasing frequency for all relative humidities, whereas at 9 °C., the modulus is insensitive to frequency changes up to about 50 % r.h., but then starts to decrease, rather sharply, with increasing humidity. Figures 20 and 21 report energy loss as a function of relat ive humidity at cu s 20 and ui s 150. The average value of E t t increases with increasing humidity at a l l humidity values, at 9 °G. At 35 and 60 ° C , the behaviour i s more complex} i t leads to a sh i f t In the posit ion of the maximum peaks. At 35 ° C . , the peak sh i f ts from 55 % *vh.._ at cu s 20 to 6 4 % r . h . at cu*150.. S imi lar ly , at 60 ° C , the peak sh i f ts from 33 % r . h . a t UJS 20 to 44 % r . h . at c o s 150. The values of E* and E B evaluated at cu s 150 are plotted versus the amount of water adsorbed at equilibrium by nylon at the humidities studied, on Figures 23 and 24.- Values for water adsortion were obtained by extrapolation of B u l l ' s data, assuming l inear relations.. Jhe data so obtained are plotted on Figure 22. S t r i c t l y speaking, extrapolation of B u l l ' s data Is not just i f iab le . . The error Introduced, however, i s 5 0 probably not very great. DISCUSSION r Schmieder and WGlf32 have examined the mechanical properties of various nylons,, over a vide temperature range and at very low frequencies, and report energy loss maxima' i n three regions,, with indications of an increase i n energy loss above 200 ° C , v i t a the onset of melting. For nylon 66„ the three maxima occur at about 153, 223, and 338 °K. These: dispersion regions are: usually referred to as the 7rx &^ and °<' dispersion regions respectively^ and the region about the melt* ing point i s referred to as the: ° ( dispersion region.. The <* region In the energy loss curves arises from the enhance sent of chain mobil i ty result ing from melting of c r y s t a l l i t e s . she other peaks are bl ieved to arise from cooperative motions of either stressed or unstressed segments of the polymer chains i n the amorphous regions. Table VII l i s t s the activation energies Shmieder and wolf calculate for motion i n the various dispersion regions,; for both nylon 6-6 and nylon 6-10, evaluated by low frequency methods. (^1 e.p.s.) Table VII*. Activation Energies calculated for nylon 6-6 and nylon 6-10 by Sehmieder and Wolf. Dispersion Region Temperature Energy of Act ivat ion of •iscoufl Flow °K. keal. /mole. Nylon 6-6 Nylon 6-10 . 350 73 163 /3' 250 21 19-27 * 170 21 20 ^hese values suggest that the ° ( ' dispersion i s quite dif ferent from either the (b or the T" dispersion, which Sehmieder and w o l f believe arise from mechanisms not too di f ferent from one another. The suggestion of Sauer et 29 30' • a l . . that the<* dispersion may result from the onset of motion of large chain segments i n the amorphous regions seems therefore reasonable. - 32-It Is believed that the ^ p e a k resul ts from tbe onset of cooperative move-ment of CRg groups within the polymer chain, ^his peak has also been observed i n polyethylene and In certain methacrylates. The or ig in of toe ($ peak i s not at a l l dear . . However, Sauer and co-workers suggest that the /3 region i n toe polyamldes i s due to segmental motion i n the amorphous region involving amide groups not hydrogen bonded to other amide groups, on the other hand, i n polyethylene, th is peak i s believed to arise from motion of side g r o u p s 2 * * S i m i l a r dispersion phenomena Have been observed for te f lon ( i polyethylenes, and some methacrylates. M