1886
A. V. TOBOLSKY AND 11.C. SHEN
in the case of nitrogen. However, this appears to be a reasonable result, as the binding of the adsorbed molecules to the surface is in all cases much stronger than the binding energy of the liquid-typical heats of adsorption of 4000 cal./mole may be compared with heats of vaporization of 1500 cal./mole-and surface energies in general show a rough proportionality to heats of vaporization or other measures of binding energy in the condensed phase. It may also be noted from Table I that the magnitude of the observed supersaturations is fairly smallabout a factor of two for the case of S2and O2on glassand that the phenomenon occurs at quite low absolute pressures. Either of these factors, together with the small amount of data available showing two-dimensional condensation, might account for the lack of other reported observations of supersaturation phenomena. It can be seen from eq. 10 that the observed critical supersaturation for two-dimensional condensation is
T'ol. 67
markedly dependent on the edge energy involved. In systems where the binding energy of the adsorbate in its three-dimensional condensed phase is high compared to the heat of physical adsorption, e.g.> for a metal vapor, one would expect to find a niuch larger value of -ye. In such a case the supersaturation required for two-dimensional coiideiisatioii would be very large, aiid three-dimensional coiidensation of the adsorbate layer to form the bulk phase would be expected to occur more easily. This subject of the relative stability of two- and three-dimensional nuclei will be treated in detail in a later paper. Acknowledgment.-The author wishes t o acknowledge the many helpful comments and suggestions of Dr. G. W. Sears of this laboratory and the continuing interest of Professor Sydney Ross of the Rensselaer Polytechnic Institute. This work was supported by the Satioiial Aeronautics and Space Agency under contract KO. NAS5- 1590.
THE EFFECT OF HI-DROGEN BONDS OK THE VISCOELASTIC PROPERTIES OF AMORPHOUS POLYMER NETWORKS1 BY A. T'. TOBOLSKY AND XI. C. SIIEK* Department of Chemistry, Princeton Universitu, Pranceton, S e w J e i sei4 Received April 19,1963 The influence of hydrogen bonds on the viscoelastic properties of amorphous polymer nehorks 11-as studied by two methods. First the modulus-temperature curves of a series of homopolymers and copolymers of various methacrylates were obtained. Secondly, the relaxation master curves of poly-2-hydroxyethyl methacrylate (hydrogen bonding) and poly-n-propyl methacrylate (nonhydrogen bonding) were obtained. It was found that the inflection temperatures T , of hydrogen-bonded networks were somewhat higher than those of structurally similar nonhydrogen-bonded networks, but this effect is not as large or as clear-cut as might have been anticipated. I n one case, that of the polymers and copolymers of hydroxyethgl methacrylate, it xas found that the rubbery plateau modulus was two t o three times as large as might have reasonably been predicted, and this may perhaps be attributable to hydrogen bonding. This result was not found in so marked a fashion for other amorphous networks where we believe hydrogen bonding should exist. The shapes of the relaxation master curves of poly-hydroxyethyl methacrylate and poly-n-propyl methacrylate are practically identical, as i u the temperature dependence of their characteristic relaxation times.
Introduction I n t'he current upsurge of biochemical interest, considerable attent'ion has been given t80studies of nat'ural macromolecules in which the role of hydrogen bonds is believed to be extremely significant', The viscoelastic behavior of certain synthetic polymers such as polyu r e t h a n ~and ~~ has also been interpreted as being strongly affected by the presence of hydrogen bonds. The stress relaxation spectrum of polyvinyl alcohol and its partia.lly acetylated4a and partially f o r ~ n a l i z e dpolymers ~~ has also been report'ed and here too one might expect hydrogen bonding to play an important role. However, in the studies mentioned a'bove it is not always clear as to what effects should be assigned to hydrogen bonds and what effects should be assigned to polymer crystallinity or to crystallizat,ion induced by stretching. Kylon 8.8 or nylon 6, polyvinyl alcohol (1) This article is based on part.of a dissertation submitted by b1. C. Shen in partial fulfillment of the requirements for the degree of Doctor of Philosollhy a t Princeton University. (2) Harvard Chemistry Fellow, 1961-1962. (3) (a) J. H. Saunders, Rubher Chem. Tech., 33, 1259 (1960); (b) F. L. Warburton, British J. A p p l . Phys., 12, 230 (1961). (4) (a) K. Fujino, J . Colloid Sei., 16, 411 (1961); (b) K. Fujino, K. Senshu, T. Horino and 1%.Kawai, Rept. P ~ o g r Polymer . P h y s . J a p a n , 5 , 115 (1962).
