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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  THE  INFLUENCE OF WATER SORPTION OH  DYNAMIC  AND THE  MECHANICAL PROPERTIES  PLASTICISIKG  EFFECT  OF HYLOK 6-6 GF WATER  by  JACQUES MARIE RAXMOND QUISTWATER B. A . , University o f B r i t i s h Columbia,  1954  A THESIS SUBMITTED US PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Master o f Science i s the Department of CHEMISTRY We accept t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  April,  1958  ABSEAGT Wuch work baa r e c e n t l y been done on s t u d i e s o f aechanical and e l a e t r l c s l dispersion phenoaana i n polymers* ^ay workers have been a c t i v e studying the effect o f 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  Eschanical  trea-teaat, copolyjaerisation, and c r o s s - l i n k i n g , such ae  v u l c a n i s a t i o n , on a large a m b e r of high polyinsre. In s p i t e o f i t s great t e c h n o l o g i c a l importance, ths effect o f hiamidity on the isechanieal prope r t i e s o f textile f i b r e s has not boon studied i n a systematic way. The present i n v e s t i g a t i o n l a an attempt at studying the i n f l u e n c e o f humidity on th© modulus and energy d i s s i p a t i o n o f nylon 6-6 sionofilaBente. The modulus and energy l o s s were determined u s i n g a low-fTequeaoy vibyoaeter, ovor the f u l l range o f r e l a t i v e h u m i d i t i e s at 9, 35$ and 60 °Q., u s i n g 15 denier nylon zaonofHaiaents. Values o f these e m p i r i c a l q u a n t i t i e s were p l o t t e d as f u n c t i o n s o f &equency and hum i d i t y , and water content. The r e s u l t s were discussed t a k i n g i n t o account the f a c t t h a t water sorted lay f i b r e s i s present predominantly i n the amorphous r e g i o n s , and might be expected t o 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 t o e x p l a i n the r e s u l t s . The values o f the tangent o f the l o s s angle vera compared w i t h recent work by Saner at a l . Using espresssions derived by F e r r y and coworkers, apparent a c t i v a t i o n energies f o r the flow processes were c a l c u l a t e d at a number o f f i s e d water contents, and were fiund t o v a r y between 26.3 and 110 kcal./mole.  In presenting the  this  r e q u i r e m e n t s f o r an  thesis in partial  advanced degree at the  of B r i t i s h Columbia, I agree that it  freely  agree t h a t for  available  the  f o r r e f e r e n c e and  permission for extensive  s c h o l a r l y p u r p o s e s may  D e p a r t m e n t o r by  fulfilment  be  s h a l l make  study.  I  the  gain  s h a l l not  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 V a n c o u v e r S, C a n a d a .  Columbia,  Head o f  thesis my  I t i s understood  copying or p u b l i c a t i o n of t h i s t h e s i s a l l o w e d w i t h o u t my  further  copying of t h i s  that  be  University  Library  g r a n t e d by  his representative.  of  for  written  financial  permission.  - 1 TABLE OF GG8TIS73 I. Theoretical and Experimental Introduction. . . .• . . . . . p. A. Historical Survey.  1.  p.  1  B. Recent Work on th© Mschanical Properties of Polymers, p.  1  1. Types of Experiiaents . . . , * . . . . . . . . . .  p.  1  i s Studied as a Function of Time or Frequency . p.  2  a. Experiments i n which Stress* Strain, or Modulus  b. Stress-Strain Experiments  p.  4  are studied as Functions of Temperature . . . . p. 2. Correlation of Tic©, and TeBg^rature Effects . . . p.  4 6  3. Influence of Humidity, Copolys&risatlon, and Irradiation. . . . . . . . . . . . . . . . . . . . . . . p.  7  c. Espsriasnts i n which Modulus end Energy Loss  0. Dielectric Studies on High Polymers  p.  9  D. Correlation between Mechanical and Dielectric dispersions i n Polymers.• • . . . . . . . . . . p. 10 E. Experimental Methods. II. Apparatus and Experiments. . . . . . . . . . .  p. 11 p. 14  A. Description of the Apparatus. . • . . • . • • • • • • p. 14 B. Calibration of the Solenoids and Determination of Parameters. III. Results. 17. discussion... . . . . . . . . . . . . . . . . . . . . . . V. Appendix VI. Bibliography . . . . . . . . . . . . . .  p. 21 p. 26 p. 31 p. 39 p, 42  THEORETICAL AKD EXPERIMi^TAL  A.  IKTRODUCTIOH  H i s t o r i c a l Survey Studies of dynamic modulus, energy l o s s ,  and stress relaxation, and creep have been performed on a variety of materials, including wood, rubber, metals, and natural and synthetic f i b r e s .  These studies were i n i t i a t e d by  Hooke who enunciated the l a v of e l a s t i c i t y bearing h i s name. As a result o f 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 a length 1.  F  and A 1 i s the elongation of  The studies of v i s c o e l a e t i c i t y 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 h i s theory of rate 2  processes, leading to a non-Hewtonian v i s c o c i t y , and by the concept of a d i s t r i b u t i o n 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, s t r a i n , or modulus  i s studied as a function of time or frequency, has been investigated most extensively.  Experiments that f a l l i n this  class include stress relaxation, creep experiments, vibrationaltorsional studies, and sound propagation.  