May, 1951
INTRINSIC
VISCOSITY-TEMPERATURE RELATIONSHIPS FOR
POLYISOBUTYLENE
1909
[CONTRIBUTION FROM THE DEPARTMENT OF CHEMISTRY OF CORNELL UNIVERSITY ]
Intrinsic Viscosity-Temperature Relationships for Polyisobutylene in Various Solvents1 BY T. G Fox, J R . , ~AND I?. J. FLORY Intrinsic viscosities of polyisobutylene fractions ( M = 1.8 X 106 to 1.88 X lo6) have been determined in various pure solvents, and in several solvent mixtures also, over wide temperature ranges. The measurements have been corrected t o zero rate of shear in addition to the usual extrapolation to infinite dilution. The results provide a rigorous test of the recent theory relating the intrinsic viscosity to polymer chain structure and t o thermodynamic parameters governing the interaction between polymer and solvent. Theory applies quantitatively within the limit of the experimental error in the results. The parameter K in the equation [ T ] = KM'/aa* is the same in different solvents, but decreases somewhat with temperature (1.08 X 10-0 at 24' t o 0.91 X 1 0 - 8 at 105'). For poor solvents the value of 8 in the equation a5 a3 = 2+b1Cni. (1 -. O / T ) M 1 / :agrees with the independently determined critical miscibility temperature for M = a. The entropy of dilution parameter $1 varies over a fourfold ratge for different solvents, contrary t o current theories of non-polar mixtures. The constant in the relationship K = @(ra/M)*/ahas the approximate value 2.1 X IOa1,which should be the same for all polymers. The root-mean-square end-to-end distance unperturbed by intramolecular interactions (other than hindrance to free rotation) for a polyisobutylene molecule with M = IO6 is computed to be 795 A. at 25". This is appreciably greater than the length, 412 A., calculated for free rotation. In cyclohexane, a good solvent, a = 1.54 a n d d T = 1225 A.
-
d?
Introduction The dependence of the intrinsic viscosity of a polymer solution on polymer-solvent interaction and on inherent structural features affecting the chain configuration has been discussed in preceding paper^.^.^.^ In particular, it has been shown from theoretical considerations that the intrinsic viscosity should depend on the molecular weight M , temperature T and solvent type in accordance with the relationships [q] = K M V d
(1)
= 2+b1cM(1- e / T ) w / 2
(2)
and a6
- (ya
Experimental Materials.-Three polyisobutylenes were fraetionated by the addition of acetone to their benzene solutions at 30°,4and five of the fractions so prepared were selected for the work reported here (Table I). Viscosity average molecular weights nvwere calculated from the intrinsic viscosities in the solvents listed in Table I by the equation [77]
=
K'&!
(3)
where the respective values of K' and a have been reported elsewhere. Viscosity-temperature relationships were obtained for three of-these fractions; for these the tabulated values of M,'/* are precise to '2%.
The quantities occurring in these equations are TABLE I defined in a preceding paper.6 A preliminary POLYISOBUTYLENE FRACTIONS investigation4 of intrinsic viscosities of polyiso% of butylene fractions in several solvents confirmed Desig- whole Solvents employed in MV ZV'/2 mol. nt. detn. the adequacy of these relationships over wide nation polymer 250-2 . . (15,000,000) . . CeHiz(40") ranges in molecular weight and temperature. 1,880,000 1371 CeH12(3O0); DIB(20"); In the work reported in this paper, equations PB5F1 23 CaHs(25') (1) and (2) have been subjected to more rigorous experimental test with the aid of more accurate PB5F2 12 1,460,000 1210 CeHi~(30'); DIB(20'); CsHs(25') measurements of intrinsic viscosities in a greater 180,000 424 CeHe(25') variety of solvents over wide ranges of temperature. PB3F2 18 54,000 . . CClr(30') The relationships established in the preceding PB3F4 2 paper6 have been employed in order to extrapolate The solvents employed were of high purity. the viscosity measurements to zero shear rate. They were distilled and dried over anhydrous This is important when measurements made in the magnesium sulfate before use. same viscometer a t different temperatures are to Viscosity Determinations.-Two Ubbelohde viscometers be compared, owing to the increase in rate of shear having efflux times for water at 20' of 100 and 250 sec., reas the absolute viscosity of the solution is decreased spectively, were calibrated for the kinetic energy correction with rise in temperature. Critical miscibility term.? Solutions were prepared by weighing the polymer measurements leading to the independent deter- in a 50- or 100-ml. flask and diluting a t a known temperathe concentration c, in grams/100 ml., being calcumination of 8 also have been carried out. The ture, lated a t other temperatures from the expansion coefficient of parameters occurring in equations (1) and ( 2 ) the solvent. The solutions were filtered into the viscometer have been evaluated for various solvents according through a medium sintered glass filter. Efflux times, which were measured with an accurate electric timer reading t o to the methods discussed previo~sly.~ (1) This investigation was carried out at Cornell University in connection with the Government Research Program on Synthetic Rubber under contract with the Office of Rubber Reserve, Reconstruction Finance Corporation. (2) Rohm and Haas Company, Inc.. Philadelphia, Pa. (3) P. J. Flory, J . Chem. P h y s . , IT, 303 (1949). (4) T. G Fox, Jr., and P. 1. Flory, J . Phys. Colloid Chcm., 68, 197 (1948). ( 5 ) P. J. Flory and T. G Fox, J r . , THIS JOURNAL, 18, 1904 (1051). (6) T. G Fox, Jr., J. C. Fox and P . J. Flory, ibid., 78, 1901 (1U51).
