boric acid McCauley and Lien6hhave shown that hexamethylbenzene is a stronger base than any (Jf the other methylbenzenes. Association Ratio.-A study was made to determine the nature of the association of chloroform with several aromatic compounds, namely, mesitylene, p-xylene, toluene, benzene, bromobenzene and chlorobenzene. This was done calorimetrically by determining the concentration a t which maximum heat evolution per mole of solution is obtained when the liquids are mixed. Plots of the heats of mixing per mole of solution yersus the mole '/o of chloroform are shown in Fig. 3. The symmetrical shape of the curves indicates that association between chloroform and an aromatic compound occurs in ;L one-to-one ratio. .liidrews and Keeler have shown that il sil\w i u t i ;~dtlsto ;til arcmidtic i~~olccule it1 a O ~ I Cto otic
ratio and, to a smaller extent, in a two to one ratio. The present investigation shows no evidence for hydrogen bond formation of two chloroform molecules with a single aromatic molecule. This lack of evidence may be due in part to a lack of sensitivity of the method, rather than to the complete absence of such association. This would be true particularly for the weak electron donors which give broad heat oi mixing-composition curves, making the location of the peaks more difficult. I t may be concluded, however, that if there is association of chloroform to aromatic compound in two to one ratio, it must exist to an extent appreciably smaller than that of one to one ratio. Acknowledgment. --The author wishes to thank Iliss Elizabeth Petersen for making the spectroscopic observations. I
RliA\A,
r 1 I 1\015
Elastoviscous Properties of Amorphous Polymers in the Transition Region. I BY J. BISCHOFF,E. CATSIFFAND *I. 1;. 'TOBOLSKY RECEIVED DECEMBER 27, 1931 Experiniental data 011 the stress-relaxation modulus E r , ( ~t ) of a GR-S gum vulcauizate at a series of temperatures in thc transition region are presented, and a "master curve" of log Q(t/K)zlcrsus log ( t / K )is thereby constructed. The charaeteristic relaxation time, K , for each temperature is defined and tabulated. A distinctive temperature, Td, is observed at which the activation energy for K is a maximum. Analytical expressions are given which describe the GR-S master-curve with great accuracy. The same aiialytical procedure can be successfully applied to data previously obtained for polymethyl methacrylate. A reduced equation is proposcd Ivhich describcs thc timc and tcmperature dependence of Q(L/K)in the transition region for both polymers
Introduction I t has been shown previously that for a givcii amorphous polymer, the stress relaxation curves determined a t different temperatures may be made to coincide by a translation along the logarithmic time axis.' This makes possible the construction of ;t composite stress relaxation curve or "master curve" valid over an extended time scale a t any qiven temperature. The master curve can be con;-eniently plotted in the form of log E:r,~o( t ) versus log (f), where E r ( t~) , the relaxation niodulus a t a temperature T , is the stress per unit strain in a sample maintained a t a constant small strain for a time, t. When plotted in this form a master curve for a given polymer is also valid a t any other temperature by simply shifting the origin of the log time axis. From the master curve LG,T ( t ) and from the miount of shift of the log time scale at each temperature ;1new function Q(t, Kj may be defined as In equation (1) A ' is a function of temperature done which will be more explicitly defined subsequently, and t has the same numerical value on both sides of the equation. The function Q ( t / K ) is a universal function of t K which is valid at all temperatures, and may therefore be called the universal inaster relaxation curve for a given polymer. (1) 1 1- l o l ~ u I & \ . i t i d I< 1) \iirircu.; I ' J l i i \ < < ( I \ O r I ) ~ ( r r v1 1 1 1 5 r o l n \ < i
(iiriif Pii\t 13, l a , 1716 i l ' l i 0 )
I
{
Alii
analytical or graphical representation oi'
Q(/ K ) together with an analytical expression or tahulation of li as a function of T are a complete representation of the viscoelastic properties of an amorphous polymer a t all times and temperatures in the range of strains where the Boltzinann superposition principle applies. They can be used in principle to calculate any other property such as dynamic modulus. In a previous paper, it was shown that the viscoelastic behavior of amorphous polymers can be classified into three distinct regions: a glassy region (Er,T ( t ) 1010.6 dynpjcm.2) where the mechanical properties depend on previous thermal history, a transition region where the relaxation modulus lies approximately between lo7 dynes/cm.2 and 1010.5 dynes/cm.2 and is independent of thermal history and of the molecular weight of the polymer, and a rubbery region where the relaxation modulus is less than lo7 to lo7 ,j dynes/cm.3 and depends on the molecular weight of the polymer and on the presence or absence of cross links.2 In this paper new experimental data for E r , ~ (of t) a GR-S gum vulcanizate a t a series of temperatures in the transition region are presented. The GR-S vulcanizate used is identical with that used and previously described. A master curve is constructed, an analytical formulation of Q(t ' K ) is given, and the K values a t different temperatures are tabuLited. The results are compared with those previr i 1 I ~ J ~ J u I ~ Lr . I .