and many polyurethaiis (e.g., those based on polyethylene adipate) are definitely semicrystalline under suitable conditions of temperature or of stretching. Even when these polymers are somewhat disrupted by copolymerization or post reaction, the crystallinity persists until quite extensive amounts of copolymeriaation or post reaction are achieved. It is, therefore, difficult to isolate the effects of hydrogen bonding from the above mentioned data since the polymers studied have varying degrees of crystallinity as well as varying degrees of hydrogen bonding. In this paper \ye have studied the viscoelastic properties of a series of methacrylate homopolymers aiid copolymers, all of which are completely amorphous under all conditions. Some of these polymers were hydrogen bonding and some were not. We have attempted to keep the variation of chain stiffness and side-chain lengths as small as possible so as to be able to isolate the influence of hydrogen bonds on the viscoelastic behavior of the polymers. Experimental Methods 2-Hydroxyethyl methacrylate (HEMA) was obtained from the Rohm and Haas Co. All other monomers were obtained from the Borden Chemical Co. Our polymer and copolymer samples
Sept., 1963
VISCOELASTIC P R O P E R T I E S O F
HYDROGEN-BOKDED POLYMER
were all prepared in the form of thin sheets obtained by photopolymerization between Pyrex glass plates. According to the manufacturer's specifications, the HEMA contains a small amount of ethylene glycol dimethacrylate. The Rohm and Haas Co. was kind enough to inform us of the exact amount of ethylene glycol dimethacrylate in the sample of HEMA which we wed. Suitable amounts of ethylene ;glycol dimethacrylate were added t o all monomers or monomer mixtures so that the final polymer sheets were all cross linked t o the same order of magnitude. The cross-link concentration is given in Tab!e I. The inhibitors were removed from the rnonomers by the usual methods and benzoin was added as a photosensitizer. Photopolymerizations were carried out between Teflon gasketed Pyrex plates in front of a G.E. RS sun-lamp for 48 hr. In all cases the polymerizations were essentially complete in this time. HOWever, traces of unpolymerized monomers were removed b;y heating the polymer sheets in vuc7io above their glass transition temperatures for a t least 48 additional hours. The weight losses were very small and the samples all reached constant weight. Four types of measurements were macle with the polymers: infrared measurements, modulus-temperature curves, creep curves, and sti-ess-relaxation curves. Thse latter two measurements were used in conjunction t o obtain viscoelastic master curves. For the infrared measurements, made exclusively on the HEMA polymer, the polymer sheet was powdered. and then mixed with halocarbon oil form Halocarbon Co. to form a The infrared spectrum was taken a t room temperature on a PerkinElmer 421 grating spectrometer in the region of 2600 to 3800 em.-'. Modulus-temperature curves were obt'ained on rectangular strips cut from the polymer sheets. The 10 see. shear modulus was measured o.n a modified Clash-Berg apparatus8 in the high modulus region and on a modified Gehman. apparatus' in the low modulus region. Dow Corning silicone fluid was used as the bath Liquid. The rate of heating was l"/min. Good agreement was obtained between the data from these two instruments. Creep modulus measurements above l o 9 dynes/cm.2 were made on a modified Clash-Berg apparatus.6 Tenney environmental equipment (model TSC 100-350) was used to achieve constant temperature control. Stress-relaxation measurements for relaxation modulus were made on a stress-relaxation balance,* and bhe Tenney environmental equipment for maintaining constant temperature was alRo used in these measurements.
IO0 W'
2 a +
80 60
I (I)
z
40
a (L c 20
uae 'u o
Results and Discussion Infrared Measurements.-On the basis of chemical intuition it would appear very probable that homopolymers or copolymers of HEMA should manifest hydrogen bonding. Nevertheless we thought it desirable to have objective evidence that hydrogen bonds do indeed exist in. HEMA homopolymer. In other polymers (polyamidesg and polyurethanslO) this evidence has been obtained by interpretation of infrared spectra. The infrared spectrum of polyhydroxyethyl methacrylate js shown in Fig. 1. An asymmetric peak was observed at -3360 cm.-l, which is the hydrogenbonded OH stretching frequency, a8 against the nonbonded frequency of -3600 cm.-l. The peak: is extremely broad, of the order of 500 cm.-1, indicating an ext'ended and conglomerate type of hydrogen bon.dingof the type 0-€1.. . .Of I t wa,s inferred by chemical intuition t'hat 0-H. , .N hydrogen bonding should exist in copolymers of hydroxyethy1 me.Lhacrylate and diet hylaminoet hyl met hacrylate. Also, it is believed that N--H. . .Khydrogen
.