0.0001 minute, were generally reproducible to *0.001 minute. Viscosities of a given solution were measured a t several temperatures with the aid of a series of constant temperature water-baths each controlled to =t0.01 ' a t the desired temperature. Duplicate measurements on a given solution a t the lowest temperature made before and after the observations a t higher temperatures were in good agreement. In those poor solvents wherein the polymer was kept a t high temperatures for as much as several days, it was necessary t o add a small amount (0.05 g./100 nil.) of phenyl(7) A.
s. T. M. Designation
D445-39T.
T. G FOX,JR.,
1910
AND
Vol. 73
P. J. FLORY
solutions at concentrations in the vicinity oi the theoretical critical volume fraction of polymer : v2 (crit.) = l/xl/s! The temperature a t which the stirred solution became turbid on slow cooling was recorded for each concentration. Since the precipitation temperature is relatively insensitive to concentration in this range, the maximum Determination of Precipitation Temperatures.temperature T,for the co-existence of two phases The critical temperature T, for complete mis- was obtained with adequate precision ( t 0 . 3 " ) cibility in a given solvent should depend on the from measurements at several concentrations. molecular weight of the polymer as Results for a solvent mixture consisting of three parts by volume of ethylbenzene and one of die/T, = ( I -t V W / X (4) where x represents the ratio of the molar volumes of phenyl ether are shown in Fig. 1. The predicted polymer and solvent according to the theory of linear relationship between T, and M-'/s is conpolymer solutions published some years ago.E firmed. From the intercept and slope of the line, Expanding in series and replacing x with ilfi/vl 0 = 300.0 OK., or 26.S°C., and b = 13. Other where V is the specific volume of the polymer and values for 0 given in Table I11 and in the second colunin of Table I V were obtained for the fractiori v1 is the molar volume of the solvent
P-naphthylamine in order to prevent degradation of the polymer. Extrapolation of the specific viscosity qap to zero rate of shear was accomplished in each case from the actual rate of shear, calculated from the dimensions of the viscometer and the viscosity of the solution, and the relationships of the previous paper.6 The magnitude of this correction a t infinite dilution is indicated in each case in Table 11.
c
to treat b merely as an empirical parameter. The desired quantity, 6, is obtained as the intercept in the plot of T, ws. X-*'?-. The critical precipitation temperature for a polyisobutylene fraction in a chosen solvent, or solvent mixture, was determined by preparing several I
I
25
5
=c0
s.50-
400\
F " -
!s.
PB n D!0 01
M. I L S O O O O -22-3-
/-
300 -
I I Polyisobutylene in 75:25 E B P E Mixture.
.I 5
05
c in g/iooml
Fig. Z.--Solution viscosity-toncentration relationships for polyisobutylene fractions in diisobutylene: the open circles and the closed circles represent qap/cand (In vr)/c, respectively.
0- 20 0
.-c
15
0
20
M - h x IO4
40
.
