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Dilute solution properties of the polyether from bisphenol ‘A’ and 4,4′ dichlorodiphenyl sulphone
European Polymer Journal, 1969, Vol. 5, pp. 319-334. Pergamon Press. Printed in England.
DILUTE SOLUTION FROM BISPHENOL
PROPERTIES OF THE POLYETHER ' A ' A N D 4,4' D I C H L O R O D I P H E N Y L SULPHONE
G. ALLEN and J. McAINSH* Department of Chemistry, University of Manchester, England
and C. STRAZmLLE Centre de Recherches sur les Maeromolecules, Strashourg, France
(Received 12 August 1968) Almlmet--Dilute solution properties of Union Carbide polysuiphone have been measured by light scattering, osmometry, and viscometry; Mark-Houwink expressions have been determined in a thermodynamically good solvent, two thermodynamically bad solvents, and one solvent at the 0-temperature. The following relationships have been obtained: [~] (ml/gm) ----0" 145 × l~lw°'s° (dimethylsulphoxide, 105" 5 °) [~] (ml/gm) ----0-103 × IV,lw°'ss (dimethylformamide, 25 °) [~] (ml/gm) ----0.079 × l~lw°'s8 (tetrahydrofuran, 25 °) [~7] (ml/grn) ----0"024 × l~w°'7" (chloroform, 25*). The values of the tmperturbed dimensions, ( < ro 2 > / M ) t, solvent-polymer interaction parameters (B and xl) and eonformational parameter (a) have been computed by applying the theories of Stockmayer-Fixrnan-Burchard, Flory-Fox-Schaefgen, Kurata-Stockmayer-Roig, Ptitsyn and InagakiSuzuld-Kurata. Because of uncertainty in the values of the various bond angles in the polymer chain the exact value of a cannot be given, but it must be close to unity. This low value is not unexpected, it is shared by other polymers containing X - P h - X links.
INTRODUCTION Tim SOLUTION properties of the polysulphone obtained by condensing 2,2-bis(4hydroxyphenyl) propane with 4,4'-dichlorodiphenyl sulphone have not previously been investigated in any detail but its thermal stability ~1) and the hydrolytic side reactions c2~ have been discussed. As can be seen from its structure
[
Me
,
--O --Ph--C--Ph--
t Me
O--Ph--SO2--Ph--
n
this polysulphone belongs to a class of molecules containing "long bonds", i.e. whose rigid chain links are not single interatomic bonds but groups, usually rings, of atoms rigidly connected,t3~ It has been shown previouslyt3.*~ that polymers containing these * On secondment from I.C.I. Ltd., Petrochemical and Polymer Laboratory, Runcorn Heath, Cheshire. 319
320
G. ALLEN, J. M c A I N S H and C. STRAZIELLE
"long bonds" tend to have unperturbed dimensions slightly greater than the free rotation values theoretically calculated. In the present work polysulphone fractions have been investigated by various techniques for the determination of the molecular characteristics such as molecular weight and unperturbed dimensions.
EXPERIMENTAL
Samples The sample used was unfractionated, commercially available, Union Carbide polysulphone prepared from 2,2-bis(4-hydroxyphenyl) propane and 4,4'-dichlorodiphenyl sulphone. This puly(aryl ether) is identified as polysulphone throughout this paper. A solution of linear polysulphone was made up in dimethylsulphoxide at 80 °. The resulting 0" 667 per cent solution was fractionated by lowering the temperature in successive increments to give eight fractions by liquid-liquid phase separation. The temperature at which each fraction was removed was determined by the onset of turbidity. The fractions were isolated by redissolving them in tetrahydrofuran and finally precipitating them in 3--4 volumes of ethanol. The white precipitate, collected by filtration through a G4 sintered glass filter under pressure, was dried in a vacuum oven at 20 ° for several hours. The results are given in Table 1 and the molecular weight distribution obtained is illustrated in Fig. 1. TABLE 1. DATA FOR THE FRACTIONATIONOF A 0" 667 PEa CE~'crSOLUTION OF POLYSULPHONE IN DIMETHYI.SULPHOXIDE Fraction
Tt,(°C)
wt. (g)
wt. ~o
Wj
SEI SE2 SE3 SFA SE5 SE6 SE7 SE8
60"0 54"0 47" 5 40" 6 35"0 28"5 21-8 17"0
1 "04 2" 67 2- 54 2" 52 1" 71 1"53 1-33 7-48
5.00 12" 82 12" 20 12-10 8" 21 7-35 6"39 35"93
0"975 0" 886 0" 761 0" 639 0" 538 0"460 0"391 0"180
Initial weight ffi 22.4 g. Efficiency -~ 93 per cent.
Physical measurements (a) Viscosity. Dilute solution viscosities of the fractions were measured at 25 _+ 0"01 ° and 105" 5 ± 0.01 ° in a n Ubbelohde dilution viscometer for which kinetic energy corrections were negligible. The usual precautions for the evaporation of solvent at high temperatures were taken and corrections were made for the changes in solution concentration. All solvents were given appropriate chemical purification. The intrinsic viscosity [7] was calculated from the reduced viscosity at three or four concentrations
by means of (i) the Hugglns relationship/s~
~
c
= [~]H + k . [,1]. 2 x c
where ks is known as the Hugglns constant, (ll) the Schulz-Blaschke relationship/~) ~"--Z~= [~]sa + ksB [~]sB X ~ , , c where ksB is known as the Schulz-Blaschke constant,
Dilute Solution Properties
A
g
321
I00
o .T= :>
0 8C
/
06C
@
,/
0.40 (..)
0201 O(
,/
1.J I 0' 25
T 0' 50
I 0.75
t00
[~] dL.g"1 (chloroform ot 25") FIG. 1. Data for the fractionatiou of polysulphone from dimethyisulphoxZde. (i/~)
" ' "-- (7) the Kraemer rclaUonsmp,
In ~r C
=
[,7]x -
k x [,7]~ 2 x
c
where kx is the Kraemer constant. (b) Osmometry. The number-average molecular weights of the fractions were measured in dimethylformamide solution with a Mechrolab 502 osmometer using membranfilter G6ttingen feinst and allerfeinst membranes at 30 ° + 0.01% Appreciable diffusion of polymer through the membrane occurred with the lowest molecular weight sample (SE8) and accordingly corrections were made. (s~ g;I° values were calculated using the relationship
Ir c
RT
M . ( l -3c A2c "-[-gA~c 2)
where A2, the second virial coefficient, depends on the polymer-solvent interactions, and g is a number which varies with the solvent. For most thermodynamically "good" solvents, g ~ 0- 25 and tends towards zero in poorer solvents. (c) light scattering. The weight-average molecular weights of the fractions were determined with a Wippler-Scheibling light scattering photometer. All measurements were carried out at 25 _ 0"01 ° using the green Hg line 546 m~. All solutions were prepared individually and then centrifuged at 14,000 rev/min for 1 hr. The data was analysed using the Zimm method.( 9~ The specific refractive increment (dn/dc) was determined with a Brice-Phoenix differential refractometer previously calibrated with aqueous sucrose solutions. The value of dn/dc for polysuiphone in dimethylformamide at 250 + 0.01 °, using light of wavelength 546 m~, was 0.199 ml. g - l . (d) Gelpermeation chromatography. The gel permeation chromatography experiments were carried out on a Waters machine equipped with four columns (10 s, l0 s, 10", 9 x 102 ~,), at room temperature. The solvents were tetrahydrofuran and chloroform. Injection time was automatic, taking place in 5 rain intervals. The pumping rate was always 1 ml/min. All the chromatograms were quite sharp and almost symmetric. The maximum of the peak was taken as the elution volume for each of the tested fractions. Calibration was carried out by plotting log 1~1,, against elution volume for a series of sharp polystyrene fractions in tetrahydrofuran and chloroform.
:E”: SE6 SE7 SE8
SE1 SE2 SE3
O-852 0.740 O-581 O-488 o-434 0.406 O-361 O-207
O-52 0.39 O-58 0.59 O-63 0.55 O-67 O-78
0.885 0.750 O-587 o-495 O-440 O-410 O-368 O-210
chloroform
0.32 O-29 O-42 o-43 0.46 O-42 O-45 O-80
O-612 O-503 O-461 O-394 O-352 0.324 O-295 O-162
O-68 0.68 O-63 O-56 O-57 O-60 O-53 O-84
O-634 0.523 O-472 O-401 O-358 O-329 O-299 O-163
0.44 0.43 0.45 0.41 0.43 0.45 0.41 O-69
0.628 O-518 O-468 0.398 0.357 O-327 O-298 O-164
Tetrahydrofuran
0.00 0.02 O-00 0.04 0.04 0.00 O-06 0.34
25”,
0.523 0.469 O-408 O-357 0.322 0.303 O-263 0.156 0.19 0.18 O-12 0.18 O-64 0.54 0.43 0.70
O-513 0.455 O-408 0.355 0.336 O-313 O-262 0.168
0.29 0.29 O-11 O-21 O-21 0.27 O-36 0.22
AT 105-Y'
0,413 0.353 0.316 O-281 O-254
O-72 O-82 l-06 l-10 l-02
O-421 O-361 O-316 0.281 0.254
Dimethylsulphoxide
AND DIMETHLYSULPHOXIDE
Dimethylformamide
TABLE 2. Vrscosrr~ DATA IN CHLOROFORM, TETRAHYDROFURAN, AND DIMETHYLFORMAMIDE AT
O-52 0.59 O-65 O-67 O-68
D i l u t e S o l u t i o n Prope rt i e s
323
RESULTS The results o f the various physical measurements are shown in Tables 2 and 3. As found for polyacenaphthylene solutions (I°) a n d poly (2:6 dimethyl phenylene oxide) solutions,
L.S. at 25 °
Os a t 30 °
Fraction
l~I. x 10-+
lg~l. x 10-*
SE1 SE2 SE3 SEA SE5 SE6 SET SE8 Unfractionated
9" 19 7"56 5-94 4-38 3"62 3"20 2" 87 1" 89 4" 00
9" 15 7"51 5-55 4"65 3"80 3-34 2" 83 1" 28 2- 04
G .P .C . a t 25 °
I~I,,L'S'/~.°" [lg:l./~dcacla 1 "01 1"01 1-07 0"94 0"95 0"96 1 "02 1"48 1" 96
1 "43 1-35 1 "26 1 "24 1"20 1-19 1" 17 2" 11 2" 38
[1~1,,/19Io1 Tin" -1"31 1 "33 1 "25 1"20 1 "25 1 "24 1" 96 2" 30
I
I'00
T
> o.
