32
PAUL DOTY, HERMAN WAGRER, AND SEYMOUR SIXGER
(9) FLORY, P.J.: J. Chem. Phys. 10, 51 (1942). (10) HUQQINS, M. L . : J. Phys. Chem. 46, 151 (1942). (11) MIE, G.: Ann. Physik [41 96, 377 (1908). A. R.: Proc. Cambridge Phil. SOC.38, 109 (1942);39,54,131 (1943). (12) MILLER, (13) STEIN,E. s., AND DOTY,P.: J. Am. Chem. SOC. 88, 159 (1946). J. W.(Lord Rayleigh): Phil. Mag. 41, 107-20, 274-9, 447-51 (1871) (14) STRUTT, (15) ZIMM, B. H . , A N D DOTY,P. M.: J. Chem. Phys. 12,203 (194).
T H E ASSOCIATION OF POLYMER MOLECULES I N DILUTE SOLUTION' PAUL DOTY', HERMAN WAGNERa,
AND
SEYMOUR SINGER'
Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn 8 , New York Received August 8 , 1946
The belief has developed that polymer molecules, in dilute solution a t least, are always molecularly dispersed, because of the lack of refuting evidence and the attractive simplicity of the assumption. I t is the purpose of this paper, however, to show that stable association of polymer molecules in solution exists under certain conditions. The work is essentially divided into two parts: in the first part the association of polyvinyl chloride in different solvent media is studied in detail by several different methods; in the second part there are described much less detailed experiments, mostly concerned with demonstrating that the stable association of polymer molecules is a general phenomenon when the system is near the point of phase separation.
I. POLYVINYL CHLORIDE The polymers used in this part of the investigation were several fractions resulting from the fractionation of a commercial polyvinyl chloride known as Geon 101 (The Goodrich Chemical Company, Cleveland, Ohio), produced in high purity for electrical applications. The unfractionated polymer had an intrinsic viscosity in cyclohexanone at 60°C. of 0.88 and a chlorine content of 56.0 per cent compared with the theoretically expected value of 56.8 per cent. The fractionation (1) was carried out by means of successive additions of 1-butanol t o a 1 per cent solution of the polymer in cyclohexanone. Twenty-
' Presented a t the Twentieth National Colloid Symposium, which was he Id a t Madison, Wisconsin, May 28-29,1946. * Present address: Department of Colloid Science, Cambridge University, Cambridge, England. 8 Present address: Department of Chemistry, Cornel1 University, Ithaca, New York. Part of this paper is from the thesis submitted by Herman Wagner in partial fulfillment of the requirements for the degree of Master of Science a t the Polvtechnic Institute of Brooklyn, June, 1946. ' D u Pont Fellow in Chemistry, 194546.
ASSOCIATION OF POLYMER MOLECULES IN SOLUTION
33
three fractions were obtained. These were regrouped according to increasing viscosity, and a refractionation was performed. The viscosity distribution curve resulting from this procedure was extremely asymmetric and narrow. Fractionation by an extraction method and a selective evaporation method resulted in distribution curves of the same general shape. The fractions used here came from the first fractionation procedure described. Unless otherwise mentioned, fraction No. 7 was used in this work. It was while investigating the temperature dependence of the osmotic pressure of this fraction dissolved in dioxane that the association was first noted. The osmoticpressure measurements at different temperatures in several solvents were carried out as part of a thermodynamic study of heats of dilution. This work has been published ( 5 ) but is summarized below in view of its relevance to the study of association. Following this summary, the investigation of the nature of the association by means of turbidity, sedimentation in the ultracentrifuge, the angular dependence of the intensity of the scattered light, viscosity, and depolarization is discussed. An interpretation of these measurements is then presented. A. OSMOTIC-PRESSURE MEASUREMENTS
(5)
The osmotic-pressure data a t different temperatures for polyvinyl chloride in cyclohexanone, butanone, and dioxane are plotted in figures 1, 2 and 3, respectively. These measurements were obtained by means of a Fuoss-Mesd osmometer in a specially constructed thermostat. The number-average molecular weights calculated from the intercepts of these plots are listed in table 1. It will be noted that these molecular weights in cyclohexanone and butanone are essentially independent of temperature but differ from each other in the two solvents. In dioxane a higher molecular weight is observed a t room temperatiire, but this decreases a t temperatures above 40°C. to a value even less than was determined in cyclohexanone. Similar measurements using fraction 12 and the unfractionated polymer dissolved in dioxane showed that the variation of molecular weight with temperature existed in other fractions and in the unfractionated polymer. The molecular weights are summarized in table 2. During all the work the solutions were stored at room temperature. It was observed that when a dioxane solution was placed in the osmometer a t a high temperature (say 70°C.),the osmotic pressure corresponding to that temperature would be exhibited as soon as a fairly reliable measurement could be made (about 5 min.). However, when the osmometer was cooled to room temperature, the osmotic pressure decreased only very slowly. If the solution was removed from the osmometer and then returned occasionally to the osmometer (at room temperature) for measurement, it was found that the osmotic pressure decreased approximately exponentially with time, requiring about a month t o return to the value it originally exhibited at room temperature. This observation is relevant to the interpretation presented later.