Fig. 1.-A
plot illustrating the observed dependence on molecular weight of the critical temperature for miscibility of polyisobutylene fractions in a 3-1 mixture of ethylbenzene arid diDhenvl ether. -~ ( 8 ) P. J. Florp, J . Chei77. P h y s . , 10, 51 (1842). Equation (4) corresponds to (21) of tllis reiercrlceivjtil K (critical) reI,luce. by ~ B ~ ~ / R =
I
1.80
I
I
1
.I 0
I
I
20
c in g./iuo rnl
Fig. 3.--The
dependence of gsp/c (open circles) and (111 T , q r ) / C (closed circles) on concentration for a polyisobutylene fraction of .If = 1,460,000in various solvents.
May, 1951
INTRINSIC VISCOSITY-TEMPERATURE RELATIONSHIPS FOR POLYISOBUTYLENE1911 TABLE I1
INTRINSIC VISCOSITY-TSMPBRATWE RELATIONSHIPS Corm. in [ q ] on extrapn. z c o rate of shear, %
T , .to Solvent
OC.
-
PB5F1, M 25 0.32 35 0.69 50 1.41 65 2.20 0 0.58 30 1.32 50 1.99 75 2.85 20 1.67 45 2.16 60 2.47 85 3.01 25 0.19 26 .19 45 .73 65 1.40 71.5 0.20 74 .20 85 .52 86 .24 105.5 .30 PB5F2, = 25 0.40 35 0.79 1.60 50 2.28 65 3.13 20 30 3.67 45 4.55 60 5.50 0 0.66 1.44 20 40 2.39 3.35 60 85 4.51 1.88 15 2.22 30 45 2.57 60 2.92 0 2.00 25 2.59 3.20 50 80 3.97 1.56 0 25 2.23 50 2.50 3.08 65 0.24 25 50 .40 .58 75 .78 100 PB3F2, kf
k
fsl,
Obrd.
171
Calcd.
1,880,000 0.47 1.58 1.55 2.26 2.25 ,375 .35 2.93 2.89 .35 3.39 3.34 2.63 2.66 Ethylbenzene 0.375 3.35 3.40 .375 3.68 3.67 .375 3.97 8.95 .375 3.86 3.91 0.37 Diisobutylene .37 3.85 3 . 8 1 3.83 3.83 .37 3.70 3.73 .37 1.32 1.37 Curved 75 :25" Curved (1.43) 1.45 EB:PE 2.34 2.40 0.40 2.89 2.96 0.40 1.36 1.38 Curved 50:50" Curved (1.55) 1.55 EB : P E 0.40 2.06 2.11 1.25 Curved Phenetole 1.25 Curved Anisole 1,460,000 0.47 1 37 1.37 Benzene 1.90 1.92 .375 2.51 2.44 .35 .35 2.80 2.82 5.15 5.13 .36 Cyclohexane .36 5.15 5.13 5.15 5.11 .36 5.15 5.14 .36 1.97 1.98 Toluene 0.375 2.56 2.59 .34 3.00 2.96 .34 .34 3.25 3.24 3.45 3 . 4 8 .34 3.26 3.27 0.37 Diisobutylene .37 3.25 3.25 3.24 3.21 .37 3.05 3.11 .37 3.22 3.18 n-Heptane 0.34 3.18 3.12 .34 2.97 3.01 .34 .34 2.88 2.93 3.60 3.56 0.34 Triptaiie 3.53 3.48 .34 3.28 3.38 .34 3.31 3.32 .34 n-Hexadecane 0.34 2.52 2 . 5 3 2.54 2.53 .34 2.53 2.54 .34 2.50 2.55 .34 180,000 0.39 0 . 3 8 Benzene 18 0.20 Curved 20 .21 Curwd ,406 .4Os .42 .43 .24 Curved 22 .45 .45 24 .2? 0.50 45 .62 .35 .59 .60 .68 .68 65 .95 .35 0 Parts by volume of ethylbenzene (EB) and phenyl ether (PE), respectively.