o-so
0.40 02; 0.15 0
I
I 02
I
I
i
04
I 06
I
I 0.8
I
T 10
"r/sp
Fro. 2. Intrinsic viscosities of the E-fractions in chloroform at 25°. (Schulz-Biaschke).
or the Huggins constants and, at concentrations greater than infinite dilution, the K r a e m e r equation gives a g o o d a p p r o x i m a t i o n to the intrinsic viscosity. These differences, have, however, no significant effect on the derived values o f the M a r k - H o u w i n k constants. F r o m the viscosity and light scattering data shown in Tables 2 a n d 3 respectively, we
324
G. ALLEN, J. McAINSH and C. STRAZIELLE
find by the method of least squares the following weight-average molecular weightintrinsic viscosity relationships for polysulphone in the solvents and at the temperatures indicated. Note that all quantities are expressed in c.g.s, units. Dimethylsulphoxide, 105.5°: ['7] = 0-145 × l~Iw°'5° Dimethylformamide, 25 °: [7] = 0 . 1 0 3
× l~[,, °'55
Tetrahydrofuran, 25 °: [~7] = 0-079 × IVlw°'Ss Chloroform, 25 °: [~7] = 0.024 X l~/[w0"72. The uncertainties are ~ 0.003 in K a n d ~ 0.02 in the exponent a. The data are shown in Fig. 3. (Because of the high polydispersity of fraction SES, the results obtained Chloroform
1.6
/
e~"
~O
Tetrahydrofuron
... o . . O . . . . . o / ° / e ~
1.5
Oimethylformamide
e/o-"
1.6 1.4 Dimethylsulphoxicle 1'6 "
)4
O/O/n~
d
/ . ~ ' / 44
I
t 4-6
I
I 4.8
I
50
LOg. M,w
FIG. 3. Viscosity-rnol¢cularweight relationships in (a) chloroform (b) t¢trahydrofuran, and (c) dimetbylformamide,all at 25°, and (d) dimethylsulphoxideat 105"5°. by light scattering and intrinsic viscosity for this fraction were not used in the evaluation of K and a.) DISCUSSION
(a) Determination of Mw/Mnfor the unfractionatedpolymer and the fractions The number-average and the weight-average molecular weights of the unfractionated polymer were determined directly by osmometry and light scattering respectively
Dilute Solution Properties
325
and found to be 20,400 and 40,000. Hence the ratio l~,dl~I° ---- 1.98. KIw and K4° for the unfractionated polymer were also calculated directly from the fractionation distribution curve and the molecular weight characteristics of each fraction. (11) By this method l~I~, ----39,000 l~I° = 24,000 I~,,,/IVI.= 1.68. The agreement between the two methods is good for ~ , , but the calculated value of l~ln is higher than that observed directly. This can be explained by considering diffusion of small molecules through the semi-permeable membrane for the lower molecular weight fractions. This diffusion causes an increase in 1VIofor the fractions and also explains why the ratio l~Iw/IVIo is less than one for certain fractions, as shown in Table 3. The results obtained by gel permeation chromatography in THF and chloroform give a higher value for the ratio 1VIw/i~Iofor the fractions than obtained directly by light scattering and osmometry measurements. This is a general phenomenon explained by taking into account the resolution power of the gel permeation chromatography machine and also the method of calculation. (t2) However, it is more likely that the true value of K,I,,/I~I° is between that obtained by G.P.C. and the light scattering/osmometry measurements.
(b) Determination of the O-temperature The 0-conditions of a polymer solution correspond to an "ideal" state at which the excluded volume effect and the long range polymer-polymer interactions in a given solvent compensate. These conditions obtain for a binary system (polymer/solvent) at a specific temperature 0. This 0-temperature can be determined by measurements of the second virial coefficient, A2, at different temperatures and extrapolating to ,42 = 0. Another method proposed by Schultz and Flory "3) for the 0-temperature determination is based on an interpretation of the liquid-liquid phase separation of the polymer solutions. This method requires the determination of the critical temperature of solutions of polymer fractions differing in molecular weight. A third method, proposed by Talamiui and Vidotto, " ' ) relates the temperature (for binary systems) for incipient phase separation to the molecular weight of the polymer. The equation for this method has the form
1
1(
K--K'
1
0.6)
where Tp is the phase separation temperature, ~, is the number-average degree of polymerization, and ~ is the entropy parameter. The constants K and K' are both functions of the polymer volume fraction. The graph of I/Tp against I/(~) °'6 is linear and from the intercept 8 isevaluated to be I05.5 °. The graph is shown in Fig. 4.
(c) The unperturbed dimensions of polysulphone From the data to hand, it is possible to evaluate the unperturbed dimensions of polysulphone by two techniques: (a) from intrinsic viscosity data at the O-point in dimethylsulphoxide by using the well-established techniques of Flory; (1s) (b) by
326
G. ALLEN, J. McAINSH and C. STRAZIELLE
/
3.4
/ 32 e /
- -
x
3"0
Vz= 5"38x I0"3
e/
Z.8
2.6 o
I
5
IO
X : °e x Io
FIo. 4. Plot of the reciprocal of the precipitation temperature against the indicated molecular size function for polysuiphone in DMSO. intrinsic viscosity measurements in tetrahydrofuran, chloroform, dimethylformamide and dimethylsulphoxide using the extrapolation techniques of Stockmayer-FixmanBurchard,(16, 17) Flory_Fox_Schaefgen,.8, 19) Stockmayer_Kurata_Roig,(2o) Ptitsyn(2~) and Inagaki-Suzuki-Kurata. (22) Method 1. The viscosity-weight-average molecular weight data taken at the 0-temperature in dimethylsulphoxide are shown in Fig. 3. The slope of the line is 0.5 and fits the limiting relation: [~7] = K M °'5. Straightforward calculations give a value o f K = 0.145 cm 3. g- ~ at 105.5 ° in dimethylsulphoxide. From K the unperturbed dimensions can be calculated, but first a correction for molecular weight heterogeneity must be applied. According to the Flory-Fox (23) relationship K = 4o (< ro 2 > / M ) 3/2 where 9~o is the hydrodynamic constant, < ro2> is an average unperturbed mean square end-to-end dimension, and M is an average molecular weight. If it is assumed that the distribution within the fractions is given by the Schulz (24) molecular weight distribution function, then the correction for heterogeneity is given by ~ow = gw
~o
r(h + 1.5) where and
gw = (h + 1)t P(h + 1)
(h + 1) l~[w h Mn where 4o has the Kirkwood-Riseman theoretical value of 2.87 x 1053 g-~.(2s, 2~
Dilute Solution Properties
327
Averaging the gel permeation chromatography results in chloroform and tetrahydrofuran gives a value of/VI,,/1VI, = 1.26 from which the parameter h is evaluated to be 3.85. It follows that gw = 0.98 and Sow = 0.98 $o. Thus for the unperturbed dimensions: ( < r o 2 > / M ) ~ = (802 -+-20) 5< 10 -11 cm. Method 2. This calculation relies purely on viscosity data in various solvents and the determination of l~lw by light scattering. In the Stockmayer-Fixman-Burchard method, hereafter denoted S-F-B, the equation used for the determination of the unperturbed dimensions is
[,/]IM ~ = K + (0.51 B ~bo) × M ÷ where B is a parameter characteristic of the polymer-solvent interaction and given by B = ~/mo 2 where/3 represents a binary cluster integral and mo the molecular weight
of the polymer segment. Thus a graph of [~]/M ~ against M * has an intercept equal to K from which the unperturbed dimensions can be evaluated. It has been pointed out ~22) that the correct estimate of K, by the S-F-B method, will be obtained if results for M > 106 are omitted, since if extrapolation is made from the region of larger M, the value of K is seriously overestimated. However, for the polysulphone under investigation, the molecular weights are such that this consideration does not arise. In the Flory-Fox-Schaefgen method, hereafter denoted F-F-S, the equation [~]2/3/M1/3 = K 2/3 + (4/3 Ks/3z*) X M/[~7]
is used for the determination of the unperturbed dimensions. However the application of this method to polar polymers or polymers in good solvents has often yielded unreliable estimates for chain dimensions (26) and often leads to a serious underestimate of K or even to a negative value of K. Some of these drawbacks have been overcome by the application of the StockmayerKurata-Roig expression, hereafter denoted S-K-R, [r/]2/3/MI/3 = K 2/3 + (0"363 $o B) g(~,,) × M2/3/['q] 1/3
where
8~n 3 g(%) = (3e 2 -I- 1) 3/2
and
a3 = ['~]/[~Ts].