l four dispersion regions are not necessarily observed i n every substance, however. The V peak i s usually referred to as toe primary absorption maximum; toe and toe T peaks, as secondary absorption maxima. Woodward, Sauer, Kline and B t o l » 7 * * > V » examined toe damping factor ( tan o* E t t / E f ) versus temperature maxima for nylon 6-6 and have reported a marked dependence of both toe magnitude of toe maximum and the temperature at which the maximum occurs on toe water content. In their experiments, they used rods of nylon approximately 0.6 to 0.8 em i n diameter and 10' to 11 em long.. Examination of *!gure 2 of their resul ts gives the following data for 308 and 333 °K.* Table VIII. Comparison between toe Results obtained i n th is investigation and Results reported by Sauer and coworkers. Treatment Estimated tan o~ Humidity 308 O K . 333 °K. Sauer Present Results Sauer Present Results 16 mos i n desiccator 0 % 0.012 0.016 0.054 0.012 As received 40 % 0.036 0.031 0.111 0.045 3 weeks at 100$ r . h . 100 % 0.070 0.036 0.01 0.018 One should not very great significance to these - 33 -results, however, since the penetration of water to the inner portions of the nylon rods has not been established. The values l isted in the col-umn "estimated Humidity*' are not Sauer's. The values quoted in the Table as "Present Results" were evaluated at to - 150, and at the stated temper* aturs and humidity. Comparison between these values and those of Sauer . show thai there exists a general agreement between their and the present work — th© trends are the saise. One should not expect detailed agreement, as th© frequencies at which Sauer evaluated these results were In the range? 600-1,000 e.p.s. The maximum values of tan 6" reported In this work are greater than the values of tan 6 for the (i peak reported by Sauer2^, and even approach the values reported by him for the of' dispersion.. It seems therefore that we are dealing with the °< 'dispersion, even at lower temperatures. In order to have a reasonable basis for comparison, i t Is dssirsbla to convert relative humidities at any temperature to the amount of water sorbed by a1 given weight of polymer.- Accordingly,- In the ensuing discussion, the graphs of E' and Ew against moisture content (Figures 23 and 24) wi l l be used. The results obtained for the energy dissipation versus moisture content can easily be explained qualitatively. %t us consider the results at 60 G 0 . At very low'we tar contents,; the energy loss is low because chain mobility i s restricted' by th© existence of fflapy hydrogen bonds. As the weight of water sorbed increases, more hydrogen bonds are broken,, segmental motion Is facilitated, and the energy dissipa-tion inoreases, because more chains can flow. Simultaneously, the force required to move a chain segment wi l l decrease with decreasing chain Inter--34-action, and a maximum v i l l ba set on the energy dissipation by this particular mechanism. As s t i l l more water is sorbed, chain Interaction is further decreased, and the energy loss will then decrease. One would therefore expect a maximum in E" to occur at some intermediate degree of freedom of motion of the chains in the amorphous region In the same way that loss maxima occur at an intermediate point in the rubber-to-glass transition range* % s proposed mechanism Is accompanied by the decrease in modulus that one would expect when chain interactions become weaker. The 35 °C energy loss data may be explained in much the same way as the 60 °G. data. The 9 °C. data can not be explained on this basis, without.some modification — one can f i t the data only to !the first half of toe proposed mechanism. Thus, the results at cu s 150 would seem to indicate that E° increases continuously with increasing moisture content, and that E* decreases beyond 40 % r.h. These results would suggest that, as increasing amounts of water ares sorbed, molecular motion is freed, but that this freeing of molecular segments Is s t i l l incomplete at toe highest value of water sorption, so that no maximum is observed*. This maximum could therefore be thought of as lying beyond toe 100 % r.h. range. The results at cu » 20 (Figure 20) seem to indicate that an energy loss maximum does exist In toe vicinity of 90 % r.h. If toe energy loss does indeed exhibit a maximum, albeit at lower frequencies, toe results could be explained In a manner analogous to toe explanation proposed for the results at toe higher temperatures. There remains toe question of why the energy loss maximum should move to lower humidities m the temperature is raised. This question can probably be explained quite satisfactorily by taking Into account toe difference in temperature between toe different determinations. Thus* as the temperature increases, the thermal energy of the chain seg-- 35 -ments v i l l increase, so that the same amount of chain motion can be achieved with less breaking of hydrogen bonds, that Is to say, more hydrogen bonds are weakened or broken by thermal agitation at higher temperatures, than at lower temperatures,, and therefore fewer hydrogen bonds have to be broken by sorbed water, with the result that, as the temperature is raised,, the. energy loss peak moves to lower moisture cont-f ent values. I Various workers have suggested that an increase in relative* humidity corresponds qualitatively to an increase in frequency for the process, and vice1* versa. Accordingly, when the energy dissipation is evaluated at to-. 20 rather than at w= 150, one should expect the maxima in energy dissipation to shift in the direction oflower humidities. Inspection of Figures 20 and 21 v i l l show that this principle appears to hold for nylon 6-6. A shift In c u from 150 to 20 causes the energy loss maximum to shift from 63 to 55 % r.h.. at 35 °C, and from 42 to 33 % r.h.. at 60 °G, An attempt to evaluate the activation energy for the viscous flow process ves made with the method of Ferry in which he calculates values for the apparent activation energy for viscous flow for a> number of polymers using the relations and .. rt (9) (10) where £* is the real part of the dynamic modulus, <^Is the temperature reduction factor used to reduce values of £' and E N to one arbitrarily chosen temperature:, using the time-temperature superposition principle, i - 36 -R Is the gas constant i n k c a l . / m o l e - ° C , and A H a i s the activation en-ergy for viscous flow. In order to apply these relat ions to the present resul ts , equations (9) and (10) were: modified to: (See Appendix.) AHf t . -- 451 (11) here A i s a gamma function defined In terms of experimentally determ-inable quantities.. I f one knows the value of A, ^  and <JE/<1(-^ ) one can calculate A H a . . Plots of E ' against l/T at various constant water content values seemed to indicate essent ia l ly two slopes, for the data were not suf f ic ient ly precise to allow further discrimination between the slopes. The slopes of the l ines for which the water content was less than 2 .