Benzene
-
of highest molecular weight (1,880,000) assuming values of b corresponding to that given above.g Results Dependence of the Specific Viscosity on Concentration.-For each combination of polymer fraction, solvent and temperature, viscosities were measured a t several concentrations so chosen as to yield relative viscosities qr in the range from 1.1 to 1.6. After correction to zero rate of shear,6 both qsp/c and (In ~ ~ ) were / c plotted against concentration as illustrated by the examples shown in Figs. 2 and 3. The intrinsic viscosity was taken as the common ordinate intercept for the straight lines drawn through the two sets of points; their slopes are related to one another in accordance with the mutually related equations'O tlip/c = hl k hI2c (5) (In qr)/c = 111 - (0.50 - k)hI2c (5') where k is a constant characteristic of the given solvent-polymer pair and independent of the molecular weight of the latter. Values found for k are included in Table 11. In good solvents these plots are linear, k is about 0.34 to 0.40, and the uncertainty in the intrinsic viscosity introduced by extrapolation does not exceed * 1%. In poor solvents at temperatures near 8 the value of k increases, and in many cases the plots become curved as illustrated in Fig. 4; the uncertainty in the extrapolation arising from curvature may introduce an error as great as * 4% in the intrinsic viscosity. Instances in which curvature was observed are indicated in Table 11.
+
25
05
c in g/ioornl
Fig. 4.-The dependence of qmP/c (open circles) and (In qr)/c (closed circles) on concentration for solution of a polyisobutylene fraction of M = 1,880,000 a t T = 8 in two solvents. (Although the data for anisole could be represented by two straight lines, the sum of their slopes would not equal the required value of 0.5.)
The intrinsic viscosities are presented in Table I1 and representative plots of [ q ] us. T are shown in Figs. 5 and 6. (9) Further work, as yet unpublished, shows that values of b are roughly the same for different solvents which do not dider too greatly in molar volume Hence, the above procedure, involving extrapolations of only about 2', is adequate for ascertaining values of 8 which are correct within *lo. (10) M. L. Huggins, THIS JOURNAL, 61,2716 (1942).
I
I
0
I
I 100
50
C',%
--I
ifhylbenl'n.
lnl"p*e
1, "C.
lo
:I
1
"-C,cH3.
..__-
,
1
-
2
1
c'_!
-
100
10
T, "C Figs. 5, ti. --- [v]---Z' relationships for a polyisobutyiene fraction of .Cf = 1,460,000 in several solvents. The experimental data are given by the circles; the curves represent the theoretical relationships expressed in equations (1) and 12).
3.6
3.0
' / T x IO' in
Determination of Primary Parameters.-Intrinsic viscosities in various solvents interpolated to T = 8 in each case are given in Table 111. Values of K calculated as the ratio of these intrinsic viscosities to the square root of the molecular weight6 are given in the last column. Confirming theoretical predictions, K appears to be independent of M and of the solvent a t a given temperature. Aside from the unexplained anomalous result for the 50 :50 ethylbenzene-diphenyl cthcr mixture, a decrease in K with increase in tctnpcraturc is indicated.
T,
36
OK-'
OC.
TABLE111 VALUES OF I< DETERMINED I N VARIOUSSoLvEms Solvent
0, " C .
[viat Q
T
K X 10'
PB5F1 1.48' 1.08 1 0 . 0 2 PB5F2 1.28" 1.06 * 0.03 PB3F2 0.45 1.06 * 0.04 75:25 EB:PE 2 6 . 8 PB5F1 1.49" 1.08 * 0.04 50:50EB:PE 76 PB5Fl 1.61a 1.17 Phenetole 86 PB5F1 1.25 0.91 * 0 . 0 5 Anisole 105.5 PB5Fl 1.25 0.91 i O . 0 5 a Interpolated or extrapolated from the data of Table 11. Benzene
24
Polymer
30
34
4.0
'/T
in
OK-'
x
4.0 103
Figs. 7, 8.-Plots of ( K ~ / 1 . 1X 10-S)(a6 - a 3 ) A W 1vs. /P 1 / T for polyisobutylene fractions in various solvents. The data for fractions with molecular weight of 1,880,000, 1,460,000 and 180,000 are represented by the open, closed and half-closed circles, respectively.
deduced from the intercepts and slopes of these lines are given in Table IV. The intrinsic visFor the purpose of calculating values of a, cosities included in the last column of Table I1 tlie siiiall decrease ill K with teiiiperature WRS have been calculated, using equations (1) and (2), assuirictl to be linear; values of I .10 X and from these parameters atid K as specified above
May, 1951
INTRINSIC VISCOSITY-TEMPERATURE RELATIONSHIPS FOR POLYISOBUTYLENE 1913
(assuming that CM changes inversely as K with temperature6). The agreement with the observed values is excellent. TABLE IV
VALUESOP INTERACTION PARAMETERS dOK.Solvent
From pptn. measurement
From
-T data
[TI
100 'hCM at
0%
$'ic?dVi
at 25%.