To estimate g (a,) it is necessary to use the values of [~d obtained at 105.5 ° in dimethylsulphoxide, thus any temperature dependence of [~Te]is neglected. According to the Ptitsyn theory, the equation used for the estimation of the unperturbed dimensions is" [rl]2/3/Ml13 = 0"786 K 2/3 -I- (0"950 z .2/3 g 2/3) X M 1/3.
Utiyama and Kurata ¢27)and Ueda and Matsumoto c2s) pointed out that, if an appropriate relation between the hydrodynamic radius ~29. 30) and the end-to-end distance is found and combined with the Ptitsyn equation, the resultant equation could yield reliable unperturbed dimensions. ¢27" 2s) A method based on this analysis has been proposed
328
G. ALLEN, J. M c A I N S H and C. STRAZIELLE
by Inagaki, Suzuki and Kurata for estimating unperturbed dimensions in good solvents and it is embodied in the equation
[~]4/S/M2/S =
0.786 K 4/s + (0"950 K 4Is z *2/a) X M 1/3.
This method is denoted I-S-K throughout this paper. However it has been pointed out by Inagaki et al. that, when experiments are conducted in the vicinityof theta conditions, data points should converge to an intercept which corresponds to K 4Is. This considerationistaken into account when dealing with the polysulphone data obtained in the bad solvents and is also applied to the value of the intercept obtained using the Ptitsyn equation. To calculate the unperturbed dimensions of polysulphone, all five equations are used and the comparative resultsfor A ----(< to2>/M)* are shown in Table 4. The TABLE 4. DATA FOR THE DI~TeitMINATION OF A FOR POLYSULPHONE IN THE INDICATED SOLVENTS A
Function/ Solvent
Temp. (°0
S-F-B
F-F-S
25
CHCIa
780
694
25
THF
818
25
DMF
811
105"5
X
lOalcm P
S-K-R
820
804 894 793*
772 818
762 873 791"
814
881 798*
813
881 797*
DMSO
780
* Modifi~l results.
0"240 ©
o
THF
o ¢) O, 160
:E =
=
•
•
DMSO
0.080
0
T I00
I 200
I-S-K
! 300
MO.5
Fio. 5. Stockmayer-Fixman-Burchard plots for polysulphone.
400
Dilute Solution Properties
329
plots obtained by the S-F-B, S-K-R, and I - S - K methods arc shown in Figs. 5, 6 and 7 respectively. Within experimental error, the S-F-B and S--K-R methods give similar values of.4, i.e. A ( S - F - B ) = (797 -t- 20) x 10 -11 cm and A(S-K-R) = (796 -t- 20) × 10 -11 cm. These results are independent of the nature of the solvent, and in good agreement with the result obtained directly from 0-point measurements.
039C
i
0230! 0'310
0.15
I I00
•
I ZOO
I 300 MZ/'/ ['r/] l/3
•
DMSO
•
I 400
@
I 500
FIG. 6. Stockmayer-Kurata-Roig plots for polysulphone.
J 3C
2o
I0 0
J
•
I I0
I 20
MI/3
I 30
•
I 40
FIG. 7. Inagaki-Suzuki-Kurata plots for polysulphone.
DMSO
330
G. ALLEN, J. McAINSH and C. STRAZIELLE
The values obtained from the F - F - S equation are dependent on the nature o f the solvent chosen and in the case of the good solvent, chloroform, an unusually low value of A is obtained, in agreement with previous observations, c26~ Both the I - S - K and the P equations yield good results for A in the good solvent. However when the data obtained from the bad solvents is corrected, as already indicated, the final values for A are in good agreement with the rest of the data. Thus it can be concluded that a value of A = (802 4- 20) x I0 -11 cm is well substantiated, and that within experimental error the temperature variation of A is negligible. It would be interesting to compare these values of A with values measured directly, for example, by light scattering. Unfortunately this is not possible because the radius of gyration of our samples is too small for accurate determinations by light scattering.
(d) Interaction parameters B and Xl The solvent-polymer interaction parameter, B, may be evaluated from the slope of the graphs used for the estimation of the unperturbed dimensions. The results obtained for B by the various extrapolations are in good agreement with one another. This parameter B may in turn be related to the Fiery interaction parameter xl c31~ by B = ~ c (1 -- 2Xl)/V~NA where e2 is the specific volume of the polymer, Vx is the solvent molar volume and NA is Avogadro's number. Table 5 lists the B and Xt values for the various solvents. TABLE 5. INTERACTION PARAMETERS
FOR POLYSULPHONE INDICATED TEMPERATURE
Solvent
B × 1027
CHCIa THF DMF DMSO
3"37 0.86 0.41 0-00
xt
AT THE
Temp. (°C)
0" 37~ 0.46s 0.480 0.50o
25"0 25.0 25- 0 105.5
(e) The conformation of polysuiphone in solution The effect of diminished free rotation about a bond as a result of steric hindrance is defined as cr : ( < re 2 >/M)~r/(< roZt >/M)* where < ro2t > is the mean-square end-to-end distance calculated on the assumption of free rotation, and a is the conformational parameter. As can be seen from Fig. 8, all the "rotatable" links in the chain are not o f the same type. The chain consists of three valence angles, denoted 01, 02 and 03 and two bond lengths, denoted I and p. The link lengths can be calculated from normal covalent bond lengths and are found to be 5.87 A and 5.64 A for I and p respectively, c3z' 33) The valence angles are not known for this molecule but from model compounds they can be estimated. They are 01 ---- 123°/4~ 02 -----109"5 °, and 03 = 104°. t33~ According to
Dilute Solution Properties
0
331
0
0
P
P
h
Ph
\
\\ \ S
C
$
FIG. 8. M o d e l c h a i n for polysulphone.
various authors ¢3' 3,..3~) the valence angle 01 at the oxygen atoms in polyether chains is usually assumed to be approximately the tetrahedral angle, 109.5 °. Since 02 and 03 are very close to this value, the first approximation for calculating the average-end-toend distance is to assume the molecule consists o f two different b o n d lengths and one valence angle equivalent to the tetrahedral angle. The appropriate equation is obtained by solving directly the expression < ro 2 > = ~ 2~ li, lj; ~3S) with Ix ---- 12 = I and 13 = 14 = p, and a = ~r - - 0. T h e result is: (ro2I~
(12 _{_p2)
--T-- = --'T---
(1 + cos a) [1 (1 - cos ~) [
(1-- p)2
(r + f)
cos a
(1 + cos ~
1
~)/
where N is the total n u m b e r o f links i.e. there are N/2 links o f length I, and N/2 links of length p. The second approximation is to assume that 0~ = 123 °, and 02 ---- 0a ---- 107 °. Thus the problem now becomes one o f a molecule consisting o f two valence angles and two b o n d lengths. The appropriate formula in this case is
(to2:) N
(I2-t-p2) (1 + c o s a i ) ( 1
-t- cos a2)[ 2 (1 -- cos al cos a2) 1--
=
( / _ p ) 2 cos.a_~ (1 +_.~.~_~s~2) ] (12..~_p2) (1 + c o s al cos a2) (1 + c o s al).l
where ~ = ~r -- 0~ and a2 = ~r -- 02 = ~r -- 107 °. It can be easily verified that when ,~ -- a2 this equation reduces to that above. The value of < ro2t > / N obtained from the first approximation is 66.31 (.A,)2. The second approximation gives a value of 78-64(/k) 2. Although 0x and 03 are not known TABLE 6. DATA FOR THE FREE ROTATION DIMENSIONS AND THE STERIC FACTOR FOR POLYSULPHONE Function
/N
A t × 1011
× 10 le First app. Second app. POLVmm 5/2--.4
66-31 78.64
a -- 802 × 10 -11 At
776 843
1.04 +_ 0 - 1 0 0 . 9 5 + O" I0
332
G. ALLEN, J. McAINSH and C. STRAZIELLE
with certainty, within the ranges 0~ = 120°-123 ° and 0a -----107°-120 ° < r 2 o l > / N is 78- 5 4- 0.2(A) 2 for the second approximation. The corresponding values o f the free rotation dimensions, A t, and the conformational parameter o, are shown in Table 6.