The second type of  experiments, i n 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 i n this f i e l d , 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 e l a s t i c i t y , the modulus increases with increasing temperatare,  Corresponding to  each sharp modulus decrease i n a transition temperature range, there i s a maximum i n energy dissipation i n vibrational experiments, a.  Experiments i n 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 behaviour of various fibres.  9  Harris,  10  Speakman  , and Meredith  11  ,  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 superimposing a l l 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, polyisobutylene, 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 a l l cases, between 10 and 10 dynes / cm , within  o the time-3eele 10  -7  - 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 i s 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. Halsey and Eyring  2,26  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 viscoelastic 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 f i t 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.  Nolle  13  has studied the mechanical  p r o p e r t i e s o f s y n t h e t i c and n a t u r a l rubber, both unvulcanlged and vulcanised, over a v i d e frequency and temperature range.  In  a d d i t i o n , he performed some experiments 6n the e f f e c t o f added carbon black, as a " f i l l e r * , on the p r o p e r t i e s o f the rubbers. I t has been postulated that the carbon b l a c k e x i s t s i n the rubber as a separate phase, and may therefore be expected t o e x e r t a marked e f f e c t on the dynamic p r o p e r t i e s o f the rubber.  H i s experiments  have, i n f a c t , confirmed t h i s v i e v . 27 Saner, K l i n e , and o t h e r s  have examined  the dynamic p r o p e r t i e s o f both c r y s t a l l i n e and n o n - c r y s t a l l i n e polymers.  They report t h a t polyethylene and p o l y t e t r a f l u o r o e t h y l e n e ,  both c r y s t a l l i n e m a t e r i a l s , e x h i b i t maxima i n the energy l o s s versus temperature curve, a t 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 g e n e r a l i s e from these  observations, f o r energy l o s s maxima have been observed a t temperatures w e l l below room temperature f o r v a r i o u s methacrylates,  \ which are amorphous. They have a l s o examined the e f f e c t o f branching 28?  on the mechanical p r o p e r t i e s o f polyethylene •* In a d d i t i o n , they have a l s o i n v e s t i g a t e d the e f f e c t of i r r a d i a t i o n on the dynamic p r o p e r t i e s o f nylon 6 - 6 , n y l o n 6 - 1 0 * and a copolymer o f nylon 6 - 6 , nylon 6 - 1 0 , and nylon 6 ,  29,30  as w e l l as the e f f e c t o f humidity on  the value and temperature o f 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 . Fitzgerald has studied the mechanical resonance d i s p e r s i o n i n t e f l o n , and r e p o r t s a s a t i s f a c t o r y  - 6agreement between experimental results and the behaviour predicted from the simple mechanical model he postulates. He obtains an activation energy of 13.2 fecal./mole. 32  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 i n Great Britain have studied the modulus and energy loss factor of various acrylic polymers, and polyethylene  over a temperature range of about  o 43*44*45 300 C.  2.  Correlation of Time and Temperature Effects. The time-temperature superposition 6  3  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 semicrystalline 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 a l .  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  21  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 a l l 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 and destroying cryatalllnity. G.  30  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 i n a way which suggests a relaxation mechanism.  Examining the system polyvinyl chloride-trio 4 cresyl phosphate at 40 C , and 20 to 1© e.p.s., and a variety  of compositions, he observed maximum change i n the electrical properties i n the range 50-70$ polyvinyl chloride, and postulated a hindrance of freedom of orientation o f dipoles i n polymeric materials i n 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 l e x i b i l i t y 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 i n the low concentration (0 to 2$) range of compositions, and concluded that this represented a viscosity phenomenon. He  -  10  discussed these dipole moments onjia theoretical basis, and showed that the results for the polyvinyl chlorlde-diphenyl system were i n agreement vith theoretical deductions. 41  Davies, Miller and Busse  carried  out investigations parallel to Fuoss*, on polyvinyl chloride plastioised with dimathylthianthrene, t r i t o l y 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 i n 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 i n Polymers.  32,42 Zeitschrift  Several papers published i n Kolloid point out the parallelism between meohanical  dispersion and dielectric relaxation phenomena i n high polymers. 42 Beyboer  reports observing two peaks i n 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 lov44  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 i n which a mass l a attached to the fibre and the free vibrations of the system are measured, and the other i n which the fibre i s subjected to forced vibrations by applying a displacement 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 i n propagating a sound wave through the polymer sample, and measuring i t s velocity and attenuation. In most vibration experiments, the  - 13 strain amplitude i s 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 0 sin(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 i n 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 i n 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  ha4iour) « * * E "  n s c ^ X a e U c te  ie  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 i n 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 temperature, and moisture content.  