( 5 ) We wish t o acknowledge the aid given us b y Dr. A . llllerhand in this experiment. (6) R . F. Clash and R. M. Berg, Ind. Eng. Chem., 34, 1218 (1942). (7) S. D. Gehman, ibid., 39, 1108 (1942). (8) A. V. Tobolsky, "Properties a n d Structure of Polymers," J o h n Wiley and Sons, New York, N. Y . ,1960, p. 143. (9) D. S. Trifan a n d J. F. Terenzi, J. Polymer Sei., 28, 443 (1958). (10) A. Mikaye, ibid.,44,223 (1960).
1887
P\TETVORKS
3800
3600
3400
3200 3000 2800 WAVELENGTH, ( CM-' ),
2600
2400
Fig. 1.-Infrared spectrum of the powder of poly-2-hydroxyethyl methacrylate in halocarbon mull.
-40
0
40
I
1
I
80
120
160
TEMPERATURE,
(OC
200
).
Fig. 2.-Modulus-temperature curves of poly-2-hydroxyethyl methacrylate, copolymer of HEMA (48)-PMA ( 5 2 ) , and poly-npropyl methacrylate.
bonding exists in poly-t-butylaminoethyl methacrylate and in copolymers of t-butylaminoethyl methacrylate and diethylaminoethyl methacrylate. No infrared studies were made with these polymers so that these statements are merely probable inferences. Modulus-Temperature Curves.-In Fig. 2 are shown the modulus-temperature curves for three polymers: polypropyl methacrylate, propyl methacrylate-hydroxyethyl methacrylate (48/52) copolymer, and polyhydroxyethyl methacrylate. The data are plotted in the form of log 3G(10) vs. T . The moduli were measured after 10 sec. For modulus values below 109 dynes/ 3G(10) is essentially equal to the tensile modulus E(10). The factor three is introduced for ease of comparison with tensile data published from this laboratory. The shapes of the curves in Fig. 2 are typical for slightly cross-linked amorphous polymers. There is a temperature region of glassy behavior, a transition region, and a rubbery plateau region. We have recently defined somewhat arbitrary char-
A. V. TOBOLSKY AKD 11. C. SHES
1888
Yol. 67
TABLE I CHARACTERISTIC PARAMETERS OF HYDROGEX-BONDING POLYMERS" FOR MODULUS-TEMPERATURE CURVES BY TORSIO~ T, Polymer
0-H
. . . 0 Bonding
3 G, (dynes/rm.l) ( x 107)
C
(moles!c.c.) i X iob)
+e
Section A
Poly-hydroxyethyl methacrylate Hydroxyethyl methacrylate (76) n-propyl methacrylate (24) copolymer Hydroxyethyl methacrylate (48) n-propyl methacrylate (52j copolymer Hydroxyethyl methacrylate (25) n-propyl methacrylate (75j copolymer Hydroxyethyl methacrylate (75) ethyl methacrylate (25) copolymer Hydroxyethyl methacrylate (50) ethyl methacrylate (50) copolymer Hydroxyethyl methacrylate (26) ethyl methacrylate (74) copolymer Hydroxyethyl methacrylate (75) methoxyethyl methacrylate (25) copolymer Hydroxyethyl methacrylate (51) methoxyethyl methacrylate (49) copolymer Hydroxyethyl methacrylate (25) methoxyethyl methacrylate (75) copolymer
96 89 77 66 88 89 81 75 68 51
2.31 1.95 1.91 0.69 2.50 2.07 1.93 2.05
...
..
2.69
7.92
1.60
79 68 56 44 23
2.38 2.08 0.71 1.58 1.36
12.58 8.84 4.02 9.31 8.03
0.89 1.11 0.84 0.80 0.80
85
2.40
6.50
1.73
67
1.22
7.65
0.75
45
0.90
6.63
0.64
33 41
0.5G 0.75
5.91 5.18
0.45 0.66
38 26
1.15 0.68
7.39 7.69
0.74 0.41
. I .