Benzene 297 297 0.55 0.51 ... 126 Cyclohexane .47 .42 Toluene 260 261 .43 .48 249 251 Ethylbenzene .37 .47 75:25 EB:PE 300 299 .58 .42 349 344 50:50 EB:PE .70 .48 Diisobutylene .12 ... 84 .19 n-Heptane .08 ... 0 .12 ... 0 Triptane .16 .10 ... 175 n-Hexadecane .11 .32 377 Anisole *. .. .. 357 . .. .. Phenetole .. Phenyl ether 421 .. .* .. Ethyl heptylatea 306 ... .. (0.1-0.15) Ethyl caproate' 330 . . .. (0.1-0.15) The parameters for these solvents are only approximate.
.
value, 2.5 X lOS, computed from the intrinsic viscosity in n-heptane using equations (1) and (2) and the parameters given above.12 @Is calculated using each of these molecular weights are given in the last two columns of Table V. Variations within each column probably are not greater than the experimental error in (Fa)*/*. Similar calculationsle from corresponding data for dilute solutions of polystyrene14 give Q = 2.1 X loz1, in agreement with the mean values based on Kunst's data for polyisobutylene in conjunction with our estimate of the molecular weight. This is somewhat smaller than the theoretical valueJ6 3.6 X 1021, based on the Kirkwood-Riseman theory. l5 Considering approximations in the theory, the agreement probably is satisfactory. The value 2.1 X loz1will be assumed in subsequent calculations. TABLEV ESTIMATION OF 0 FROM THE RESULTS OF KUNST
.
.
Discussion The results presented above demonstrate that the theory embodied in equations (1) and (2) is adequate for the representation of the temperature dependence of the intrinsic viscosity of polyisobutylene in a wide variety of solvents. In fact, there is no indication of any systematic deviation exceeding the experimental error. The ability of these relationships to account for the dependence of the intrinsic viscosity on molecular weight over a wide range was established in a previous investigat i ~ n . This ~ is implicit also in the plots of Figs. 7 and 8, where data for polymers of different molecular weight are superimposed. In particular, these results again emphasize that K is independent of M and the solvent (at a given temperature) within experimental error. It follows that @ (see ref. (5)) is essentially constant a t a value inappreciably below its asymptotic upper limit throughout the range investigated. Further confirmation of the theory is provided by the excellent agreement between the values of 8 obtained from precipitation studies in the poorer solvents and those deduced from the viscositytemperature measurements (Table IV). In the better solvents, 8 is too low to be determined from precipitation measurements, and the long extrapolation required for its determination from intrinsic viscosity-temperature data increases the uncertainty to perhaps * 20'. Evaluation of @.-Values of r2 obtained by Kunst" from the angular dissymmetry of scattered light for polyisobutylene solutions permit estimation of the value of @ according to the relationship = [~lM(F~)--l/r (see ref. (5), equation (17)). His results for a polyisobutylene fraction in nheptane and various n-heptane+-propanol mixtures are given in Table V. The molecular weight, 1.9 X lo6, reported by Kunst is lower than the (11) E. D. Kunst, Rcc. frav. chim., 69, 125 (1950)
T
Solvent
%-Heptane
+
n-Heptane lO%propanol n-Heptane 20% propanol n-Heptane 27%propanol
+ +
06.
( ~ [?I~ $01.9XMXlo-" ~IO* calcd. ~ 2.5Musing: X 108
25 1860 4.50 1.33 60 1750 4.00 1.41
1.75 1.86
25 1710 4.00 1.52 25 1320 2.30 1.90 60 1640 3.50 1.61
2.00 2.50 1.98
60 1330 2.40 1.94
2.56
Average
1.6 * 0.2 2.1
0.3
Dimensions of the Randomly Coiled Polymer Chain.-The normal mean-square end-to-end distance E?, i. e., the mean-square I in the absence of effects due to interactions between the segments and their environment, for a molecule of molecular weight M may be calculated from K , using the above value of Thus, values of the ratio ?d/M a t 0, 25 and 100' as given in Table VI were computed from K using equation (16) of reference (5). Similarly, cos 9 was computed from equation (20) of that paper; corresponding values of arc cosine (cos 4) also are included in Table VI. For purposes of illustration, root-mean-square end-toend distances fi for M = lo6, calculated from the results given in the third column of Table VI, are given in the fifth column. The corresponding values calculated from equation (19) of reference (5) assuming free rotation, i. e., assuming that = 0, and taking 8 = 109.5' and 10 = 1.54 A,, are given in the sixth column. Finally, comparisons are shown between the actual chain and the equivalent freely jointed chain3 comprised of 2 segments of length I, each segment being free to orient a t random with respect to its neighbors.