£ g. water per 100 g.. ny l ln a l l l ay between 3.70 and 4.06 x l O 3 ^ dynes-°C. /cm 2 and were averaged to 3.89 x l O 1 ^ dynes- 6 C./cn$. At about 2.-5 g water per 100 g of nylon, an intermediate elope of 4.94 x lO^was recorded, and at water contents i n excess of 4 g*» two slopes, 6.98 and 7.78 x lO^were obtained, and averaged to 7.38 x 10?"^  dynes- °0 . /cm 2 . The slopes were averaged i n th is way because i t was f e l t that the methods used were net suf f ic ient ly precise to enable one to discriminate between the values* The function A was calculated for each humidity fo r which i t was required, as described i n the appendix*. Table IX summarises the results for the apparent activation energyAH a . Activation energies l i s t e d by Ferry^ for eight amorphous polymers such as rubbers, polyvinyl acetate and polymethyl-methacrylate range from 14 to 82 kcal. /mole. th is would suggest that the values herein obtained, with the exception of the two values i n excess of 100 kcal. /mole,, are: not too unreasonable. I f increasing water content exerts a p las t lc ls ing - 37 -effeet upon the nylon, causing a breaking of hydrogen bonds in the amorph-ous regions, the general trend of the 9 °C activation energies seems reasonable, although the magnitudes of some of toe activation energies are somewhat alarming. It should be remembered also that at 232 °K., and high humidities, according to Sauer's results, the energy dissipation phenomenon would correspond to the ft peak, with a tan £ maximum at 250°K. for toe dessiccated sample. The increase in activation energy with increasing water sorption at 60 °C. might be explained on toe basis of hydrogen bondrupture freeing far greater molecular segments.. At this temperature one Is working in toe region of toe Vpeak, for which reported activation energies are much greater.. The 35 °C results could then be explained on the basis of a transition from the behaviour at 9 °C to toe behaviour at 60 °C. Table IX.. Activation %ergies for Viscous Flow,, in kcal./mole. Water Content g.. water per 100 g nylon. Activation Energies 9 °P. 35 °C 60 °C. 1.0 110 43.8 26.3 2.0 49.0 28.8 4.0 43.8 51.4 102 It Is not clear at present what interpretation can be given to these results.. It has been suggested that the first two grams of water adsorbed by Kylon 6 exists in toe polymer as bound water. It has not been established that such is toe case for nylon 6-6, but i f i t were, then any water adsorbed below this limit could provide very little plasti-cisation, and one would expect little change in toe value of toe modulus. Such would appear to be the case at 9 and 39 °C.» but not at 60 °C, where the change In modulus at water contents lower than 2 g. per 100 g. nylon Is very marked.. It Is believed that water Is adsorbed only within 51 amorphous regions. Starkweather maintains that water tends to catalyse crystallisation in nylon? If crystallinity were. In fact, greatly enhanced, one would expect an increase in modulus. Although the results do not show an increase in modulus with increasing water content, i t is possible that this increase in modulus due to an increase in crystallinity is masked by the more pronounced enhancement of motion,, due to freaking of hydrogen bonds by sorbed water In the amorphous regions* Ferry53 Qnd Andrews^ have both noted that i f a polymer system is represented by an infinite array of relaxation mechanisms for which one can write some distribution function 0 (T) , then there exists a relation between the imaginary part E* of the complex modulus and the rate of change of the real