4.47 4.40 4.62 3.69 6.25 8.47 9.18 5.75
2.44 2.09 1.95 0.88 1.89 1.16 1.00 1.68
Nonhydrogen bonding
Poly-ethyl methacrylate Ethyl methacrylate (50) n-propyl methacrylate (50) copolymer Poly-n-propyl methacrylate Methoxyethyl methacrylate (49) n-propyl methacrylate (51) copolymer Poly-methoxyethyl methacrylate 0-H
. . . N bonding
Section B
Hydroxyethyl methacrylate (75) diethylaminoethyl methacrylate (25) copolymer Hydroxyethyl methacrylate (52) diethylaminoethyl methacrylate (48) topo1y mer Hydroxyethyl methacrylate (27) diethylaminoethyl methacrylate (73) copolymer S-H
. , . N bonding
t-Butylaminoethyl methacrylate (50) diethylaminoethyl methacrylate (50) copolymer Poly-t-butylaminoethyl methacrylate Nonhvdrogen bonding
Diethylaminoethyl methacrylate (49 j n-propyl methacrylate (51) copolymer Poly-diethylaminoethyl methacrylate a Copolymer compositions are given in parentheses on a % mole fraction basis.
acteristic parameters to characterize the modulus-temperature curves of amorphous po!ymers.ll The inflection temperature TI is defined as tlie temperature a t which SG(l0) = lo9 dynes/cm.2. The glassy modulus 3G1 is defined for definiteness as the value of 3G(10) measured 30' below T,. (The modulus-temperature curves are quite flat in this region.) The rubbery plateau modulus 3G2 for these cross-linked polymers is the value of 3G(10) measured 50' above Ti in this study. Another characteristic parameter s is defined as the negative slope of log 3G(10) us. T at T = T,, Le., at 3G(10) = lo9 dynes/cma2. The values of T, aiid 3G2obtained in these studies are shown in Table I. (In this table copolymer compositions are expressed as mole per cent.) I n other studies it has been shown that for amorphous polymers TI is generally from 2 to 10' higher than T , as measured from specific volume-temperature curves. Trends that are observed in Ti values are therefore also valid for T, values. The Glassy Region and Transition Region.-Since the accuracy of the instrument we used is not very great in the very high modulus region, we prefer to regard our results on the glassy moduli as semiquantitative. The exact value of 3G1 depends to some extent on the thermal history of the sample and on very slight (11) A . V. Tobolsky a n d M. Takahashi, J . A p p l . Polymer Sci., in press.
traces of moistiire. Generally speaking, for all of the polymers studied in this paper, the values of 3G1 lie between 2 X 1O1O dynes/cm.2 and 4 X 1O1O dynes/cm.2. KO systematic trends are observed which depend 011 whether or not the polymer is hydrogen bonded. Despite this negative result, intuitively one tends to feel that tlie presence of hydrogen bonds should affect the viscoelastic properties in the glassy region. 1% here these bonds should be relatively stable. We mere surprised to observe that the hydrogen-bonded polymers are more fragile in the glassy state than the noiibonded ones. Perhaps studies at very low temperatures, or high frequency vibrational studies, will e\-entually show some difference. The values of the parameters T, and s characterize the transition region. As a point of reference me might recall the well known fact that the Ti (or T g )values of the n-alkyl methacrylate series decrease with increasing length of side chain. A perusal of Table I shows that the TI value of a hydrogen-bonded polymer is generally somewhat higher than that of a corresponding nonhydrogen-bonded polymer of similar structure and length of side chain. For example, TI for poly-2-hydroxyethyl methacrylate is 96"; for poly-n-propyl methacrylate T, is 56'; for polyethyl methacrylate TI is 79". The fact that TI is highest here for poly-2-hydroxy-
Sept., 1963
VISCOELASTIC PROPERTIES OF HYDROGEN-BONDED POLYMER KETWORKS
ethyl methacrylate is reasonable, attributable in part to hydrogen bonding. However, it is likely that the solubility parameter and cohesive energy density for this polymer is also higher than for the other two polymers. It is well established that T, (or T,) increases with iiicreasing solubility parameter in a series of otherwise structurally similar polymers. Hence it is difficult in this case to separate the effect of hydrogen bonding froin the effect of increased solubility parameter. The variation of T , with weight fraction of HEMA in a series of copolymers with nonhydrogen bonding monomers such as ethyl methacrylate, propyl methacrylate, etc., shows the general nionotonic variation with composition displayed by other copolymer systems. The data can be reasonably well fitted by the equation proposed by Wood12for the variation of T , with copolymer concentration. The values of s all lie within a rather narrow range: 0.10 0.03. Once again no trends are observable depending on whether or not the polymers are hydrogen bonded. The Rubbery Plateau.-The equation of state for rubber elasticity yields the following formula for the rubbery shear modulus GB.