as functions of frequency, 4s i n most cases one i s dealing  with a set of viscosities or relaxation times, the resultant viscosity w i l l be frequency dependent.  -uAPPARATU3 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 i n 16 shear, as described by Dillon, Prettyman and. H a l l . Descriptions of the Apparatus. The apparatus used i s sketched schematically i n 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 c o i l lying i n a radial magnetic field which traverses the annular space E i n the magnetic c i r c u i t shown i n 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 i n the magnetic field and insure that there i s no contact between the c o l l and the sides of the angular gap i n 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 i n turn inserted  15 i n t o a s l o t at each end o f the abaft of the v i b r a t o r u n i t and made f a s t there v i t h a small pin H.  The other end of the filaments  pass, through a r e l a t i v e humidity and temperature adjusting boxes J , to pulleys K at the end o f the apparatus, and are tensioned by the weights L .  The filaments may be clamped at various p o s i t i o n s 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 c o a x i a l l y on a horizontal spindle and l y i n g i n a r a d i a l magnetic f i e l d .  The  solenoid c o l l s consisted r e s p e c t i v e l y of about 2, 25, and 90 turns o f 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 o f a Leeds and Northrup thermomilliammeter whose f u l l scale reading could be adjusted t o 2, 10, or 50 milliamperes.  The frequency of  v i b r a t i o n of the transducer assembly could be changed continuously by a l t e r i n g the frequency o f the applied electromotive f o r c e , which I s , i n f a c t , the frequency o f v i b r a t i o n .  The apparatus could be tuned to  mechanical resonance by adjusting the frequency o f the HewlettPackard low frequency o s c i l l a t o r used.  The exact resonant frequency  could be determined by determining the frequency at which the amplitude of v i b r a t i o n was a maximum f o r a given current value, o r , f o r frequencies i n excess o f 10*- e . p . s . , by that frequency at which the peak to peak amplitude o f the voltage across the solenoid c o i l was a maximum as displayed on an o s c i l l o s c o p e .  The l a t t e r method was used  as much as p o s s i b l e , inasmuch as s t r a y mechanical v i b r a t i o n s of the system as a whole seemed to have a l e s s 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 46  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 a l l 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 i s 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 a i r could be altered to practically any desired value by adjusting the volume of a i r passing through the drying columns and saturating vessels.  When no a i r 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$6 could be obtained. Essentially the same experimental set-up was used to determine the mechanical properties at 9 following modifications.  v,#  ' with the  In order to condense out as much water as  possible, the compressed a i r stream was passed through cooling c o l l s located immediately i n front of the cooling fan used to cool the room. Then I t was passed through a glass water trap to remove condensed water, and, f i n a l l y , through two columns, one packed with glass wool, tVo remove small spray droplets, and another packed with anhydrous calcium chloride.  Part of this a i r stream was then passed through  saturating vessels; these were, however, not held i n constant temperature baths. The humidity of the a i r stream was adjusted as i n o the 35 G. work. During the course of any particular experiment, the temperature of the a i r stream was measured periodically. Although the o ' room temperature was maintained at 2 plus or minus 0 . 2 C., i t was found that the temperature of the a i r stream could not be lowered to o this temperature, but remained quite constant at 9 plus or minus 0 . 3 C. Using freshly peeked drying towers, i t was possible to attain relative humidities below 5% - the l i m i t of the sensing elements - nominally  - 13 listed in the results as *0* relative humidity, because the recorder indicated a reading of 0.  The maximum humidity attained was 96$.  