CONCLUSION The value o f o = 1.03 4 - 0 - 1 0 for 01 = 109.5 ° is not entirely unexpected as polymers containing X - - P h - - X links show similar low values o f 0 (4. aa-4a) These results suggest that it is the phenylene ring system which causes the low value o f o and not the nature o f X. The most significant factor would a p p e a r to be the length o f the rigid link - - - X - - P h - - X - - and the apparently small energy differences between the various rotational isomers since it is noticeable that for these polymers not only is o _~ 1 but also the temperature dependence o f chain dimensions is small. This conclusion is further supported by the fact that aliphatic polysulphones, which have normal main chain linkages consisting o f single o-bonds, e.g. poly(hexene-1 sulphone) (44.45) and poly(2-methyl-l-pentene-1 sulphone) (44) have conformational parameters o f 1-71 and 2.05 respectively. Acknowledgements--J. McAinsh thanks Professor H. Benoit for laboratory facilities and stimulating
discussion, and the University of Manchester for granting leave of absence. REFERENCES (1) W. F. Hale, A. G. Farnham, R. N. Johnson and R. A. Glendinning, J. Polym. Sci. AI, 2399 (1967). (2) R. N. Johnson and A. G. Famham, J. Polym. Sci. AI, 2415 (1967). (3) J. M. Barrales-Rienda and D. C. Pepper, Europ. Polym. J. 3, 535 (1967). (4) P. Akers, G. Allen and M. Bethel, Polymer, to be published (1968). (5) M. L. Huggins, J. Am. chem. Soe. 64, 2716 (1942). (6) G. V. Schulz and F. J. Blaschke, J. prakt. Chem. 158, 130 (1941). (7) E. O. Kraemer, Ind. Engng Chem. 30, 1200 (1938). (8) A. J. Staverman, Recl. Tray. chim. Pays-Bas, Belg. 70, 344 (1951). (9) B. H. Zimm, J. chem. Phys. 16, 1099 (1948). (10) J. M. Barrales-Rienda and D. C. Pepper, Polymer 8, 337 (1967). (11) C. Mussa, J. Polym. Sci. 26, 67 (1957). (12) H. Benoit, Z. Grubisic, P. Rempp, D. Decker and J. G. Zilliox, J. chim. Phys. 63, 1507 (1966). (13) A. R. Schultz and P. J. Flory, J. Am. chem. Soc. 74, 4760 (1952). (14) G. Talamini and G. Vidotto, Makromolek. Chem. U0, 111 (1967). (15) P. J. Flory, J. chem. Phys. 17, 303 (1949). (16) W. H. Stockmayer and M. Fixman, J. Polym. Sci. C1, 137 (1963). (17) W. Burchard, Makromolek. Chem. 50, 20 (1961). (18) T. G. Fox and P. J. Flory, J. Am. chem. Soc. 73, 1909 (1951). (19) J. R. Schacfgen and P. J. Flory, J. Am. chem. Soc. 70, 2709 (1948). (20) M. Kurata, W. H. Stockmayer and A. Roig, J. chem. Phys. 33, 151 (1960). (21) O. B. Ptitsyn, Vysokomolek. Soed. 3, 1673 (1961). (22) H. Inagaki, H. Suzuki and M. Kurata, J. Polym. Sci. C15, 409 (1966). (23) P. J. Flory and T. G. Fox, J. Polym. Sci. 5, 745 (1950). (24) G. V. Schulz, Z. phys. Chem. !]43, 25 (1939). (25) J. G. Kirkwood and J. Riseman, J. chem. Phys. 16, 565 (1948). (26) M. Kurata and W. H. Stockmayer, Adv. Polym. Sci. 3, 196 (1963). (27) H. Utiyama and M. Kurata, Rep. Prog. poly. Phys., Japan 1, 31 (1964). (28) M. Ueda and S. Matsumoto, Report presented at the 13th Annual meeting of the Society of Polymer Science, Japan, Kyoto (1964). (29) H. Yamakawa and M. Kurata, J. chem. Phys. 29, 311 (1958). (30) M. Kurata, H. Yamakawa and H. Utiyama, Makromolek. Chem. 34, 139 (1959). (31) P.J. Flory, Principles of polymer chemistry, Cornell University Press, Ithaca, N.Y., U.S.A. (1953).
Dilute Solution Properties
333
(32) L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, N.Y., U.S.A (1945). (33) J. Syme, Acta crystallogr. 13, 1 (1960). (34) W. H. Stockmayer and L. L. Chart, J. Polym. Sci. A2(4), 437 (1966). (35) A. Ciferri, C. A. J. Hoeve and P. J. Flory, J. Am. chem. Soe. 83, 1015 (1961). (36) J. E. Mark and P. J. Flory, 3". Am. chem. Soc. 88, 3702 (1966). (37) J. E. Mark, Jr. Polym. Sci. !!4, 825 (1966). (38) M. V. Volkenstein, Configurationai Statistics of Polymer Chains. Interscience (1963). (39) M. L. Wallach, Polymer Preprints 6, 860 (1965). (40) G. V. Schulz and A. Horbach, Makromolek. Chem. 29, 93 (1959). (41) G. Sitaramaiah, J. Polym. Sci. A3, 2743 (1965). (42) M. L. Wallach, Polymer Preprints 6, 52 (1965). (43) G. C. Berry, H. Nomura and K. G. Mayhan, J. Polym. Sci. A2, 1 (1967). (44) T. W. Bates, J. Biggins and K. J. Ivin, Makromolek. Chem. 87, 180 (1965). (45) H. A. Ende, K. J. Ivin and G. Meyerhoff, Polymer 3, 129 (1962). R£~sumd-----Lespropri&ds en solution dilute d'une polysulphone fournie par l'Union Carbide ont 6t6 rnesur~s par diffusion de la lumi~re, par osrnom6trie et par viscosim&ric. Les expressions de MarkHouwink ont 6t6 d6termin~s dans le cas d'un bon solvant, de deux rnauvais solvants et d'un solvant la ternp6rature them. Les relations suivantes ont 6t6 obtcnue : [7] (cma/g) = 0,145 × l~lw°'s° (dim6thylsulfoxyde; 105,5 °) (cm3/g) = 0,103 × l~lw°.ss (dim6thylformamide; 25 °) (cm3/g) = 0,079 × l~lw°,ss (tetrahydrofurane; 25 °) (cma/g) = 0,024 × l~lw°'va (chloroforme; 250). Lcs vaieurs des dimensions non pertur~es (< ro2>/M) I/2, des param~tres d'interaction solvantpolyrn~re (Bet XI) et du pararn~tre conformationnel (a) ont 6t6 calculus en appliquant les th6ories de: Stockmayer-Fixman-Burchard, Flory-Fox-Schaefgen, Kurata-Stockmayer-Roig, Ptitsyn and Inagaki-Suzuki-Kurata. En raison de l'inccrtitude sur les valeurs des diff6rents angles de valence dans la chaine polym~rique, la valeur exacte de a ne peut ~tre donn~e. Elle doit cependant &re voisine de l'unit6. Cette faible vaieur, ayant d~j~ 6t6 t r o u v ~ pour d'autres polym~res renfermant des liaisons X-Ph-X, n'est pas surprenante. Sommario--Sono state effettuate misure osmometriche, viscosimetriche e di "light scattering" delIe proprieta delle soluzioni diluite del polisulfone Union-Carbide; si sono determinate espressioni di Mark-Houwink in un solvente termodinamicamente buono, due solventi termodinamicamente cattivi e in un solvente a temperatura teta. Sono state ottenuete le seguenti relazioni: [,fl (cm~/g) = 0,145 × I~I,Y"s° (dimetilsulfossido, 105,5 °) (cma/g) = 0,103 × l~I,,°'ss (dimetilformamide, 25 °) (cm3/g) = 0,079 x l~lw°.ss (tetraidrofurano, 25 °) (cm~/g) = 0,024 x l~Iw°.~2 (eloroformio, 25 °) I vaiori delle dimensioni non perturbate ( < r o ' > / M ) !/2, i parametri di interazione solventepolimero (B e XI) e il parametro conformazionale (a), sono stati ealcolati applicando le teorie di Stockmayer-Fixman-Burchard, Flory-Fox-Schaefgen, Kurata-Stoekmayer-Roig, Ptitsyn and Inagaki-Suzuki-Kurata. A causa delrincertezza nei valori dei vari angoli di legarne nella catena polimerica, non pub essere dato resatto valore di a, tuttavia esso deve essere vicino all'unita. Questo valore basso non ~ inaspettato, essendo condiviso da altri polimeri, contenenti legami X-Ph-X. Zusammenfassung--Die Eigenschaften in verd(innter L/Ssung von Union Carbide Polysulfonen wurden durch Lichtstreuung, Osmometrie und Viskosit~it untersucht. Die Mark-Houwink Beziehungen wurden bestimmt in einem thermodynamisch guten und zwei thermodynamisch sehlechten L6sungsmitteln, und in einem L6sungsmittel bei Theta-Temperatur. Es wurden folgende Gleichungen erhalten: [,fl (cma/g) = 0,145 × 1~1,,°'s° (dimethylsulfoxid, 105,5 °) (crn3/g) = 0,103 × l~I,,°'ss (dimethylformamid, 25 °) (cma/g) ----0,079 x l~i,,°.ss (tetrahydrofuran, 25 °) (cma/g) = 0,024 × 1~1~,°'v, (chloroform, 25°).
334
G. ALLEN, J. McAINSH and C. STRAZIELLE
Die Werte ffir die ungestOrten Dimensionen ( < r o ' > / M ) 1/', die Parameter tier L~sungsmittelPolymer Wechselwirkung (B und x J) und der Konformations-Parameter (a) wurden berechnet unter Zugrundelegung der Theorien von Stockmayer-Fixman-Burchard, Flory-Fo×-Schaefgen, KurataStockmayer-Roig, Ptitsyn und Inagaki-Suzuki-Kurata. Wegen der Unsicherheit in Bezug auf die verschiedenen Bindungswinkel in der Polymerkette kann f~ir a k¢in exakter Wert angegeben werden; er muB aber nahe bei 1 liegen. Dieser niedrige Wert ist nicht unerwartet, da er auch bei andern Polymeren mit X - P h - X Bindungen gefunden wird.