G2 = @nRT
(1) In eq. 1, n is the concentration of network chains in moles/cc., R is the gas constant, and T is the absolute temperature. @ is the front factor, which is unity a t all temperatures for an ideal rubber network; for a noiiideal rubber @ may differ from unity and may or may not vary with temperature.13 Ethylene glycol dimethacrylate is a tetrafunctional cross-liiiking agent : hence t v o distinct network chains can be associated with each cross-linking molecule. Equation 1 can be rewritten as
GP = 2@ecRT (2) I11 eq. 2 , c is the moles of ethylene glycol dimethacrylate per cc. of polymer. The quantity e is the cross-link ei’ficiency defined and measured by Fox and Loshaek.14 For very 10w cross-link densities such as those used in our present study e cannot be measured and Fox and Loshaek assumed that e is unity in these cases. The quantity e a t higher cross-link densities depends very much on nhether the polymerization is carried out below or above the glass transition temperature of the polymer. TTe retain the quantity e in our equations and tables though we agree that e is probably quite close to unity for these low cross-link densities. For uniformity Gz was measured a t 153’. Time effects such as relaxation or creep were very small at this temperature so that Gz(lO) is very nearly an equilibrium rubbery modulus. Inasmuch as c is knomi and G:! is measured, can be computed from eq. 2 . These values are listed in Table I. The front factors are all computed at 153’ in this paper. We have shown in a previous paperla that in a Feries of alkyl acrylates and alkyl methacrylates that the @e values are not TTery dependent on cross-link density, but Wood, J . Polymer Sit., 28, 319 (1958). (13) A . V. Tobolsky, D. W. Carlson, and N. Indictor, zbzd., 6 4 , 175 (1961). (14) S Loshaek and T.G Fox, J . Am. Chem. Soc., 75,3544 (1953).
, O ?
I
04 0.6 08 M O L E FRACTION H E M A .
1889
I 10
Fig. 3.-Front factors @e of the 2-hydroxyethgl methacrylate copolymers of ethyl, 7%-propyl,and methoxyethyl methacrylates us. the mole fraction of HEMA.
appear to vary IT it h the structure of the monomer unit. The front factors are close to unity for short side chains and showed a definite decrease with increasing length of the side chain. If we temporarily omit HEMA polymers and copolymers from consideration, the data in Table I also show a tendency for the front factors to decrease with increasing size of the side chain. This includes the poly-t-butylaminoethyl methacrylate in which we think that IS-H. . .N bonding exists. I n previous studies’s we had found that the front factors of acrylate and methacrylate netsorks containing carboxyl groups (which can hydrogen bond) are normal. On the other hand the front factor for polyhydroxyethyl methacrylate is unexpectedly high, namely 2.44, and so too are the front factors for the HEMA copolymers. It is conceivable that the manufacturer’s value for the amount of ethylene glycol dimethacrylate in HERIA is too low by a factor of two. If this were true, the front factor for these polymers ~ ~ o u be l d normal. Honever it is more likely that the manufacturer’s value is correct and another explanation is required. It has been suggested that hydrogen bonds can act as bona fide cross links in the same manner as covalent cross links. If this explanation were used, the concentration of hydrogen bonds acting as cross links in polyHEMA would be about 4.5 X low5mole/cc. This is a minute fraction of the possible hydrogen bond coiiceiitration in this polymer. It is also possible that structural features other than thc Icngth of the 11531A unit affect Ihr front factor of tlic rubbery iic~tworkiof this polymc~r. Wc can conclude by sayiiig tliat tlic rubbery platcau modulus of cross-liiikd Hh31A1polymcm is ti\ o or thrcc tiincs as high as I\ ould I i a i ~twtlii cxpcctcd from coinparativc studies 011 otlicr polyinclrh. ‘I’lii5 inay possihly be associated u ith hydivgc~iihoiidiiig. Master Curves 0f Viscoelastic Behavior.- h I a s t ( ~ c u i i w I\ ci’r ohtaintd for thr visc~otllasti v t)cha\+w of poly-2-hydroxydhyl mcthariylatc aiid poly-n-propyl mrthacrylatc. ‘l’hrsc ti\ o polyinm 11PI-csclrctcd hecause tlicy are rc~lulivvly similar i i i rnolcc~ularstriicturc, size of side chaiti, d c . , cxccpt for tlic Iiydrogcn bonding ahil ity of 1’11 14:A I .1. ];or coiistruction of thc master CU~V(’s, crccp mcasurcnicwts on the Clash-Rcrg instruniciit wcrc used for modulus mcasuremciit~abovc l o 9dyiics/cm.2. Relaxa(19) A .