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 range so that, with some overlap between s  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 a i r stream was adjusted by combining a dried and a wet stream of a i r i n appropriate proportions. The wet a i r was obtained by passing compressed a i r through the saturating vessels as before, but this time the o i l bath temperature was maintained at 75 ° C . The two a i r streams were combined in an a i r manifold immersed i n the water circulating bath maintained at 60.0 plus or minus 0.05 ° C . After passing through a heat exchanger also immersed i n the water bath, the a i r 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 t h i s difficulty, a stream of compressed a i r was made to flow at each end of the tranducer assembly, i n such a way as t o deflect the moist a i r emanating from the chambers, thereby preventing condensation of water on the transducer. As this a i r flow interfered i n 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 symmetrical 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 v i b r a t i n g spindle by gram weights approximately equal to h a l f the denier value of the filaments, e . g . , S g f o r 15 denier n y l o n , and allowed to creep under t h i s applied load f o r sixteen to twenty hours before he experiment, and was kept under t h i s tension during the? experiment. During the tensioning and conditioning period «~- u s u a l l y over night — c o n t r o l o f the humidity was u s u a l l y w i t h i n 5 $ o f the required humidity. J u s t preceding, and during the actual v i b r a t i o n a l experiment, the humidity was manually adjusted, i f necessary, t o the required humidity. Overall v a r i a t i o n i n the humidity during the actual experiment was 1 to 2 %, depending on the temperature.  In a l l experiments, the v i b r a t i o n a l amplitude was approximately 0.15 % s t r a i n , i n most cases, several determinations o f the mechanical p r o p e r t i e s , on d i f f e r e n t filaments, were made. When s u f f i c i e n t data, u s u a l l y three runs, had been gathered at a given humidity, the humidi t y was increased by about 10 $ . The e n t i r e humidity range was scanned i n t h i s way, the r e s u l t s were plotted i n rough fashion In order to keep track o f 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 o f the system, the v i b r a t i o n a l amplitude, and the current required f o r that amplitude were recorded. At 35 ° C , the temperature and humidity were recorded as w e l l ; at 9 ° C , r e l a t i v e humidity o n l y . At these two temperatures, the humidity during the course o f the experiment was determined as the? average o f these readings. At 60 ° G , the average r e l a t i v e humidity was obtained by i n t e g r a t i n g the area under the' recorder t r a c e .  •  ~ 21 the resonant frequency o f the system was altered  by changing the length of the filament clamped, and by Increasing the mass on the v i b r a t i n g s p i n d l e . The l a t t e r method merely required p l a c i n g small weights; from 2 to 100  g on the v i r a t i n g s p i n d l e . Using these methods, i t  was possible to obtain readings over somewhat more than one cycle o f l o g arithmic frequency.  B. C a l i b r a t i o n o f the Solenoids and Determination o f Parameters.  The solenoids, or v i b r a t o r u n i t s , were c a l i b r a t e d so that the fiorce they exerted could be determined from the current floowing through them . To do t h i s , the magnet-vibfator assembly was set up v e r t i c a l l y 1  i n such a way that the v i b r a t o r u n i t could be suspended f r e e l y In the magn e t i c gap> by a l i n e a r c a l i b r a t e d s p r i n g , ^fae v i b r a t o r was centered v i ^ l u ^ the magnetic gap, and was then loaded with a succession of a n a l y t i c a l weights The v i b r a t o r was brought back to I t s unloaded p o s i t i o n by passing d i r e c c t 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  gravitational  constant! K, the modulus o f the s p r i n g , and A x i s the distance between .loaded end unloaded p o s i t i o n s o f the vibrator u n i t . Ixperiaentation allowed, however, that the corrections r e s u l t i n g from d i f f e r e n c e s i n the exact p o s i tions o f the v i b r a t o r u n i t between the loaded and unloaded p o s i t i o n s could be neglected, as these corrections amounted to o n l y a few tenths o f one percent, at the » r y most. Accordingly, F s Mg was considered t o give a value s u f f i c i e n t l y close to the actual v a l u e . A p l o t of F against i ,  the  current i n milliamperes, w i l l give a straight l i n e o f slope T d y n e s per milliampere. &n alternating current whose root mean square v a l u e , read o f f the a l t e r n a t i n g current milliampere, i s i exerts a maximum force It  i s t h i s maximum force which Is used In the c a l c u l a t i o n o f  l . w  Fmax = </2H7  - 22 Two different vibrator assemblies were constructed during the course of this work. The f i r s t assembly's main c o i l was accidenta l l y burned out midway i n the 9 °C work. Both consisted of three solenoid coilss one large* of about 90 to 95 turns, a smaller c o i l of 25 to 30 turns, and another, smaller yet, of 1 to 2 turns. In the calibration of the large c o i l s , 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 i n Table I. Table I. Coil Calibrations. F i r s t Assembly lumber of turns  Second Assembly  Calibration Faetor  Mumber of turns  dyne/ma.  Calibration Factor dyne/ma.  93  50.0  90  60.2  25  12.09  30  20.3 1.40  %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 * dt* dt where R s and  1  F ^ ^ coscot  „ • %  .  v  P -2|E' 1  * P,  (2)  (3) (4)  A  P^ i s a correction factor for the ^ r t i c a 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 i n the filaments. It i s given by  » F/to,x, at resonance,  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  where  «  , -  F ^ * ( Mu) - P ) 2  =  (©)  —  ( Mcu and  (5)  2  - p )2 4, i2u>2  a ' = Unax  Differentiation with respect to time, and use of equations (6) and ( 7 ) shows that x ^  = F 0 /-[(Mu) 2 - P ) 2 * B 2 c u 2 }  i  (8)  g 2 2 i uegligible compared to {Mui - ff for values of u> which are not 2  w  a  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 i n fable I I . Table I I . Mass Sali^r^tions. F i r s t Assembly Effective Mass M, i n grams. 