DILUTE SOLUTION FROM BISPHENOL
PROPERTIES OF THE POLYETHER ' A ' A N D 4,4' D I C H L O R O D I P H E N Y L SULPHONE
G. ALLEN and J. McAINSH* Department of Chemistry, University of Manchester, England
and C. STRAZmLLE Centre de Recherches sur les Maeromolecules, Strashourg, France
(Received 12 August 1968) Almlmet--Dilute solution properties of Union Carbide polysuiphone have been measured by light scattering, osmometry, and viscometry; Mark-Houwink expressions have been determined in a thermodynamically good solvent, two thermodynamically bad solvents, and one solvent at the 0-temperature. The following relationships have been obtained: [~] (ml/gm) ----0" 145 × l~lw°'s° (dimethylsulphoxide, 105" 5 °) [~] (ml/gm) ----0-103 × IV,lw°'ss (dimethylformamide, 25 °) [~] (ml/gm) ----0.079 × l~lw°'s8 (tetrahydrofuran, 25 °) [~7] (ml/grn) ----0"024 × l~w°'7" (chloroform, 25*). The values of the tmperturbed dimensions, ( < ro 2 > / M ) t, solvent-polymer interaction parameters (B and xl) and eonformational parameter (a) have been computed by applying the theories of Stockmayer-Fixrnan-Burchard, Flory-Fox-Schaefgen, Kurata-Stockmayer-Roig, Ptitsyn and InagakiSuzuld-Kurata. Because of uncertainty in the values of the various bond angles in the polymer chain the exact value of a cannot be given, but it must be close to unity. This low value is not unexpected, it is shared by other polymers containing X - P h - X links.
INTRODUCTION Tim SOLUTION properties of the polysulphone obtained by condensing 2,2-bis(4hydroxyphenyl) propane with 4,4'-dichlorodiphenyl sulphone have not previously been investigated in any detail but its thermal stability ~1) and the hydrolytic side reactions c2~ have been discussed. As can be seen from its structure
[
Me
,
--O --Ph--C--Ph--
t Me
O--Ph--SO2--Ph--
n
this polysulphone belongs to a class of molecules containing "long bonds", i.e. whose rigid chain links are not single interatomic bonds but groups, usually rings, of atoms rigidly connected,t3~ It has been shown previouslyt3.*~ that polymers containing these * On secondment from I.C.I. Ltd., Petrochemical and Polymer Laboratory, Runcorn Heath, Cheshire. 319
320
G. ALLEN, J. M c A I N S H and C. STRAZIELLE
"long bonds" tend to have unperturbed dimensions slightly greater than the free rotation values theoretically calculated. In the present work polysulphone fractions have been investigated by various techniques for the determination of the molecular characteristics such as molecular weight and unperturbed dimensions.
EXPERIMENTAL
Samples The sample used was unfractionated, commercially available, Union Carbide polysulphone prepared from 2,2-bis(4-hydroxyphenyl) propane and 4,4'-dichlorodiphenyl sulphone. This puly(aryl ether) is identified as polysulphone throughout this paper. A solution of linear polysulphone was made up in dimethylsulphoxide at 80 °. The resulting 0" 667 per cent solution was fractionated by lowering the temperature in successive increments to give eight fractions by liquid-liquid phase separation. The temperature at which each fraction was removed was determined by the onset of turbidity. The fractions were isolated by redissolving them in tetrahydrofuran and finally precipitating them in 3--4 volumes of ethanol. The white precipitate, collected by filtration through a G4 sintered glass filter under pressure, was dried in a vacuum oven at 20 ° for several hours. The results are given in Table 1 and the molecular weight distribution obtained is illustrated in Fig. 1. TABLE 1. DATA FOR THE FRACTIONATIONOF A 0" 667 PEa CE~'crSOLUTION OF POLYSULPHONE IN DIMETHYI.SULPHOXIDE Fraction
Tt,(°C)
wt. (g)
wt. ~o
Wj
SEI SE2 SE3 SFA SE5 SE6 SE7 SE8
60"0 54"0 47" 5 40" 6 35"0 28"5 21-8 17"0
1 "04 2" 67 2- 54 2" 52 1" 71 1"53 1-33 7-48
5.00 12" 82 12" 20 12-10 8" 21 7-35 6"39 35"93
0"975 0" 886 0" 761 0" 639 0" 538 0"460 0"391 0"180
Initial weight ffi 22.4 g. Efficiency -~ 93 per cent.
Physical measurements (a) Viscosity. Dilute solution viscosities of the fractions were measured at 25 _+ 0"01 ° and 105" 5 ± 0.01 ° in a n Ubbelohde dilution viscometer for which kinetic energy corrections were negligible. The usual precautions for the evaporation of solvent at high temperatures were taken and corrections were made for the changes in solution concentration. All solvents were given appropriate chemical purification. The intrinsic viscosity [7] was calculated from the reduced viscosity at three or four concentrations
by means of (i) the Hugglns relationship/s~
~
c
= [~]H + k . [,1]. 2 x c
where ks is known as the Hugglns constant, (ll) the Schulz-Blaschke relationship/~) ~"--Z~= [~]sa + ksB [~]sB X ~ , , c where ksB is known as the Schulz-Blaschke constant,
Dilute Solution Properties
A
g
321
I00
o .T= :>
0 8C
/
06C
@
,/
0.40 (..)
0201 O(
,/
1.J I 0' 25
T 0' 50
I 0.75
t00
[~] dL.g"1 (chloroform ot 25") FIG. 1. Data for the fractionatiou of polysulphone from dimethyisulphoxZde. (i/~)
" ' "-- (7) the Kraemer rclaUonsmp,
In ~r C
=
[,7]x -
k x [,7]~ 2 x
c
where kx is the Kraemer constant. (b) Osmometry. The number-average molecular weights of the fractions were measured in dimethylformamide solution with a Mechrolab 502 osmometer using membranfilter G6ttingen feinst and allerfeinst membranes at 30 ° + 0.01% Appreciable diffusion of polymer through the membrane occurred with the lowest molecular weight sample (SE8) and accordingly corrections were made. (s~ g;I° values were calculated using the relationship
Ir c
RT
M . ( l -3c A2c "-[-gA~c 2)
where A2, the second virial coefficient, depends on the polymer-solvent interactions, and g is a number which varies with the solvent. For most thermodynamically "good" solvents, g ~ 0- 25 and tends towards zero in poorer solvents. (c) light scattering. The weight-average molecular weights of the fractions were determined with a Wippler-Scheibling light scattering photometer. All measurements were carried out at 25 _ 0"01 ° using the green Hg line 546 m~. All solutions were prepared individually and then centrifuged at 14,000 rev/min for 1 hr. The data was analysed using the Zimm method.( 9~ The specific refractive increment (dn/dc) was determined with a Brice-Phoenix differential refractometer previously calibrated with aqueous sucrose solutions. The value of dn/dc for polysuiphone in dimethylformamide at 250 + 0.01 °, using light of wavelength 546 m~, was 0.199 ml. g - l . (d) Gelpermeation chromatography. The gel permeation chromatography experiments were carried out on a Waters machine equipped with four columns (10 s, l0 s, 10", 9 x 102 ~,), at room temperature. The solvents were tetrahydrofuran and chloroform. Injection time was automatic, taking place in 5 rain intervals. The pumping rate was always 1 ml/min. All the chromatograms were quite sharp and almost symmetric. The maximum of the peak was taken as the elution volume for each of the tested fractions. Calibration was carried out by plotting log 1~1,, against elution volume for a series of sharp polystyrene fractions in tetrahydrofuran and chloroform.
:E”: SE6 SE7 SE8
SE1 SE2 SE3
O-852 0.740 O-581 O-488 o-434 0.406 O-361 O-207
O-52 0.39 O-58 0.59 O-63 0.55 O-67 O-78
0.885 0.750 O-587 o-495 O-440 O-410 O-368 O-210
chloroform
0.32 O-29 O-42 o-43 0.46 O-42 O-45 O-80
O-612 O-503 O-461 O-394 O-352 0.324 O-295 O-162
O-68 0.68 O-63 O-56 O-57 O-60 O-53 O-84
O-634 0.523 O-472 O-401 O-358 O-329 O-299 O-163
0.44 0.43 0.45 0.41 0.43 0.45 0.41 O-69
0.628 O-518 O-468 0.398 0.357 O-327 O-298 O-164
Tetrahydrofuran
0.00 0.02 O-00 0.04 0.04 0.00 O-06 0.34
25”,
0.523 0.469 O-408 O-357 0.322 0.303 O-263 0.156 0.19 0.18 O-12 0.18 O-64 0.54 0.43 0.70
O-513 0.455 O-408 0.355 0.336 O-313 O-262 0.168
0.29 0.29 O-11 O-21 O-21 0.27 O-36 0.22
AT 105-Y'
0,413 0.353 0.316 O-281 O-254
O-72 O-82 l-06 l-10 l-02
O-421 O-361 O-316 0.281 0.254
Dimethylsulphoxide
AND DIMETHLYSULPHOXIDE
Dimethylformamide
TABLE 2. Vrscosrr~ DATA IN CHLOROFORM, TETRAHYDROFURAN, AND DIMETHYLFORMAMIDE AT
O-52 0.59 O-65 O-67 O-68
D i l u t e S o l u t i o n Prope rt i e s
323
RESULTS The results o f the various physical measurements are shown in Tables 2 and 3. As found for polyacenaphthylene solutions (I°) a n d poly (2:6 dimethyl phenylene oxide) solutions,
L.S. at 25 °
Os a t 30 °
Fraction
l~I. x 10-+
lg~l. x 10-*
SE1 SE2 SE3 SEA SE5 SE6 SET SE8 Unfractionated
9" 19 7"56 5-94 4-38 3"62 3"20 2" 87 1" 89 4" 00
9" 15 7"51 5-55 4"65 3"80 3-34 2" 83 1" 28 2- 04
G .P .C . a t 25 °
I~I,,L'S'/~.°" [lg:l./~dcacla 1 "01 1"01 1-07 0"94 0"95 0"96 1 "02 1"48 1" 96
1 "43 1-35 1 "26 1 "24 1"20 1-19 1" 17 2" 11 2" 38
[1~1,,/19Io1 Tin" -1"31 1 "33 1 "25 1"20 1 "25 1 "24 1" 96 2" 30
I
I'00
T
> o.