V. Tobiilsky, I). \V. Catls)n
N
Imllctur, nnd h l . C. Shrn,
J . I’oliimei Sci., 61, S 23 (1962). (16) L 13. W r 1 4 r l d , J. R. Littlf. and LV I: bnlstenliolmc, shtd , 66 (l(Ml2).
15;
A. V. TOBOLSKY AKD 11. C. SHEN
1890
I -6
I -2
-4
I
I
I
I
0
2
4
6
Vol. 67
8
L O G t ,( SEC.).
3G,(t) us. log t for poly-n-propyl methacrylate.
Fig. 4.-Log
T-Ti
,
-
Fig. 6.-Log K(T ) / K (T , ) us. 5" T , for poly-2-hydroxyethyl methacrylate and poly-n-propyl methacrylate.
1 -8
-6
I 0
I -2
-4
I
I
2
4
6
8
LOG t , ( S E C . ) .
Fig. &-Log
3G,(t) us. log t for poly-Zhydroxyethyl methacrylate.
tioii measurements on the relaxation balance were used for modulus measurements below lo9 dynes/cm. z. Sample preparations were made with the greatest care in these studies. Samples were first heated in a vacuum oven above their glass transition temperature for a t least 48 hr. and then were stored in a desiccator. Trays of calcium chloride were kept in the creep and stress-relaxation ovens to prevent water absorption by the samples. The samples were annealed above their glass transition temperatures and then cooled slowly (about 6 hr.) to the temperature of measurements. For temperatures below Ti where the modulus values are generally above lo9 dynes/cm.2, the Clash-Berg apparatus was used to measure creep in shear. The measurements of torsional deflection at constant torque us. time yield a value of shear compliance J ( t ) or the shear creep modulus Gc(t)
G4t)
1/J(t) (3) For temperatures above T,, where the modulus values are in general below lo9 dynes/cm.2, we used a stressrelaxation balance, which measures a tensile relaxation modulus E, (t). The tensile modulus is related to the shear modulus and the bulk modulus B as
E
=
=
(3 - E/3B)G
(4)
Inasmuch as the bulk modulus for polymers (or for liquids) is in excess of 1O'O dyiies/cm.2, the measured values of the tensile modulus E,(!) (for vaIues below
lo9 dyiies/cm.2) were related to the shear relaxatioii modulus as = 3Gr(t) (5) The shear creep modulus measured in the ClashBerg instrument were converted to shear relaxation modulus by the f ~ r i n u l a ' ~
G,(t) = (sin mn/mn)G,(t) (6) In formula 6, m is the negative slope of the plot of log G, (t) vs. log t evaluated at time t. Using formulas 5 and 6, the primary data for $ ( t ) and E,(t) were converted to 3Gr(t). The results for polypropyl methac~ylateand polyhydroxyethyl inethacrylate are plotted in Fig. 4 and 5 in the form of log 3G,(t) us. log t . Good agreement was obtained between the two methods of measurement iii the region of lo9dynes/cm.2. According to the time-temperature superposition principle1* thzse plots are superposable by horizontal translation along the log time axis. This enables us to extrapolate the data a t any temperature to both shorter and longer times to construct the "master curved' at each temperature as shown in Fig. 4 and 5 . Characteristic Parameters from the Master Curves.From the master curves me can define a characteristic relaxation time K ( T ) , namely, the time required at temperature T for 3G,(t) to attain a value of l o 9dynes/ cmaZ. By definition K(T,) is equal to 10 see. In Table I1 we shorn the experimental results for log K ( T ) / K ( T i ) for various values of T - T, for both polyhydroxyethyl methacylate and poly-n-propyl inethacrylate. I n Fig. 6 a plot of this data is shown; apparently the relation is nearly linear near T = T,. (17) H. Leaderman, in "Rheology," Val. 11, edited by F. R . Eirich, Academic Press, New York, N. Y . ,1958. (18) See ref. 8, pp. 144-151.