5
(12) The molecular weights used in the present paper are based primarily on the relationship between molecular weight and intrinsic viscosity in diisobutylene published by one of us several years ago. See, THIS JOURNAL, 66, 372 (1943). (13) T. G Fox, Jr., and P. J. Flory, Tars JOUI~NAL, 78, 1915 (1951). (14) P. Outer, C. I. Carr and B. H. Zimm, J . Chum. P h y s . , 18, 830 (1950). (15) J. G. Kirkwood and J. Riseman, ibid., 16, 565 (1948).
T.G Fox, JR,,A
1914
Zl, it follows from Taking r8 = ZP and equation (19) of reference ( 8 ) thnt njZ = 1/10 = [ (1
- cos 6)/(1 + COS
e)] (1 iZi-i)/(i- Cos)I
(6)
TABLEVI NORMALDIMENSIONS OF THE RANDOMLY COILEDPOLYISOBUTYLENE CHAIN UNPERTWED BY THERMODYNAMIC INTERACTIONS
n/Z
C;g)’/z in A. for M = 108 X 108
X 10‘7
Afc cosine (cG)
1)
1.10
25
1.06 0 93
6.49 6.32 5 80
54.3’ 54.8’ 56 9’
K
T, OC.
100
i;a/~)
Calcd. Calcd. for free from rot. col. 3
806 795 762
412 412 412
number of chain atom Per equvalent Ratio segment
1.95 1.93 1.85
7.6 7.4 6.8
The size of the statistical segment at different temperatures as given in the last column of Table VI was computed from this equation. The absolute maghitudes of the dimensional parameters given in Table VI are, of course, subject to the uncertainty in the numerical value of @. Comparisons of the relative values of the calculated dimensions for different temperatures, however, are significant. Inspection of Table VI demonstrates that hindrance to rotation increases the average linear dimensions of the polyisobutylene chain by a factor of approximately two. Increasing the temperature apparently has the effect of preferentially overcoming the barrier to rotation in the direction of increasing 4, inasmuch as 7%decreases slightly with elevation of the temperature. The dimensions of the coiled polymer chain in a given solvent depend on the thermodynamic interaction with that solvent. For a polyisobutylene molecule of M = 106 a t 25’ in cyclohexane, cy = 1.54 and (72>1/3 = 795 X 1.54 or 1220 A.; in benzene a t 24O, cy = 1 and (;*)‘/a = 795 A. Thus, for a high molecular weight polyisobutylene in a good solvent the two factors respohsible for the increase in size of the molecule over that for the random flight configuration with free rotation appear to be comparable in maghitude.