o-so
0.40 02; 0.15 0
I
I 02
I
I
i
04
I 06
I
I 0.8
I
T 10
"r/sp
Fro. 2. Intrinsic viscosities of the E-fractions in chloroform at 25°. (Schulz-Biaschke).
or the Huggins constants and, at concentrations greater than infinite dilution, the K r a e m e r equation gives a g o o d a p p r o x i m a t i o n to the intrinsic viscosity. These differences, have, however, no significant effect on the derived values o f the M a r k - H o u w i n k constants. F r o m the viscosity and light scattering data shown in Tables 2 a n d 3 respectively, we
324
G. ALLEN, J. McAINSH and C. STRAZIELLE
find by the method of least squares the following weight-average molecular weightintrinsic viscosity relationships for polysulphone in the solvents and at the temperatures indicated. Note that all quantities are expressed in c.g.s, units. Dimethylsulphoxide, 105.5°: ['7] = 0-145 × l~Iw°'5° Dimethylformamide, 25 °: [7] = 0 . 1 0 3
× l~[,, °'55
Tetrahydrofuran, 25 °: [~7] = 0-079 × IVlw°'Ss Chloroform, 25 °: [~7] = 0.024 X l~/[w0"72. The uncertainties are ~ 0.003 in K a n d ~ 0.02 in the exponent a. The data are shown in Fig. 3. (Because of the high polydispersity of fraction SES, the results obtained Chloroform
1.6
/
e~"
~O
Tetrahydrofuron
... o . . O . . . . . o / ° / e ~
1.5
Oimethylformamide
e/o-"
1.6 1.4 Dimethylsulphoxicle 1'6 "
)4
O/O/n~
d
/ . ~ ' / 44
I
t 4-6
I
I 4.8
I
50
LOg. M,w
FIG. 3. Viscosity-rnol¢cularweight relationships in (a) chloroform (b) t¢trahydrofuran, and (c) dimetbylformamide,all at 25°, and (d) dimethylsulphoxideat 105"5°. by light scattering and intrinsic viscosity for this fraction were not used in the evaluation of K and a.) DISCUSSION
(a) Determination of Mw/Mnfor the unfractionatedpolymer and the fractions The number-average and the weight-average molecular weights of the unfractionated polymer were determined directly by osmometry and light scattering respectively
Dilute Solution Properties
325
and found to be 20,400 and 40,000. Hence the ratio l~,dl~I° ---- 1.98. KIw and K4° for the unfractionated polymer were also calculated directly from the fractionation distribution curve and the molecular weight characteristics of each fraction. (11) By this method l~I~, ----39,000 l~I° = 24,000 I~,,,/IVI.= 1.68. The agreement between the two methods is good for ~ , , but the calculated value of l~ln is higher than that observed directly. This can be explained by considering diffusion of small molecules through the semi-permeable membrane for the lower molecular weight fractions. This diffusion causes an increase in 1VIofor the fractions and also explains why the ratio l~Iw/IVIo is less than one for certain fractions, as shown in Table 3. The results obtained by gel permeation chromatography in THF and chloroform give a higher value for the ratio 1VIw/i~Iofor the fractions than obtained directly by light scattering and osmometry measurements. This is a general phenomenon explained by taking into account the resolution power of the gel permeation chromatography machine and also the method of calculation. (t2) However, it is more likely that the true value of K,I,,/I~I° is between that obtained by G.P.C. and the light scattering/osmometry measurements.
(b) Determination of the O-temperature The 0-conditions of a polymer solution correspond to an "ideal" state at which the excluded volume effect and the long range polymer-polymer interactions in a given solvent compensate. These conditions obtain for a binary system (polymer/solvent) at a specific temperature 0. This 0-temperature can be determined by measurements of the second virial coefficient, A2, at different temperatures and extrapolating to ,42 = 0. Another method proposed by Schultz and Flory "3) for the 0-temperature determination is based on an interpretation of the liquid-liquid phase separation of the polymer solutions. This method requires the determination of the critical temperature of solutions of polymer fractions differing in molecular weight. A third method, proposed by Talamiui and Vidotto, " ' ) relates the temperature (for binary systems) for incipient phase separation to the molecular weight of the polymer. The equation for this method has the form
1
1(
K--K'
1
0.6)
where Tp is the phase separation temperature, ~, is the number-average degree of polymerization, and ~ is the entropy parameter. The constants K and K' are both functions of the polymer volume fraction. The graph of I/Tp against I/(~) °'6 is linear and from the intercept 8 isevaluated to be I05.5 °. The graph is shown in Fig. 4.
(c) The unperturbed dimensions of polysulphone From the data to hand, it is possible to evaluate the unperturbed dimensions of polysulphone by two techniques: (a) from intrinsic viscosity data at the O-point in dimethylsulphoxide by using the well-established techniques of Flory; (1s) (b) by
326
G. ALLEN, J. McAINSH and C. STRAZIELLE
/
3.4
/ 32 e /
- -
x
3"0
Vz= 5"38x I0"3
e/
Z.8
2.6 o
I
5
IO
X : °e x Io
FIo. 4. Plot of the reciprocal of the precipitation temperature against the indicated molecular size function for polysuiphone in DMSO. intrinsic viscosity measurements in tetrahydrofuran, chloroform, dimethylformamide and dimethylsulphoxide using the extrapolation techniques of Stockmayer-FixmanBurchard,(16, 17) Flory_Fox_Schaefgen,.8, 19) Stockmayer_Kurata_Roig,(2o) Ptitsyn(2~) and Inagaki-Suzuki-Kurata. (22) Method 1. The viscosity-weight-average molecular weight data taken at the 0-temperature in dimethylsulphoxide are shown in Fig. 3. The slope of the line is 0.5 and fits the limiting relation: [~7] = K M °'5. Straightforward calculations give a value o f K = 0.145 cm 3. g- ~ at 105.5 ° in dimethylsulphoxide. From K the unperturbed dimensions can be calculated, but first a correction for molecular weight heterogeneity must be applied. According to the Flory-Fox (23) relationship K = 4o (< ro 2 > / M ) 3/2 where 9~o is the hydrodynamic constant, < ro2> is an average unperturbed mean square end-to-end dimension, and M is an average molecular weight. If it is assumed that the distribution within the fractions is given by the Schulz (24) molecular weight distribution function, then the correction for heterogeneity is given by ~ow = gw
~o
r(h + 1.5) where and
gw = (h + 1)t P(h + 1)
(h + 1) l~[w h Mn where 4o has the Kirkwood-Riseman theoretical value of 2.87 x 1053 g-~.(2s, 2~
Dilute Solution Properties
327
Averaging the gel permeation chromatography results in chloroform and tetrahydrofuran gives a value of/VI,,/1VI, = 1.26 from which the parameter h is evaluated to be 3.85. It follows that gw = 0.98 and Sow = 0.98 $o. Thus for the unperturbed dimensions: ( < r o 2 > / M ) ~ = (802 -+-20) 5< 10 -11 cm. Method 2. This calculation relies purely on viscosity data in various solvents and the determination of l~lw by light scattering. In the Stockmayer-Fixman-Burchard method, hereafter denoted S-F-B, the equation used for the determination of the unperturbed dimensions is
[,/]IM ~ = K + (0.51 B ~bo) × M ÷ where B is a parameter characteristic of the polymer-solvent interaction and given by B = ~/mo 2 where/3 represents a binary cluster integral and mo the molecular weight
of the polymer segment. Thus a graph of [~]/M ~ against M * has an intercept equal to K from which the unperturbed dimensions can be evaluated. It has been pointed out ~22) that the correct estimate of K, by the S-F-B method, will be obtained if results for M > 106 are omitted, since if extrapolation is made from the region of larger M, the value of K is seriously overestimated. However, for the polysulphone under investigation, the molecular weights are such that this consideration does not arise. In the Flory-Fox-Schaefgen method, hereafter denoted F-F-S, the equation [~]2/3/M1/3 = K 2/3 + (4/3 Ks/3z*) X M/[~7]
is used for the determination of the unperturbed dimensions. However the application of this method to polar polymers or polymers in good solvents has often yielded unreliable estimates for chain dimensions (26) and often leads to a serious underestimate of K or even to a negative value of K. Some of these drawbacks have been overcome by the application of the StockmayerKurata-Roig expression, hereafter denoted S-K-R, [r/]2/3/MI/3 = K 2/3 + (0"363 $o B) g(~,,) × M2/3/['q] 1/3
where
8~n 3 g(%) = (3e 2 -I- 1) 3/2
and
a3 = ['~]/[~Ts].