part E' with frequency. This relation may be represented approximately by E» ~ dE»/dlog ^  (12) Inspection of Table V shows that, for most modulus determinations, the value is positive, and varies from values too small to be evaluated, to a large value of 6.6 x 10^ dynes/cm2. A closer examination of dEn/dlogto at 35 and 60 °C. also shows that there is general agreement in behaviour between E" and dE'/dlogu; y i.e., the latter also exhibits a maximum value at some intermediate humidity range. If one ignores the negative slopes at 9 °G. — all except that for 30 % r.h. are sufficiently small to be question-able — one might expect the energy loss to be constant in the low humidity region, and then to increase rather sharply.. The results at this temperature are not sufficiently precise to permit more detailed treatment. APPENDIX Equation (?) can be readi ly derived, not, as might be expected, from a function of toe type £ - f ( u->, T , °~-r) but from a function of toe type , In E» = f(co , lnoOa T ,T) (13) We know experimentally that c u a . - r » £ ( u j J I T ) s o that E ' = £•( u u , T ) By suitable par t ia l d i f ferent iat ion ve obtain The dynamic modulus can be plotted as a single curve against reduced frequency <*^ . Tide curve applies to a l l temperatures., therefore E' has a unique value, irrespective of temperature i f i t i s considered as a func-t ion of reduced frequency.. The l a s t term i n equation (14) i s precisely the rate of change of E* with respect to temperature at constant reduced frequency, and i e equal to zero* ('^f^-E'} • *=. 0 We therefore obtain \ ^ T L I ^ ^ T / T I ?T L (9) I t i s desirable to modify equation (10) in such a way that i t can be used-to calculate activation energies from the present resu l ts . w a. .^0k) (10) Remembering that d( l /T) - - l / r 2 dT. . (10) becomes - ID -Since ^ C ^ - ^ - i - l y ^ » r ) w© may write RT'3- ~ A * C O N S * A N ^ U J % Substituting this relation into (9) One definition of the distribution function for relaxation times is where ^  is the distribution function, and # is a gamma type correction factor, and is represented by. equation (18) Rearrangement of (15) yields JL&~ e' I]d&~t» - 0 Remembering that dflncfaf)^ = din u> since e T is constant i f T is constant} Equation ( 9 ) becomes! Rearrangement yields, at constant to , Since din E' = dE«/E« and d(l/T) = /(l/T^dT, we finally obtain, ^ " /A- \ a* constant "J (11) Thus, one can calculate the apparent activation energy If one knows the value of the distribution function and knows the slop© of a plot of dynamic modulus* at a fixed frequency, against the reciprocal of the absolute temperature.. It must be noted that the applies ability of the time-temperature superposition principle is assumed In this derivation. There are a number of ways whereby <$) (-Intu) may be evaluated, for K J (15) 0(-e*,ou) =, BE'Xi-^eyj^) ( 1 6 ) cp(-e^uu)- cL&^i'/cte^uj (17) - 41 -A and & are second approximation factors defined by A , ( 2 . - w ) / a r ( a - K ) r ( i * r § . x ) { 1 8 ) & . z r ( % - £ ) r ( * * » ) (19) where m i s the negative slope of a plot of log 0from a preliminary/first approximation calculation against the log of the relaxation time t, or c u ~ ' The second approximation i s satisfactory only i f A s B s i . a i s ordinari-l y positive because 0 is usually a decreasing function of cT. The aeroth order approximation for 01s given by <P - EM.. The f i r s t order approximation i s obtained by setting A = B *1» If m lies between 0 and 1, A and B l i e between 0.5 and 1.0. Distribution functions were calculated at a number of relative humidities at e l l temperatures.. Distribution functions were fi r s t calculated at a number of relative humidities at 35 and 60 °C. using a l l three relations (15 to 17).