Estimation of Thermodynamic Parameters.-
Employing ?$/M from Table VI and taking 1.10 ior the specific volume of polyisobutylene, the value of C M Va~t 25’ as comput6d by aquation (12) of reference (5) is approximately qual to 3.4. $1 and ~1 (Table VII) were obtained according to the methods previously discuwd6 from this value of C M Vand ~ the figures listed in Table IV for $1 X C M Vand ~ 0. $1 appears in all cases t~ be much less than one-half, the approximate valu? given by the lattice theory of polymer solutions.**16 Since the numerical coefficient in equation (12) of ref. ( 5 ) may be somewhat in error owing to inaccuracies in the theory,6 the above value of and the absolute magnitudes of +1 (and of x1 as well) are correspondhgly uncertain. The relatitre values of (and of ~ 1 in ) the various solvents, however, are
e,
(18) M L Huggins, J &C% , 43, 1 (1042)
.46Qd
P h y s Z h c ? ~,. 46, l i l (19421, .4nlz
V
Y
m
VOl. 73
P.J. FLORY
TABLEVI1 THE THERMUDYNAMIC INTERACTION PARAMETERS
AT
Solvent
$1
Benzene Cyclohexane Toluene Ethylbenzene 75:25 EB:PE 50:50 EB:PE Diisobutylene n-Hexadecane n-Heptane Triptane
0.15 .14
0.15 .059
.I4
.12 ,117
25’
RI
.I4 17 21 .056 ,094 .035 .047
.17 24 ,016 055 0 0
significant. The unexpectedly large variations (fourfold) in the entropy coefficient $1 shown in Table VI1 appear to be related to the spatial character of the solvent molecules. For those solvents having cyclic structures, which are relatively compact and symmetrical (e. g., benzene, toluene and cyclohexane), $1 = 0.15, but it is consistently lower for the less symmetrical acyclic solvents capable of assuming a number of different configurations. There appears to be no correlation between $1and the heat of mixing. This is demonstrated by the presence of “good” and “poor” solvents in each of the above groups; e. g., both benzene and cyclohexane have similar values for $1, and for both n-heptane and ethyl heptylate is lower by a factor of three or four. The conclusion drawn from these results that $1 varies so greatly with the geometrical character of the solvent is supported by the work of Schick, Doty and Zimm17 on osmo:ic pressure-concentrationtemperature relationships for polystyrene in various solvents. Current theoriessJ6of p o l r solutions fail to take into account the speci c geometrical character of the solvent in relation to the polymer segment. It is obvious from the above results that this is a serious deficiency which must be borne in mind in applications of these theories. Values of KI given in Table VI1 indicate that heats of mixing of polyisobutylene are very low for aliphatic solvents but are much higher in aromatic solvents and in ethers, as would be expected. Solvents for a non-polar polymer suFh as polyisobutylene may be classified according to the values found for the intrinsic viscosity and for its temperature coefficient. Thus in a “geometrically good” solvent, where the entropy of mixing (as measured by $1) is high the observed intrinsic viscosity will be relatively high, or will approach a high value at high temperatures. In a “geometrically poor” solvent (where $1 is small) the viscosity will be relatively low. In either case, in a “thermally good” solvent wherein the heat of mixing (as measured by ~ 1 is ) low, the viscositytemperature coefficient will be low; while in a “thermally poor” solvent (wherein KI is large), this coe&cient will be relatively high. A possible complication could arise from the variation of [ q ] with T due to a decrease in K with T. This variation is small in the present case, but in some instances might be large. (17) hl I k l i i c k P Doty and B 11 Zimm, 530 (19501
?HIS
JOURNAL,
74,
May, 1951
INTRINSIC VISCOSITY RELATIONSHIPS FOR POLYSTYRENE
Acknowledgment.-The authors are indebted to Joyce C. Fox who carried out the major
1915
part of the experimental work. ITHACA,
RECEIVED SEPTEMBER 22, 1950
N. Y .
[CONTRIBUTION FROY TKE DEPARTMENT OF CHEMISTRY OP COBNELL UNIVERSITY I
Intrinsic Viscosity Relationships for Polystyrene1 BY T. G Fox,J R . ] ~AND P. J. FLORY Intrinsic viscosities of polystyrene fractions (M = 7.0 X lo4 t o 1.27 X 1Oe) have been determined in various solvents a t several temperatures. Critical miscibility temperatures 9 in the limit of infinite molecular weight were found t o be 307 and 343°K.for polystyrene in cyclohexane and in ethylcyclohexane, nspwtivel From intrinsic viscosities measured in these solvents a t temperatures equal to their respective e's, K in the equation [7r= KM%u8 was found to be about 8.0 X 10-4 a t 34" and about 7.3 X lo-' a t 70". Present data, as well as other data from the literature, are well represented by the above equation in conjunction a i t h the relationship d a8 = 2+1Cy(1 e/T)MVswhere u is the factor representing the linear expansion of the polymer coil due to interactions. The entropy of dilution parameter $1 has been found t o be about 0.1 for the solvents with cyclic structures; for methyl ethyl ketone is about 0.01. The universal viscosity constant Q in the relationship K = @(rt/Id)'/s has been calculated t o be 2.1 X 10" on the basis of data of Outer, Carr and Zimm on molecular dimensions of polystyrene in solution as deduced from the dissymmetry of scattered light. The root-mean-square distance separating the ends of a polystyrene chain in the absence of interactions of the polymer segments with their environment, apart from hindrances t o free rotation, is calculated to be 730 A. at 25" for a polystyrene of M = lo6; the calculated distance for free rotation is 302 A. In benzene, a good solvent, a t 25", LY E 1.5 and the root-mean-square distance between the ends of the chain is ca. 1100 A. The polystyrene molecule appears to be more extended than is one of polyisobutylene having the same number of chain atoms.