To estimate g (a,) it is necessary to use the values of [~d obtained at 105.5 ° in dimethylsulphoxide, thus any temperature dependence of [~Te]is neglected. According to the Ptitsyn theory, the equation used for the estimation of the unperturbed dimensions is" [rl]2/3/Ml13 = 0"786 K 2/3 -I- (0"950 z .2/3 g 2/3) X M 1/3.
Utiyama and Kurata ¢27)and Ueda and Matsumoto c2s) pointed out that, if an appropriate relation between the hydrodynamic radius ~29. 30) and the end-to-end distance is found and combined with the Ptitsyn equation, the resultant equation could yield reliable unperturbed dimensions. ¢27" 2s) A method based on this analysis has been proposed
328
G. ALLEN, J. M c A I N S H and C. STRAZIELLE
by Inagaki, Suzuki and Kurata for estimating unperturbed dimensions in good solvents and it is embodied in the equation
[~]4/S/M2/S =
0.786 K 4/s + (0"950 K 4Is z *2/a) X M 1/3.
This method is denoted I-S-K throughout this paper. However it has been pointed out by Inagaki et al. that, when experiments are conducted in the vicinityof theta conditions, data points should converge to an intercept which corresponds to K 4Is. This considerationistaken into account when dealing with the polysulphone data obtained in the bad solvents and is also applied to the value of the intercept obtained using the Ptitsyn equation. To calculate the unperturbed dimensions of polysulphone, all five equations are used and the comparative resultsfor A ----(< to2>/M)* are shown in Table 4. The TABLE 4. DATA FOR THE DI~TeitMINATION OF A FOR POLYSULPHONE IN THE INDICATED SOLVENTS A
Function/ Solvent
Temp. (°0
S-F-B
F-F-S
25
CHCIa
780
694
25
THF
818
25
DMF
811
105"5
X
lOalcm P
S-K-R
820
804 894 793*
772 818
762 873 791"
814
881 798*
813
881 797*
DMSO
780
* Modifi~l results.
0"240 ©
o
THF
o ¢) O, 160
:E =
=
•
•
DMSO
0.080
0
T I00
I 200
I-S-K
! 300
MO.5
Fio. 5. Stockmayer-Fixman-Burchard plots for polysulphone.
400
Dilute Solution Properties
329
plots obtained by the S-F-B, S-K-R, and I - S - K methods arc shown in Figs. 5, 6 and 7 respectively. Within experimental error, the S-F-B and S--K-R methods give similar values of.4, i.e. A ( S - F - B ) = (797 -t- 20) x 10 -11 cm and A(S-K-R) = (796 -t- 20) × 10 -11 cm. These results are independent of the nature of the solvent, and in good agreement with the result obtained directly from 0-point measurements.
039C
i
0230! 0'310
0.15
I I00
•
I ZOO
I 300 MZ/'/ ['r/] l/3
•
DMSO
•
I 400
@
I 500
FIG. 6. Stockmayer-Kurata-Roig plots for polysulphone.
J 3C
2o
I0 0
J
•
I I0
I 20
MI/3
I 30
•
I 40
FIG. 7. Inagaki-Suzuki-Kurata plots for polysulphone.
DMSO
330
G. ALLEN, J. McAINSH and C. STRAZIELLE
The values obtained from the F - F - S equation are dependent on the nature o f the solvent chosen and in the case of the good solvent, chloroform, an unusually low value of A is obtained, in agreement with previous observations, c26~ Both the I - S - K and the P equations yield good results for A in the good solvent. However when the data obtained from the bad solvents is corrected, as already indicated, the final values for A are in good agreement with the rest of the data. Thus it can be concluded that a value of A = (802 4- 20) x I0 -11 cm is well substantiated, and that within experimental error the temperature variation of A is negligible. It would be interesting to compare these values of A with values measured directly, for example, by light scattering. Unfortunately this is not possible because the radius of gyration of our samples is too small for accurate determinations by light scattering.
(d) Interaction parameters B and Xl The solvent-polymer interaction parameter, B, may be evaluated from the slope of the graphs used for the estimation of the unperturbed dimensions. The results obtained for B by the various extrapolations are in good agreement with one another. This parameter B may in turn be related to the Fiery interaction parameter xl c31~ by B = ~ c (1 -- 2Xl)/V~NA where e2 is the specific volume of the polymer, Vx is the solvent molar volume and NA is Avogadro's number. Table 5 lists the B and Xt values for the various solvents. TABLE 5. INTERACTION PARAMETERS
FOR POLYSULPHONE INDICATED TEMPERATURE
Solvent
B × 1027
CHCIa THF DMF DMSO
3"37 0.86 0.41 0-00
xt
AT THE
Temp. (°C)
0" 37~ 0.46s 0.480 0.50o
25"0 25.0 25- 0 105.5
(e) The conformation of polysuiphone in solution The effect of diminished free rotation about a bond as a result of steric hindrance is defined as cr : ( < re 2 >/M)~r/(< roZt >/M)* where < ro2t > is the mean-square end-to-end distance calculated on the assumption of free rotation, and a is the conformational parameter. As can be seen from Fig. 8, all the "rotatable" links in the chain are not o f the same type. The chain consists of three valence angles, denoted 01, 02 and 03 and two bond lengths, denoted I and p. The link lengths can be calculated from normal covalent bond lengths and are found to be 5.87 A and 5.64 A for I and p respectively, c3z' 33) The valence angles are not known for this molecule but from model compounds they can be estimated. They are 01 ---- 123°/4~ 02 -----109"5 °, and 03 = 104°. t33~ According to
Dilute Solution Properties
0
331
0
0
P
P
h
Ph
\
\\ \ S
C
$
FIG. 8. M o d e l c h a i n for polysulphone.
various authors ¢3' 3,..3~) the valence angle 01 at the oxygen atoms in polyether chains is usually assumed to be approximately the tetrahedral angle, 109.5 °. Since 02 and 03 are very close to this value, the first approximation for calculating the average-end-toend distance is to assume the molecule consists o f two different b o n d lengths and one valence angle equivalent to the tetrahedral angle. The appropriate equation is obtained by solving directly the expression < ro 2 > = ~ 2~ li, lj; ~3S) with Ix ---- 12 = I and 13 = 14 = p, and a = ~r - - 0. T h e result is: (ro2I~
(12 _{_p2)
--T-- = --'T---
(1 + cos a) [1 (1 - cos ~) [
(1-- p)2
(r + f)
cos a
(1 + cos ~
1
~)/
where N is the total n u m b e r o f links i.e. there are N/2 links o f length I, and N/2 links of length p. The second approximation is to assume that 0~ = 123 °, and 02 ---- 0a ---- 107 °. Thus the problem now becomes one o f a molecule consisting o f two valence angles and two b o n d lengths. The appropriate formula in this case is
(to2:) N
(I2-t-p2) (1 + c o s a i ) ( 1
-t- cos a2)[ 2 (1 -- cos al cos a2) 1--
=
( / _ p ) 2 cos.a_~ (1 +_.~.~_~s~2) ] (12..~_p2) (1 + c o s al cos a2) (1 + c o s al).l
where ~ = ~r -- 0~ and a2 = ~r -- 02 = ~r -- 107 °. It can be easily verified that when ,~ -- a2 this equation reduces to that above. The value of < ro2t > / N obtained from the first approximation is 66.31 (.A,)2. The second approximation gives a value of 78-64(/k) 2. Although 0x and 03 are not known TABLE 6. DATA FOR THE FREE ROTATION DIMENSIONS AND THE STERIC FACTOR FOR POLYSULPHONE Function
A t × 1011
× 10 le First app. Second app. POLVmm 5/2--.4
66-31 78.64
a -- 802 × 10 -11 At
776 843
1.04 +_ 0 - 1 0 0 . 9 5 + O" I0
332
G. ALLEN, J. McAINSH and C. STRAZIELLE
with certainty, within the ranges 0~ = 120°-123 ° and 0a -----107°-120 ° < r 2 o l > / N is 78- 5 4- 0.2(A) 2 for the second approximation. The corresponding values o f the free rotation dimensions, A t, and the conformational parameter o, are shown in Table 6.