• Examinatlonof these results seemed to indicate that the distribution function defined by the relation (17) was most sensitive to changes in humidity. The relation (18) was rejected because small changes In dlnE*/dlnuj would not materially alter the factor 1 - dlnEtt/dlnuj j. i,©., ^>as thus defined i s relatively insensitive in changes in the slope of In E R against lnu> plots, at least for low values of the slope.. Accordingly, distribution functions were calculated for a l l experiments using the relation (17)s these distribution functions are reported versus relative humidity and moisture sorption on Figures 25 and 26 respectively. \ . BIBLIOGRAPHY 1. Al f rey, T . , Mechanical Behaviour of High Polymers. V o l . ¥1 of High Polymers. flew York: Interscience Publishers. Inc . . 1948 PP 54 f f . 2. -Eyring, H . , H. J . White, G halsey, fi. S te in , and C. H. Reichardt, Mechanical Properties of Text i les . Parts I to XI . tmm. Re^flrch £.Jj5. 295, 451 (1945), l £ 13, 53, 124, 201, 329, 335, 378, 382, 635 (1946). . Glasstone, S . , K. J . La id ler , and H. Eyr ing, The theory of Rate Processes Sew York: McGraw-Hill Book Company, Inc. , 1941. Burte, H . , G. Halsey, and J . H. B i l l o n , Texti le Research g. 18 449 (1948). 3. For a recent review, see Tobolsky, A. ? * , £. AP PI . Phva. 27 673 (1956). 4vhKuhn, W „ Helv. China. Acta. 30 307, 464, 839 .(1947). 5. Becker, R., Pj^bl^me £§£ technlschen Sfegnetlsierungskurve. Ber l in: Springer Verlag, 1938. 6. Ferry, J . D., £ . Am. Chem. Soc. 22 3746 (1950). For a recent review, see Ferry , J . D., Structure and Mechanical Frggertlfg Si SlSJMsat i n Hz§&k, der BoehTOlymeren. V o l . IV. BerlimSprlnger Verlag, 1956 pp. 372 f f . 7. Ch i ld , W. G . , and J . S. Ferry, £ . Col lo id Science 12 389 (1957), and preceding papers. 8. Leaderman, B . , Has&e. and Creep Properties of Filamentous Materials and Other High Polymers. Washington, D. C : Texti le Foundation, 1943. 9. Harr is , M., L. R. Missell, and L. J . Fourt, £ . Research S a t l . Bur. SJgntedg 21 73 (1942) 10. Speakman, J . B . , £ . Texti le Inst. & T102 (1947) 11* Meredith, R., £ . Texti le Inst. & T107 (1945) 1 12. Tobolsky, A. V . , and E . Cats i f f , jr. Polymer S c i . 19 111 (1956). Tobolsky, A. V . , and J . R. McLoughlin, £ . Jftys. Chem. & 989 (1955) Ca ts i f f , E . , J . Offenbach, and A. V.. Tobolsky, J . Col lo id S c i . i i 48 (1956) 13. Hol le , A. W., £ . A P P I . Phya. £9. 753 (1948)} J . Polymer Sc^. 5 1 (1950). 14. Ashworth, J . N . , and J . D. Perry, J . j}m. Chem. s o c . 71 662 (1949). Smith, T. L . f J . D. Ferry, and F. W. Sehremp, £ . A P P I . Phys. J2G-144 (1949). 15. ^ i t te , R. S . , D. G. Ivey, B. A. Mrowca, and E Guth, J . APPL. Phys. 2£ 481, 486 (1949). 16. D i l l o n , J . BY, I. B. Prettyman, and G. L . H a l l , £ . Apol. Phys. £5. 309 (1944). D i l lon , <T. H . , And S . D. Gehman, India Rubber World 115 6 l , 217 (1946) 17. Dune 11, B. A . , and J . H. D i l l o n , Texti le Research J . . Q 393 (1951). Tobolsky, A. V . , B. A. Dohell , and R. D. Andrews, Texti le Research £ . 21 404 (1951). I Dunell, B. A . , and G. Halsey, Texti le Research g. 18 178 (1948). 18. Gehman, S. D,, D. E . Wooford, R. B. Stambaugh, and P. J . Jones, Ind. I k . 3J 1032 (1941)} £ | 694 (1943). 