4.69 24.64 . ..  Second Assembly  leighed Mass  Effective Mass  gram  M>. i n g.  Weighed Mass g;  4.08  4.51  4.40  25.04  16.6  16.1  Several mass ealibfations were performed on each of the two vibrator assemblies. % f f l e a l 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 i n Tables III and I?.. The values reported for  i n the; f i r s t column In  Table III were obtained by plotting x/F versus tu and drawing smooth curves through the p o i n t s T h i s met hod was not deemed satisfactory,  as the uncer-  tainty In the exact position of the inflection point was very great} sometimes this uncertainty amounted to 20  Accordingly, subsequent values  Table III. Ri Correction Factors for F i r s t Transducer Assembly. Total weight of transducer assembly and added mass. gram  R} factor. In dyne-sec./cm, evaluated for experiments at 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 i n 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 i n the f i r s t column of Table IV were; obtained; for the assembly with colled leads going  - 25 from the solenoid coils to fixed terminals placed on top o f the magnet, the lower values reported i n the second column were obtained for straight leads simply curved upwards from the solenoid terminals to the fixed terminals on the magnet. Table 17.  Correction Factors for Second Transducer Assembly..  Total weight of transducer assembly and added mass.  Rj_ factor, In dyne-sec/cm, 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  13.63  1.73 1.91  14.12  3.58  1.91  15.96  ...  1.63  19.35  —  1.65 1.88  25.1 29.8  3.55  1*59  41.2  4.82  1.96  55.1  4.44  2.72  80.2 105.3  2.37 —  3.49  RESULTS  The dynamic modulus E* o f nylon i s p l o t t e d as s> function o f logar.tlthmlc frequency at a number o f r e l a t i v e humidities at 9» 35 and 60 ° C . i n Figures 3» U and 5 r e s p e c t i v e l y . Inspection o f the 9 oC. r e s u l t s shows t h a t , i n most eases, the dynamic modulus Increases with increasing frequency. This increase I s not so great as ttiat reported by  21 Fujino e t a l .  f o r Nylon 6., I t  i s not a t a l l c l e a r why the modulus  decreases with increasing frequency i n the region 19 t o 60 % r . h . A c l o s e r examination o f the r e s u l t s at any humidity w i t h i n the range- shows that some experiments e x h i b i t an Increase; i n E» vit3i increasingrfrequency*. The foremeationed a f f e c t may be? spurious, f o r the slopes observed at?higher humidities might l e a d one to believe that only a decrease i n elope to zero, followed by an i n c r e a s e , to rather large values, with increasing r e l a t i v e humidity may occur. The r e s u l t s are not s u f f i c i e n t l y p r e c i s © , however, to permit detailed a n a l y s i s . ?&e 35 and 60 o&. r e s u l t s f o r the dynamic modulus show more r e g u l a r i t y ,  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 o f Table ? . It  was found t h a t , although i n d i v i d u a l runs were  f a i r l y consistent within themselves,, showing only small deviations from l i n e a r i t y , , d i f f i c u l t y was experienced i n reproducing these v a l u e s , at the same humidity.. Examination o f the r e s u l t s at 35 ° C . and 63 % r . b . shows 5  that the two runs do not superimpose at a l l . Results f o r each run were plotted against logarithmic frequency; and the best s t r a i g h t l i n e  drawn  through them. These; straight l i n e s were averaged to give the l i n e s reported on the graphs.  - 27 _ Table  Slopes of E* against log 9 GC.  r.h. 0  35  Slope 0  graphs, i n dynes/em2 x 1 0 " ^ # ° C  60  °G.  r.h.  Slope  r.h.  Slope  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  - ©as  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  56.2  - 0.54  51.2  - 0.54  51.0  0  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, i n 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 i n the: graphs, as they overlapped one another•• This situation Is especially true with respect to those determinations i n 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} i n 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 i n excess of 65 %* i t appears to increase gain with increasing frequency. These conclusions mayfe*checked by examining the; values fir ne slope of the graphs of E a against logcu i n Table VI. The. slopes o f the energy loss; versus logarithmic frequency curves do not appear to increase wit© increase i n relative humidi t y . 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 l i n e 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 arbitrarily chosen values of oo  (E®) were evaluated at  and were plotted an toe I B versus: log W J  graphs, to give the straight line reported i n the B s u 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 =• constant l i n e s , 8  included for purposes of comparison.  Table VI. Slopes of E* against log  2  35 0 C .  9 °C r.h.  graphs. In dynes/cm x 10-9. 60 °C,  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  51.2  - 0.29  51.0  0  ©  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  80.