(;,
11, 1lrauc.r
itiifl
.\, I< licniictt, i b i , l , 6 ,
(io!)
mrtlincryla(r \\-a5 rrported a s 10.5° I,?. S. Loshaek. 312th meeting. .itncrican I'hysicai Socicty, Coinnibus, 0 , hlzirch 2 2 , 1052.
July 3 , 1932
ELASTOVISCOUS PROPERTIES
OF f ~ M O R P I I O U SPOLYMERS I N 'lkANSITION
other polymers should soon decide whether it is accidental. In order to compare the temperature dependence of the mean relaxation time K for both polymers, i t seemed advisable to introduce a reduced temperature, T R = T/Td, and a reduced characteristic relaxation time K R = K/Kd. A complete description of each polymer can then be provided by presenting the master curve, and along with the master curve a graphical presentation of the variation of log K R with TR. This latter was achieved in Figs. 2 and 4 by considering the abscissa of the master curves as a log K R scale and indicating along the upper border of the graph the values of reduced temperature TR that correspond to the experimentally observed values of log KR. The T R keys shown in Figs. 2 and 4 for GR-S and polymethyl methacrylate are not identical. This is perhaps to be expected since the master curves themselves are not identical.
I ~ E C I U N 3381
[log Q ( t / K ) - log (E~Ez)'/~I/[log(Ei/Ez)'/zI
as a function of h log t/K as can be seen by inspection of equation (7). It is reasonable to speculate about the result of placing the T R keys for the two polymers on such a reduced master curve. Since the abscissa of the reduced master curve is h log (t/K), the T R keys can be compared by plotting h log K R versus TR. As can be seen from Fig. 5, such a plot gives the same curve for both polymers. This means that the same T R key applies to both polymers on the reduced master curve. A reduced equation which applies for both can therefore be written
where y
(t/K)*= ( ~ K / K and R ) ~LR
=
=
t/&.
T R. 1.5
1.024 1.003 1.037 1.011 0.995 0.971 0.951
1.o
I~,l.,l.,j.l~.'..l.l,
0.75
10
I
I
CL
2
c
i; go 0.50 10 .. a
2 9
h 3
5 04
w-
0.25 e
M
5 8
3
-4
-2
0 log
2
4
Oh).
Fig. 4.-log Q ( I / K ) versus log ( t / K ) for polymethyl methacrylate; also -d log Q(t/K)/d log ( t / K ) for polymethyl methacrylate.
Reduced Equation for Viscoelastic Behavior of GR-S and Polymethyl Methacrylate.-The master curves for stress relaxation of GR-S and polymethyl methacrylate could be made practically identical if one were to plot
2 %
0.5
M
U
-
-e -0.5
- 1.0 - 1.5 1.00 1.02 1.04 TR. Fig. 5 . 4 log K R versus T R for GR-S arid polyincthyl methacrylate: 0, GR-S; 0 , polymethyl methacrylate. 0.96
In the region 0.93 proximated by
0.98
< TR < 1.05, K R may be ap-
h log KR = - 3 6 ( T ~ - 1)
(10)
Additional experimental data on other amorphous polymers will be necessary to test the generality of equations (9) and (10). PRINCETON, NEWJERSEY