19. Lyons, W. J . . Texti le Research J . 19 123 (1949). 20. Bal lou, J . ¥ . , and J . C. Smith, £... A P P I . Phys. ^ 493 (1949). 21. Ftyino, K. , H. Kawal, and T . Horiho, Texti le Research J . 25 722 (1955). 22. Hamburger, W. J . , Texti le Research J . 3,8 102, 705 (1948). 23. Hammerle, W. G . , and D. B. Montgcmmery, Texti le Research £ . 22. 595 (1953). 24. Williams, M. L . , and J . D. Ferry, J . Polymer S c i . i i 169 (1953). 25. Meredith, R., ^ a n j c a l Properties- fi£ Texti le Fjbres Hew York* Inter-science Publishers, Inc . , 1956 pp. 77 f f . 26. Halsey, G . , H. J . White, and H. Eyring, Texti le Research £ . i 5 295 (1945). 27. Sauer, J . A . , and D. E.. K l ine , J . Polymer S c i . i £ 491 (1955). ^oodward, A.. E „ , C. W. Deeley, B. £., K l ine , and J . A.. Sauer, J . msmz i S l - & 383 (1957)} M 109 (1958). 28. K l ine , D. £ . , J . A. Sauer, and A . E./Woodward, £ . Fqlymar S c j . 2g 455 (1956). - 44 * 29. Woodward, A*, E..» J. A., Saner, 6. W.. Deeley, and 0.. E.. Kline, £. Colloid §s&. IZ 363 (1957). 30. Deeley, G.W.., A.. E.. Woodward, and J. A.. Sauer, J.£EEl» 28 1124 (1957) . : 31. Fitzgerald, E.. R., J. Chem.Phys. 22 1180 (1957). 32. Schmieden k., and I. Wolf„ feltaherlft £2& U 9 (1953). Fuehs, O. , H. Thura, and K. Wolf, Mtgfftorftfft 12£ 27 (1958). Wolf, K., and K.. Sehmleder, MsgES! SplfinUft^g 2JA, 732 (1955) Proceedings of the International Symposium on Macromolecular Chemistry, Turin,, Italy, 1954.- Distributed In North America by Interscience Publishers, Inc, Rew York. 33. Price, S. J. W., and B. A. Dunell, J.Polymer Sjgl. 2& 305 (1955). 34.. Bueche, F. M., P^Jyjss. |ei. gg 113 (1956). 35. Yoshitomi,, T., K. Kagamatsu,- and K. Koslyama, J. Polymer Sci. 27, 335 (1958) . 36.. Tokita,, N., sfaaUL M - » 2P. 515 (1956). 37. Price,. S.. J. W., A*. D. Mcintyre,. J.. P. Pattlson, and B., A., Dunell, 2$2&te fymtiMh.l* 2& 276 (1956). 38. Msyer, K., H., and W., Lotmar, fialv., Chlm.. Acta? 12 68 (1936). see also Meredith* R.,, op., cit., p.. 119. 39. Tokita, H., and K., Kanamsru* Polymer Sci. 22 255 (1958). 40. Fuoss, R. M., £. Ajg.. Chem., Soc. 60 456 (1938) j §1 2329*2334 (1939)f 62 369, 378 (19a). Fuoss, M.., and J. G.. Kirkwood, £. Am. Chem. Soc. 385 (1941). 41. Davies, J.. M., R.. F. Miller, and W.. F.. Basse, Jm,. chem. Soc. £ 2 361 (1941). 42. Heyboer, J . , KoUold geitsehflft 148 36 (1956).. Jenckel, 1., Kolloid Zeltschrlft 12£ 142 (1954). 43. Hoff, K A. W.,f Deutsch* K.., and Reddish, £. Polymer Sci. 12 565 (1954). 44. Hoff, E„ A.. W., D. w.. Bobinson, and A.. H. Willbourn, £. Polymer Sci. U 161 (1955). * 45 -45. Oakes, «. G., and Robinson, D. W . , J. Polymer §cj>. £4. 505 (1954). 46. Powell, R . W . . ffftoc. Phys. S Q Q . 48. 406 (1936). 47* Aserlcan Instrument Company, Inc., Catalogue HumWr 4T4780. 4$. American Instrument Company, Inc., Catalogue Number 4-4815 through ' •.' • 4*4822. 49. Quins, F. G., private communication. 50. Bull , H. 8., £ . Gbem. 66 1499 (1944). see also forward, M. V . , and S . T . Smith, J.Textile that* ^  T158 (1955) as well as Abbott, N. J . , and A. C Goodings, g, flffliftjtta IBS&. Ml 7232(1949). 51. Bailwood, A. J . , and Horrobini S., Trans.. FaradZSee. 42B 84 (1946) 52. Starkweather* H.. W., Jr., G.. E.. Moore, J.EB. Hansen* T. M. Soder, and R. E. Brooks, £ . Polymer 3d. 21 189 (1956). 53. Ferry, J, D.* §.. R . . Fitzgerald, M* F. Williams* a^d L. B. Grandise, J.- A P P J . Phys. jgg 717 (1951). 54. Andrews., R... D.