$  - 0.27  70.7  - 0.44  82.7  -0.32  76.0  - 0.29  89.2  - 0,21  85.0  - 0.13  96,0  - 0.30  93.8  - 0.19  86.0  0  88.3 93.5  - 0.65  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. Thefirmerrepresents 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 a l l relative humidities, whereas at 9 °C., the modulus i s insensitive to frequency changes up to about 50 % r.h., but  then s t a r t s to decrease, rather sharply, with increasing humidity. Figures 20 and 21 report energy l o s s as a function o f r e l a t i v e humidity at cu s 20 and ui s 150. The average value o f E  t t  increases with i n c r e a s i n g  humidity at a l l humidity v a l u e s , at 9 ° G . At 35 and 60 ° C , the behaviour i s more complex} i t leads to a s h i f t In the p o s i t i o n o f the maximum peaks. At 35 ° C . , the peak s h i f t s from 55 % *vh.._ a t cu s 20 to 6 4 % r . h . at cu*150.. S i m i l a r l y , at 60 ° C , the peak s h i f t s from 33 % r . h . a t  UJS  20 to 44 %  r . h . at c o s 150.  The values o f E* and E  B  evaluated at cu s 150 are  p l o t t e d versus the amount o f water adsorbed at equilibrium by nylon at the humidities studied, on Figures 23 and 24.- Values f o r water adsortion were obtained by extrapolation o f B u l l ' s d a t a , assuming l i n e a r r e l a t i o n s . . he J  data so obtained are p l o t t e d on Figure 22. S t r i c t l y speaking, extrapolation o f B u l l ' s data Is not j u s t i f i a b l e . . The e r r o r Introduced, however, i s probably not very great.  50  DISCUSSION  r Schmieder and W G lf32 have examined the mechanical properties o f various nylons,, over a vide temperature range and at very low frequencies, and report energy l o s s maxima' i n three regions,, with indications o f an increase i n energy l o s s above 200 ° C , v i t a the onset of melting. For nylon 6 6 „ the three maxima occur at about 153, 223, and 338 °K. These: dispersion regions are: u s u a l l y referred to as the and  7r  x  &^  °<' dispersion regions respectively^ and the region about the melt*  ing point i s referred to as the: ° ( dispersion region.. The <* region In the energy l o s s curves a r i s e s from the enhance sent of chain m o b i l i t y r e s u l t i n g from melting o f c r y s t a l l i t e s .  s  he other peaks are b l i e v e d to  arise from cooperative motions o f e i t h e r 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 f o r motion i n the various dispersion regions,; f o r both nylon 6-6 and nylon 6-10, evaluated by low frequency methods. (^1  e.p.s.)  Table VII*. Activation Energies calculated f o r nylon 6-6 and nylon 6-10 by Sehmieder and Wolf. Dispersion Region  Temperature °K.  Energy o f A c t i v a t i o n o f •iscoufl Flow 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 d i f f e r e n t the (b or  the T" d i s p e r s i o n , which Sehmieder and o l f believe a r i s e from w  mechanisms not too d i f f e r e n t 29 30' al..  from e i t h e r  from one another. The suggestion o f Sauer e t  • that the<* dispersion may r e s u l t from the onset o f motion o f  large chain segments i n the amorphous regions seems therefore  reasonable.  - 32I t Is believed that the ^ p e a k r e s u l t s from tbe onset o f cooperative movement o f CRg groups within the polymer chain, ^his peak has also been observed i n polyethylene and In c e r t a i n methacrylates. The o r i g i n o f toe ($ peak i s not a t a l l d e a r . . 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 t o other amide groups, on the other hand, i n polyethylene, t h i s peak i s believed t o a r i s e from motion o f side g r o u p s * * S i m i l a r dispersion phenomena Have been observed 2  for teflon  (i  polyethylenes, and some methacrylates. M l four dispersion  regions are not  necessarily observed i n  every substance, however. The  peak i s u s u a l l y referred to as toe primary absorption maximum;  toe  V  and  toe T peaks, as secondary absorption maxima.  Woodward, Sauer, Kline and B t o l » 7 * * > V » examined toe damping f a c t o r ( tan o* E / E t t  f  ) versus temperature maxima f o r nylon 6-6  and have reported a marked dependence o f both toe magnitude o f toe maximum and the temperature a t which the maximum occurs on toe water content. In t h e i r experiments, they used rods o f nylon approximately 0.6 to 0.8 em i n diameter and 10' to 11 em long.. Examination o f *!gure 2 o f t h e i r r e s u l t s gives the following data f o r 308 and 333 ° K . * Table V I I I . Comparison between toe Results obtained i n t h i s i n v e s t i g a t i o n and Results reported by Sauer and coworkers. Treatment  Estimated Humidity  16 mos i n desiccator As received 3 weeks at 100$ r . h .  0%  40 % 100 %  tan o~ 308 O K . 333 ° K . Sauer Present Sauer Present Results Results  0.012 0.036 0.070  0.016  0.054  0.012  0.031  0.111  0.045  0.036  0.01  0.018  One should not very great significance t o these  - 33 results, however, since the penetration of water to the inner portions of the nylon rods has not been established. The values l i s t e d i n the column "estimated Humidity*' are not Sauer's. The values quoted i n 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 E w against moisture content (Figures 23 and 24) w i 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 0 . At very low'we tar contents,; the energy loss G  i s 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 dissipation inoreases, because more chains can flow. Simultaneously, the force required to move a chain segment w i l l decrease with decreasing chain Inter-  -34action, 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 i s 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 i s 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 i s 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 i s 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 i s raised,, the. energy loss peak moves to lower moisture contf ent values. I Various workers have suggested that an increase in relative* humidity corresponds qualitatively to an increase i n frequency for the process, and vice * versa. Accordingly, when the energy dissipation 1  is evaluated at to-. 