.
-
-
solvent and temperatureg* lo have been reported by several investigators] and more recently the mean-square extension T2 of polystyrene chains has been obtained in various solvents through measurements on the angular dissymmetry of light scattered by dilute solutions.l*J* For the [ q ] = KM1/3cu3 (1) successful application of equations (1) and (2), - LY3 = 2 +L.lcM(i - e/T)Mi/Z (2) however, intrinsic viscosities at the temperature T = 8 are virtually required for reliable evaluation K = Q(Z/M)'/n (31 of K; this constitutes the k s t step in the deterCM = 27(26/'/~a/~N)(~z/vl)( M/?)'/Z mination of all other quantities appearing in the = 1.4x 10-24 (G~/v,)(Q/K) (4) above equations. Such measurements have been The various quantities appearing in these equations carried out in the present investigation. With are defined in preceding papers.*t5 their aid, previously reported intrinsic viscosity Equations (1) and (2) have been subjected to data (and some additional results reported here) rigorous test in their application to precisely and results of chain dimension measurements are measured intrinsic viscosities of polyisobutylenes6J interpreted in the light of the relationships preover wide ranges in molecular weight and tempera- sented above. ture and in a number of different solvents. The Experimental adxquacy of these relationships has been coniirmed and the various parameters have been evaluated. Materials.-Four polystyrenes were prepared The present paper is concerned with the similar treat- by bulk polymerizations of styrene a t 60' in the ment of intrinsic viscosities of polystymne, and with presence of benzoyl peroxide according to the the deduction from such data of the ratio a / M method described elsewhere.I2 Details of the characterizing the configuration of the chain, and the polymerizations are summarized in Table I. The determination of the thermodynamic parameters 0 polymers were fractionated by the addition of and $1 for polystyrene in several solvents. Experi- methanol to their dilute (1to 2 g./100 cc.) solutions mental data on the dependence of intrinsic viscosities in methyl ethyl ketone a t 30°.12 Seven of the of polystyrenes on molecular weights and on fractions were selected for the work reported here. The percentage of the corresponding whole polymer (1) This investigation was carried out at Cornel1 University in conrepresented by each of these fractions] t0geth.r nection with the Government Research Program on Synthetic Rubber with their viscosity-average molecular weights M under contract with the Office of Rubber Reserve, Reconstruction Finance Corporation. are listed in Table I. The latter were calculated (2) Rohm and Haas Company, I n c , Philadelphia, Penna from the intrinsic viscosities in benzene using the (3) P. J. Flay, I . Chum. Phys., 17,303 (1949). relationship* Joururm,,78, 1904 (1961). (4) P. J. Flory and T. G Fox, Jr., THIS Introduction The results of the application of the theory of intramolecular interactions in dissolved polymer molecules to the interpretation of their intrinsic viscosities are sumrnerized in the equations3i4
(6) See also in this connection, P. J. Florp and W. R. Krigbaum, J . Chem. Phys., 18, 1086 (1960). (6) T. 0 Fox, Jr., and P.J. Flory, J . P1p. Colloid Chum., 68, 197 (1949). (7) T.G Fox, Jr.. and P. J. Flory, TIXISJOUBNAL, 79, 1909 (1861). ( 8 ) R. H.Ewart and H. C. Tingey, Abstracts of papers presented at the 111th Meeting of the American Chemical Society, Atlantic City, N. J., April 14-18 (1947).
log Be = (log
I?]
+ 4.013)/0.74
(5)
(9) L. H. Cragg and J. E. Sirnkins, Con. J . Research, BP7, 961 (1049). (lo) F. D.Kunst, Rcc. irao. ckim., 69, 126 (1960). (11) P. Outer, C.I. Cprr and B. H. Zimm, J . Chcm. Phys., 18, 830
(1950). JOURNAL, 70, 2384 (1948). (12) T . G Fox, Jr., and P. J. Flory, THIS