« Ind. .Eng. Ghem., 44 707 (1952). Figure 1. Schematic diagram of the Filament Vibrator. Figure 2. Detail of magnet assembly of filament vibrator and detail of vibrator unit showing the transducer coil. m 1 • • • m •c •oe* 2fA Figure 3. Dynamic modulus E' as a function of log frequency at 9 ° C . and various humidities. 20 30 50 70 100 200 20 30 50 70 100 F R E Q U E N C Y Figure 4 * Dynamic modulus E' as a function of l o g frequency at 3 5 °C. and various humidities. I 1 • . • • I ..... . I I I . 2 0 3 0 5 0 7 0 100 2 0 0 20 3 0 5 0 7 0 100 2 0 0 F R E Q U E N C Y sec Figure 5* Dynamic modulus £* as a function of log frequency et 60 ° C . and -various humidities. 2 I 0 I 0 f 2* 2 — i i 3 -3 n o * V 4 UJ z 2 ui 4 3 5 4 3 *—r 9 5 % 19.0% 3 8 3 % 51.0% 6 7 6 % 8 6 0 % 9 3 5 % _ 5 4 % 16.3% * * * * V 3 0 0 % 4 8 2 % 5 8 4 % 7 6 0 % 8 8 3 % L 2 0 3 0 5 0 7 0 100 2 0 0 2 0 3 0 5 0 7 0 100 2 0 0 3 0 0 F R E Q U E N C Y sec'1 Figure 6. Energy Lose E" ee e function of log frequency at 9 ° C . and various humidities. 1.5 1.0 15 1.0 20 •T 1.5 • o ~ 2 5 S 2 0 j? 25 K -© 2 0 3 c-. i n 3 2.5 2.0 2.0 5 1.5 U J 1.5 10 0.5 22X 39% SIX 56X XT 80X _ 8 -• o — J 1 I I M i I j_ •3IX -' • 4«X 8 5\ I I I M I I i L 20 30 40 60 80 100 200 20 30 40 60 80 100 200 FREQUENCY CO sec"' Figure 7. Energy loss 5" as a function of log frequency at 35 °C . and various humidities. - ' • » 1 -2 -I — 0 - -CSX 20.5% 2 8 2 % 3 7 9 % 51 2 % 59 .8% 7 0 . 7 % 8 5 0 % J _ l ' I • I " I L ia3% 25.1% 3 5 . 4 % 4 1 . 0 % , 5 7 2 % • . * . .. • < 11 >•» 6 3 . 4 % 7 6 . 0 % 9 3 . 8 % i — i I I I I I I L 2 0 3 0 5 0 7 0 100 2 0 0 2 0 3 0 5 0 7 0 100 2 0 0 F R E Q U E N C Y s e c - ' Figure 8. ^ r g y loss E* as • function of log frequency at 6 0 °C. and various humidities. Figure 9. Log/^  as a funetion of log to at 9 °G. and 9.5 % r.h., or 0.94 % water sorption. Figure 10. Log >| ae a funotion of log cu at 9 °C. and 48.2 % r.h., or 3.3 % water sorption. Figure 11. Log as e function of log u> et 9 °C and 76.0 percent r.h., or 5.35 % water sorption. oo, cycles sec. 20 30 50 80 100 150 200 Figure 12. Log 7 as a function of log cu at 35 °C. and 13.8 percent r.h., or 0.92 % water sorption. 1 1 1 1 1 1 1 1 1 I I l _ \ - N » \ o a \ — — r- ^ - 2 % X \ • s CvJ E — o . a — — tn 4) c ° & . -o r _ s=r \ " i l l oo, cycles sec. i i I I i 11 I I 15 2*0 " 30 40 60 80 100 150 200 Figure 13. Log q as a function of log cu at 35 °C. and 56.2 % . r.h., or 3.25 % water sorption. I — — Figure 14. Log ^ as a function of log circular frequency at 35 °C. and 82.7 % r.h.» or 5.25 % water sorption. Figure 15* Log rj as a function of logic at 60 °G. and 20,5 % r.h., or 0*95 $ water sorption. Figure 16. Log as a function of log to,at 60 °G. and 63*4 % r.h*, or 3,10, % water sorption. Figure 17. Log n as a function of log u) at 60 ° C and 93*8 % r.h., or 5.45 % water sorption. Figure 1 3 . J-ynaaic modulus E' evaluated at ui =20 plotted against relative humidity. 60*C I I ! ' I I I i 20 40 60 80 100 R E L A T I V E H U ' ^ i S i ^ Y 1. Figure 1 9 * Dynamic modulus E' evaluated at = 150 plotted against relative humidity. RELATIVE HUMIDITY % Figure 21. Energy loss E" evaluated at u*»150 plotted against relative humidity. Figure 22. Weight percent of water sorbed by 100 g. of stretched nylon, at 9 , 35, and ° C . The data are taken by extrapolation from Bull* results. Figure 23. Dynamic modulus E » , evaluated at uJ -150 plotted against the weight of water adsorbed per 100 g. nylon. 30 RELATIVE HUMIDITY % Figure 25. D i s t r i b u t i o n function 0, evaluated at 0/3,150, plotted against r e l a t i v e humidity. 


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