20 rather than at w= 150, one should expect the maxima i n 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 cu 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 i n which he calculates values for the apparent activation energy for viscous flow for a> number of polymers using the relations (9)  and  ..  rt  (10)  where £* i s the real part of the dynamic modulus, <^Is the temperature reduction factor used to reduce values of £' and E to one arbitrarily N  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 a c t i v a t i o n e n -  ergy f o r viscous flow. In order to apply these r e l a t i o n s to the present r e s u l t s , equations (9) and (10) were: modified t o : (See Appendix.) AHft.  --  (11)  451  here A i s a gamma function defined In terms of experimentally determinable quantities.. I f  one knows the value of A, ^  and <JE/<1(-^) one can  calculate A H . . P l o t s o f E ' against l/T at various constant water content a  values seemed to indicate e s s e n t i a l l y two slopes, f o r the data were not s u f f i c i e n t l y precise to allow further discrimination between the slopes. The slopes of the l i n e s f o r which the water content was l e s s than 2 . £ g . water per 100 g.. n y l l n a l l l a y between 3.70 and 4.06 x l O ^ d y n e s - ° C . / c m 3  2  and were averaged to 3.89 x l O ^ d y n e s - C . / c n $ . At about 2.-5 g water per 1  100 g of n y l o n , an intermediate  6  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?"^ d y n e s - ° 0 . / c m . The slopes were 2  averaged i n t h i s way because i t was f e l t that the methods used were net s u f f i c i e n t l y precise to enable one to discriminate between the values* The function A was calculated f o r each humidity f o r which i t was required, as described i n the appendix*. Table IX summarises the r e s u l t s f o r the apparent a c t i v a t i o n e n e r g y A H . Activation energies l i s t e d by Ferry^ f o r a  eight amorphous polymers such as rubbers, p o l y v i n y l acetate and polymethylmethacrylate range from 14 to 82 k c a l . / m o l e . t h i s would suggest that the values herein obtained, with the exception of the two values i n excess o f 100 kcal./mole,, are: not too unreasonable.  If  increasing water content exerts a p l a s t l c l s i n g  - 37 effeet upon the nylon, causing a breaking of hydrogen bonds in the amorphous 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 V p e a k , 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. 1.0  Activation Energies 9 °P.  35 °C  60 °C.  110  43.8  26.3  2.0  49.0  4.0  43.8  28.8 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 i s toe case for nylon 6-6, but i f i t were, then any water adsorbed below this limit could provide very l i t t l e plasticisation, and one would expect l i t t l e 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 i s possible that this increase i n modulus due to an increase in crystallinity i s masked by the more pronounced enhancement of motion,, due tofreakingof hydrogen bonds by sorbed water In the amorphous regions* Ferry53 nd Andrews^ have both noted that i f a Q  polymer system i s 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 i s positive, and varies from values too small to be evaluated, to a large value of 6.6 x 10^ dynes/cm . A closer examination of dE /dlogto at 2  n  35 and 60 °C. also shows that there i s 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. — a l l except that for 30 % r.h. are sufficiently small to be questionable — 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 r e a d i l y d e r i v e d , n o t , as £ -  be expected, from a function o f toe type but from a function of toe type  f ( u->, T , °~-r)  ,  In E» = f ( c o , l n o O a , T )  (13)  T  We know experimentally that  might  c u a . - » £ ( u j T ) s o that r  J I  E ' = £•( u u , T )  By suitable p a r t i a l d i f f e r e n t i a t i o n 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, i r r e s p e c t i v e of temperature i f i t i s considered as a funct i o n o f reduced frequency.. The l a s t term i n equation (14)  i s precisely  the rate of change o f E* with respect to temperature at constant reduced  ('^f^-E'}  frequency, and i e equal to zero*  We therefore  \ ^ It  T  •  *=. 0  obtain  L  I ^ ^ T / T I  i s desirable to modify equation (10)  ?T  L  i n such a way that i t  (9) can be  used-to calculate a c t i v a t i o n energies from the present r e s u l t s . w a.  .