Sept., 1963
VISCOELASTIC PROPERTIES
OF
HYDROGEN-BONDED POLYMER
1891
SETKORKS
TABLEI1 THEDEPENDEKCE OF RELAXATIOK TIMESK ( T ) ON TEMPERATURE T T ,OC.
50.8 72.2 84.0 90.5 92.6 97.0 98.0 101.4 108.6 123.6 -0.9 10.6 19.2 27.9 35.5 42.0 45.5 51.5 53.0 59.5 67.5 76.6
-
Ti,
O C .
KV)
log __ K(Ti)
Poly-2-hydroxyethyl Methacrylate -47.2 8.45 -25.8 5.85 -14.0 5.12 -7.4 3.50 - 5.4 1.87 - 1.0 0.25 0.0 0.00 3.3 -0.85 10.6 -2.33 25.6 -4.46 Poly-n-propyl Methacrylate -52.1 -43.3 -33.8 -25.1 -17.5 -11.0 - 7.5 - 1.5 0.0 6.5 14.5 23.5
8.87 7.62 5.97 4.72 3.62 1.92 0.26 0.00~ -1.14. -2.29 -4.04:
TABLE I11
PPMAG
Ti, "C. 3G1, dynes/cm.2 3G2, dynes/cm.2
96 56 1.87 X 1O1O 1.82 x 10'0 1.23 X 10' 1.49 x 107 S 0.10 0.09 P .24 .24 n .53 .50 a Cross linked by ethylene glycol dimethacrylate (c = 8.72 X 10-5 mole/cc.).
p
=
-6
-4
-2
I
I
0
2
4
!
I
6
8
LOG [t/K(T)],
Fig. 7.-Log 3G,(f) us. log [ t / K ( T ) for ] poly-2-hydroxethyl methacrylate and for poly-n-propyl methacrylate.
11.11
CHARACTERISTIC PARAMETERS O F POLY-2-HYDROXYIDTHYL METHACRI-LATE AKD PoLY-n-moPn METHACRYLATE PHEMA
I -8
0.240
This iesult is not inconsistent with the WLF equation,lg which can be rewrittenz0
(19) M. E. Williams, R. F.Landel, and J. D. Ferry, J . Am. Chem. SOC., 77,3701 (1953). (20) See ref. 8, up. 162-166.
Since p' is much smaller than p , eq. 8 reduces to eq. 7 for values of T close to T,. The quantity p varies somewhat from polymer to polymer and may be considered to be another characteristic parameter.20 A reduced master curve valid for all t h e , and temperatures can be obtained by plotting log 3G,(t) cs. log ( t / K ( T ) ) . The results for both polymers are shown in Fig. 7 . It is quite striking to observe how similar are these reduced master curves for the hydrogen bonded and iionhydrogen-bonded polymers. The viscoelastic properties of these polymers in the transition legion are practically identical if one accounts for the relatively modest difference in T,. The final characteristic parameter is n, which is the negative slope of the log 3Gr(t) us. log t plot a t 3 G r ( t ) = lo9 dyiiee/cm.z. The value of n for PHEMA is 0.53 and for PPMA the value is 0.50. The theoretical value predicted by the Rouse-Bueche t h e ~ r y ~ lis- ~0.50 ~ in the low-modulus portion of the transition region. In Table I11 the characteristic parameters TI, 3G1, 3G2, s, p , and n are presented for poly-Zhydroxyethyl methacrylate and poly-n-propyl methacrylate. I n summary, the viscoelastic properties of amorphous hydrogen-bonded polymers seem to differ from those of nonhydrogen-bonded ones in that the former systems generally have higher values of transition temperatures aiid rubbery moduli, while the transition region slopes are quite similar. Acknowledgment.-The support of the Office of Naval Research and of the Goodyear Tire aiid Rubber Company is gratefully acknowledged. (21) P. E. Rousrs, J . Chrm. Phys., 21, 1272 (1953). (22) F. Bueche, kbtd., 221, 603 (1954). (23) XI. E. Williams, J . Polymer Set , 62.57 (1962).