CONCLUSION The value o f o = 1.03 4 - 0 - 1 0 for 01 = 109.5 ° is not entirely unexpected as polymers containing X - - P h - - X links show similar low values o f 0 (4. aa-4a) These results suggest that it is the phenylene ring system which causes the low value o f o and not the nature o f X. The most significant factor would a p p e a r to be the length o f the rigid link - - - X - - P h - - X - - and the apparently small energy differences between the various rotational isomers since it is noticeable that for these polymers not only is o _~ 1 but also the temperature dependence o f chain dimensions is small. This conclusion is further supported by the fact that aliphatic polysulphones, which have normal main chain linkages consisting o f single o-bonds, e.g. poly(hexene-1 sulphone) (44.45) and poly(2-methyl-l-pentene-1 sulphone) (44) have conformational parameters o f 1-71 and 2.05 respectively. Acknowledgements--J. McAinsh thanks Professor H. Benoit for laboratory facilities and stimulating
discussion, and the University of Manchester for granting leave of absence. REFERENCES (1) W. F. Hale, A. G. Farnham, R. N. Johnson and R. A. Glendinning, J. Polym. Sci. AI, 2399 (1967). (2) R. N. Johnson and A. G. Famham, J. Polym. Sci. AI, 2415 (1967). (3) J. M. Barrales-Rienda and D. C. Pepper, Europ. Polym. J. 3, 535 (1967). (4) P. Akers, G. Allen and M. Bethel, Polymer, to be published (1968). (5) M. L. Huggins, J. Am. chem. Soe. 64, 2716 (1942). (6) G. V. Schulz and F. J. Blaschke, J. prakt. Chem. 158, 130 (1941). (7) E. O. Kraemer, Ind. Engng Chem. 30, 1200 (1938). (8) A. J. Staverman, Recl. Tray. chim. Pays-Bas, Belg. 70, 344 (1951). (9) B. H. Zimm, J. chem. Phys. 16, 1099 (1948). (10) J. M. Barrales-Rienda and D. C. Pepper, Polymer 8, 337 (1967). (11) C. Mussa, J. Polym. Sci. 26, 67 (1957). (12) H. Benoit, Z. Grubisic, P. Rempp, D. Decker and J. G. Zilliox, J. chim. Phys. 63, 1507 (1966). (13) A. R. Schultz and P. J. Flory, J. Am. chem. Soc. 74, 4760 (1952). (14) G. Talamini and G. Vidotto, Makromolek. Chem. U0, 111 (1967). (15) P. J. Flory, J. chem. Phys. 17, 303 (1949). (16) W. H. Stockmayer and M. Fixman, J. Polym. Sci. C1, 137 (1963). (17) W. Burchard, Makromolek. Chem. 50, 20 (1961). (18) T. G. Fox and P. J. Flory, J. Am. chem. Soc. 73, 1909 (1951). (19) J. R. Schacfgen and P. J. Flory, J. Am. chem. Soc. 70, 2709 (1948). (20) M. Kurata, W. H. Stockmayer and A. Roig, J. chem. Phys. 33, 151 (1960). (21) O. B. Ptitsyn, Vysokomolek. Soed. 3, 1673 (1961). (22) H. Inagaki, H. Suzuki and M. Kurata, J. Polym. Sci. C15, 409 (1966). (23) P. J. Flory and T. G. Fox, J. Polym. Sci. 5, 745 (1950). (24) G. V. Schulz, Z. phys. Chem. !]43, 25 (1939). (25) J. G. Kirkwood and J. Riseman, J. chem. Phys. 16, 565 (1948). (26) M. Kurata and W. H. Stockmayer, Adv. Polym. Sci. 3, 196 (1963). (27) H. Utiyama and M. Kurata, Rep. Prog. poly. Phys., Japan 1, 31 (1964). (28) M. Ueda and S. Matsumoto, Report presented at the 13th Annual meeting of the Society of Polymer Science, Japan, Kyoto (1964). (29) H. Yamakawa and M. Kurata, J. chem. Phys. 29, 311 (1958). (30) M. Kurata, H. Yamakawa and H. Utiyama, Makromolek. Chem. 34, 139 (1959). (31) P.J. Flory, Principles of polymer chemistry, Cornell University Press, Ithaca, N.Y., U.S.A. (1953).
Dilute Solution Properties
333
(32) L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, N.Y., U.S.A (1945). (33) J. Syme, Acta crystallogr. 13, 1 (1960). (34) W. H. Stockmayer and L. L. Chart, J. Polym. Sci. A2(4), 437 (1966). (35) A. Ciferri, C. A. J. Hoeve and P. J. Flory, J. Am. chem. Soe. 83, 1015 (1961). (36) J. E. Mark and P. J. Flory, 3". Am. chem. Soc. 88, 3702 (1966). (37) J. E. Mark, Jr. Polym. Sci. !!4, 825 (1966). (38) M. V. Volkenstein, Configurationai Statistics of Polymer Chains. Interscience (1963). (39) M. L. Wallach, Polymer Preprints 6, 860 (1965). (40) G. V. Schulz and A. Horbach, Makromolek. Chem. 29, 93 (1959). (41) G. Sitaramaiah, J. Polym. Sci. A3, 2743 (1965). (42) M. L. Wallach, Polymer Preprints 6, 52 (1965). (43) G. C. Berry, H. Nomura and K. G. Mayhan, J. Polym. Sci. A2, 1 (1967). (44) T. W. Bates, J. Biggins and K. J. Ivin, Makromolek. Chem. 87, 180 (1965). (45) H. A. Ende, K. J. Ivin and G. Meyerhoff, Polymer 3, 129 (1962). R£~sumd-----Lespropri&ds en solution dilute d'une polysulphone fournie par l'Union Carbide ont 6t6 rnesur~s par diffusion de la lumi~re, par osrnom6trie et par viscosim&ric. Les expressions de MarkHouwink ont 6t6 d6termin~s dans le cas d'un bon solvant, de deux rnauvais solvants et d'un solvant la ternp6rature them. Les relations suivantes ont 6t6 obtcnue : [7] (cma/g) = 0,145 × l~lw°'s° (dim6thylsulfoxyde; 105,5 °) (cm3/g) = 0,103 × l~lw°.ss (dim6thylformamide; 25 °) (cm3/g) = 0,079 × l~lw°,ss (tetrahydrofurane; 25 °) (cma/g) = 0,024 × l~lw°'va (chloroforme; 250). Lcs vaieurs des dimensions non pertur~es (< ro2>/M) I/2, des param~tres d'interaction solvantpolyrn~re (Bet XI) et du pararn~tre conformationnel (a) ont 6t6 calculus en appliquant les th6ories de: Stockmayer-Fixman-Burchard, Flory-Fox-Schaefgen, Kurata-Stockmayer-Roig, Ptitsyn and Inagaki-Suzuki-Kurata. En raison de l'inccrtitude sur les valeurs des diff6rents angles de valence dans la chaine polym~rique, la valeur exacte de a ne peut ~tre donn~e. Elle doit cependant &re voisine de l'unit6. Cette faible vaieur, ayant d~j~ 6t6 t r o u v ~ pour d'autres polym~res renfermant des liaisons X-Ph-X, n'est pas surprenante. Sommario--Sono state effettuate misure osmometriche, viscosimetriche e di "light scattering" delIe proprieta delle soluzioni diluite del polisulfone Union-Carbide; si sono determinate espressioni di Mark-Houwink in un solvente termodinamicamente buono, due solventi termodinamicamente cattivi e in un solvente a temperatura teta. Sono state ottenuete le seguenti relazioni: [,fl (cm~/g) = 0,145 × I~I,Y"s° (dimetilsulfossido, 105,5 °) (cma/g) = 0,103 × l~I,,°'ss (dimetilformamide, 25 °) (cm3/g) = 0,079 x l~lw°.ss (tetraidrofurano, 25 °) (cm~/g) = 0,024 x l~Iw°.~2 (eloroformio, 25 °) I vaiori delle dimensioni non perturbate ( < r o ' > / M ) !/2, i parametri di interazione solventepolimero (B e XI) e il parametro conformazionale (a), sono stati ealcolati applicando le teorie di Stockmayer-Fixman-Burchard, Flory-Fox-Schaefgen, Kurata-Stoekmayer-Roig, Ptitsyn and Inagaki-Suzuki-Kurata. A causa delrincertezza nei valori dei vari angoli di legarne nella catena polimerica, non pub essere dato resatto valore di a, tuttavia esso deve essere vicino all'unita. Questo valore basso non ~ inaspettato, essendo condiviso da altri polimeri, contenenti legami X-Ph-X. Zusammenfassung--Die Eigenschaften in verd(innter L/Ssung von Union Carbide Polysulfonen wurden durch Lichtstreuung, Osmometrie und Viskosit~it untersucht. Die Mark-Houwink Beziehungen wurden bestimmt in einem thermodynamisch guten und zwei thermodynamisch sehlechten L6sungsmitteln, und in einem L6sungsmittel bei Theta-Temperatur. Es wurden folgende Gleichungen erhalten: [,fl (cma/g) = 0,145 × 1~1,,°'s° (dimethylsulfoxid, 105,5 °) (crn3/g) = 0,103 × l~I,,°'ss (dimethylformamid, 25 °) (cma/g) ----0,079 x l~i,,°.ss (tetrahydrofuran, 25 °) (cma/g) = 0,024 × 1~1~,°'v, (chloroform, 25°).
334
G. ALLEN, J. McAINSH and C. STRAZIELLE
Die Werte ffir die ungestOrten Dimensionen ( < r o ' > / M ) 1/', die Parameter tier L~sungsmittelPolymer Wechselwirkung (B und x J) und der Konformations-Parameter (a) wurden berechnet unter Zugrundelegung der Theorien von Stockmayer-Fixman-Burchard, Flory-Fo×-Schaefgen, KurataStockmayer-Roig, Ptitsyn und Inagaki-Suzuki-Kurata. Wegen der Unsicherheit in Bezug auf die verschiedenen Bindungswinkel in der Polymerkette kann f~ir a k¢in exakter Wert angegeben werden; er muB aber nahe bei 1 liegen. Dieser niedrige Wert ist nicht unerwartet, da er auch bei andern Polymeren mit X - P h - X Bindungen gefunden wird.