^0k) Remembering that d ( l / T ) -  - l / r d T . . (10) becomes 2  (10)  - ID Since  ^C^-^-i-ly  w© may write  RT' -  ^  »  r  ~  3  )  A  *  C  O  N  S  *  A  N  ^  U  J  %  Substituting this relation into (9)  One definition of the distribution function for relaxation times i s  where ^ i s the distribution function, and # i s a gamma type correction factor, and i s represented by. equation (18)  JL&~ e' I d&~t»  Rearrangement of (15) yields  ]  - 0  Remembering that dflncfaf)^ = din u> since e i s constant i f T i s constant} T  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 i s assumed In this derivation. There are a number of ways whereby <$) (-Intu) may be evaluated, for K  (15)  J  0(-e*,ou)  =, BE'Xi-^eyj^)  cp(-e^uu)-  ( 1 6 )  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  )  z r ( % - £ ) r ( * * » )  where m i s the negative slope of a plot of log  {  1  8  )  (19)  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 ordinaril y positive because 0 i s usually a decreasing function of cT. The aeroth order approximation for 01s given by <P - E .. The f i r s t order approximation i s obtained by setting A = B * 1 » M  I f m l i e s 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 f i 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 i n humidity. The relation (18) was rejected because small changes In dlnE*/dlnuj would not materially alter the factor 1 - dlnE /dlnuj j. i,©., ^>as thus defined i s relatively insensitive i n tt  changes i n the slope of In E against lnu> plots, at least for low values R  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. A l f r e y , T . , Mechanical Behaviour o f High Polymers. V o l . ¥1 o f High Polymers. flew York: Interscience P u b l i s h e r s . I n c . . 1948 PP 54 f f . 2. -Eyring, H . , H. 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Chem.Phys. 22 1180 (1957). 32. Schmieden k., and I. Wolf„  feltaherlft  Fuehs, O . , H. Thura, and K. Wolf,  £ 2 & U 9 (1953). Mtgfftorftfft 1 2 £ 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. | e i . 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, fymtiMh.l*  2$2&te  2& 276 (1956).  38. Msyer, K., H., and W., Lotmar, fialv., Chlm.. Acta? 12 68 (1936). see also Meredith* R.,, op., cit., p.. 119. 39. Tokita, H., and K., Kanamsru*  Polymer Sci. 22 255 (1958).  40. Fuoss, R. M., £. Ajg.. Chem., Soc. 60 456 (1938) j §1 2329*2334 (1939)f 62 369, 378 (19a). Fuoss, M.., and J. G.. Kirkwood, £. Am. Chem. Soc. 385 (1941). 41. Davies, J.. M., R.. F. Miller, and W.. F.. Basse, 361 (1941).  Jm,. hem. Soc. £ 2 c  42. Heyboer, J . , KoUold geitsehflft 148 36 (1956).. Jenckel, 1., Kolloid Zeltschrlft 1 2 £ 142 (1954). 43. Hoff, K A. W., Deutsch* K.., and (1954). f  Reddish, £. Polymer Sci. 1 2 565  44. Hoff, E„ A.. W., D... Bobinson, and A.. H. Willbourn, £. Polymer Sci. w  U 161 (1955).  * 45 45. Oakes, «. G., and Robinson, D. W . , J. Polymer §cj>. £4. 505 (1954). 46. Powell, R . W . . ffftoc. Phys. SQQ. 48. 406 (1936). 47* Aserlcan Instrument Company, Inc., Catalogue HumWr 4T4780. 4$. 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,flffliftjttaIBS&. Ml 7232(1949). 51. Bailwood, A. J . , and Horrobini S., Trans.. FaradZSee. 42B 84 (1946) 52. Starkweather* H.. W., Jr., .. E.. Moore, J.EB. Hansen* T. M. Soder, G  and R. E. Brooks, £ . Polymer 3 d . 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 o f the Filament V i b r a t o r .  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  FREQUENCY  Figure 4 * Dynamic modulus E' as a f u n c t i o n o f l o g frequency a t 3 5 °C. and v a r i o u s h u m i d i t i e s .  I  1  •  .  20  •  •  30  I  ..... . 50  7 0 100  I 200  FREQUENCY  Figure 5*  I 20  I  30  5 0 7 0 100  .  200  sec  Dynamic modulus £* a s a function o f log frequency e t 60 ° C . and -various humidities.  2 I  54%  *—r  0  * * * * 95%  I  V  16.3%  0  f  19.0%  2*  300%  2 — i  3  n o  i 3  z  ui  51.0%  *  V UJ  383%  482%  584%  760% 676%  4  2  860%  4  883%  3 5  935%  4  3  20  30  50 70  100  _  200  20  FREQUENCY  Figure 6.  30  5 0 7 0 100  L  200 300  sec'  1  Energy Lose E" ee e function o f log frequency a t 9 ° C . and various humidities.  1.5 1.0 15  •3IX  22X  '  1.0  •T • o ~  4«X  39%  20  -  •  1.5 SIX  25  S  20 56X  j? 25 K -© 2 0 3 2.5  XT  c-.  in  2.0  3  2.0  5  1.5  80X  8 5\  _8-  UJ  • o —  1.5 10 0.5  20  1I  J 30 40  I M i I 60 80 100  j_  200  FREQUENCY  20  I 30 40  I  I M I I 60 80 100  i  L  200  CO sec"'  Figure 7. Energy l o s s 5" as a function o f l o g frequency at 35 ° C . and various humidities.  -  CSX  '•»  ia3%  20.5%  25.1%  282%  35.4%  379%  41.0%  51 2 %  572%  ,  • . * . .. • < 11 >•» 59.8%  70.7%  1  76.0%  -  2  -  I  —  0  63.4%  -  850%  J_l  20  30  '  I  • I "  I  50  70  100  93.8%  i  L 200  FREQUENCY  — 20  30  i  I I I I I I 50  70  100  L 200  sec ' -  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,  20  30  cycles  50  sec.  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 11  11  l  II  _\ -  —  N  »\ o a  \  — r-  - 2  ^  %  \  X  •  CvJ  s  E —  —  o  .a  — tn  °&.  4)  -oc  r  s=r  _  \  oo, " 15  i  l  2*0  l  " 30  i 40  cycles i  I I 60  sec. i  11  80 100  I I 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 = 2 0 plotted against r e l a t i v e humidity.  60*C  I 20  I  ! 40 R E L A T I V E  '  I  I  60 HU'^iSi^Y  Figure 1 9 * Dynamic modulus E' evaluated at relative humidity.  I  i  80 1.  = 150 plotted against  100  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 a t uJ -150 p l o t t e d against the weight o f water adsorbed per 100 g. nylon.  30  RELATIVE  Figure 25.  HUMIDITY %  D i s t r i b u t i o n f u n c t i o n 0, evaluated a t 0/3,150, p l o t t e d a g a i n s t r e l a t i v e humidity.  


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