34
PAUL DOTY, HERMAN WAGNER, AXD SEYMOUR SINGER B. LIQHT-SCATTERING MEASUREMEKTS
The osmotic-pressure data reveal how the number-average molecular weight varies with temperature. It would appear that knowledge of how the weightaverage molecular weight varies with temperature would be valuable. A weight-average molecular weight can be determined by the light-scattering
GEON
*
7-
6.C
5.(
Tvc 4.c
3.C
I
2 .O
C (%)
0.8
I
FIG.1. Osmotic pressure of polyvinyl chloride in cyclohexanone at various temperatures
method (3, 10, 14), which involves the determination of the turbiditv, of the difference in refractive index between solvent and solution, and, if the molecules exceed a few hundred Angstroms in extent, the angular dependence of the intensity of the scattered light. Moreover, the latter information can be interpreted t o yield information concerning the size of the dissolved molecules.
ASSOCIATION O F POLYMER MOLECULES IN SOLUTION
35
If the intensity of the scattered light is not symmetrical about QO", it has been reduced by the interference of light scattered from different parts of the same molecule (10). Consequently, the turbidity (as measured by scattering at 90") is less than it would be if this interference were absent (Rayleigh scattering). The factor required to increase the measured turbidity to the value that would be exhibited if there were no intramolecular interference can be obtained from a measurement of the ratio of the intensity of the light scattered forward and backward at a pair of angles symmetrical about 90". This ratio is designated as the dissymmetry. The measurement of this quantity, its use in correcting the
FIG.2. Osmotic Dressurea
of polyvinyl chloride in butanone
observed turbidity, and its interpretation in terms of molecular size are discussed in Section D of Part I. The relation between the turbidity T (corrected), the refractive-indes increment, anlac, the concentration c, and the molecular weight M is given by
The refractive index of the solvent is denoted by n,the wave length of light in a vacuum by A, and Avogadro's number by N o . The coefficient of C / T on the left is denoted by H . The constant B is the slope of osmotic-pressure plots,
36
PAUL DOTY, HERMAN WAGNER, AND SEYMOUR SINQER
such as in figures 1-3. Thus a plot of Hc/+ against c should give a straight line whose intercept is the reciprocal of the weight-average molecular weight.
i
DIOXANE
77
4.0
-47
FIQ.3. Oemotio pressure of polyvinyl chloride in dioxane at V ~ L ~ ~ Otemperstura US Apparatus For measuring the turbidity as a function of temperature a simple photoelectric instrument was constructed. A diagram of the apparatus is shown in figure 4. The source of illumination is a lOO-watt AH-4 lamp (A) which is mounted in a metal housing (B). The light from this lamp is rendered parallel by a lens (C) mounted in the housing and then passes through a glass filter (D) which transmits the green mercury line (5461 A.). This nearly parallel mono-
37
ASSOCIATIOA' OF POLYMER MOLECULES I N SOLUTIOK
chromatic light is then partially reflected by means of two pieces of plate glass (E) mounted at 45" to the incident beam to a Weston photronic cell (F). The photronic cell is mounted about 6 in. away from the main part of the apparatus to minimize temperature changes due to the thermostat, since the photronic cell output is somewhat temperature sensitive. The cell is used to measure the intensity of the beam produced by the mercury lamp, since it receives a small constant fraction of this light from the two glass plates. It has a sensitivity TABLE 1 Apparent number-average molecular weights of fraction 7 SOLYENT
TEMPEPATURE
'C
MOLECULAR WEIGET
.
Cyclohexanone. . . . . . . . . . . . . . .
29.8 47.8 69.0
99,000 98,500 93,500
Butanone, ....................
24.6 49.6
117,000 121,000
Dioxane. ......................
14.0 38.0 47.0 68.0 77.0
210,000 211,000 142,000 111,000 86,500
TABLE 2 Apparent number-average molecular weights of other polyvinyl chlorides dissolved in diozane TEMPERATURE
'C
1
MOLKCULAR WZlOBT
.
Fraction 12..........................
29.7 45.7 55.1 70.6
131,000 107,000 w,500 84,000
Unfractionated .......................
31.1 49.9 71.9
107,000 88,000 77,500
of about 4.4 microamperes per foot candle to white light and its response is very nearly linear, especially when there is close to zero potential difference across it. This may be accomplished by using the circuit (2, 13) shown in the lower left of figure 4. To take a reading switch SI is closed and the ammeter G is read. With SI still closed, Sz is also closed and the ammeter is read again. If the two ammeter readings do not agree, the potential across the photronic cell is not zero and so the rheostat is adjusted until it is. This arrangement helps to increase
38
PAUL DOTY, HERMAN WAGSER, AND SEYMOUR SIPI’GER
the sensitivity, reduce the effect of temperature variations, and increase the linearity of response. To determine whether the response was linear, the transmission of a piece of optically flat glass, essentially a neutral filter, was measured in a photoelectric colorimeter and in this instrument. The agreement was within experimental error for this one measurement, as well as for successive measurements made with several pieces stacked together. I n the latter case, the “known per cent transmission” of the graph was taken as the transmission for a single piece of the nth power, where n is the number of pieces. The major fraction of the light beam continues upward, enclosed by a wooden
FIG.4. The photoelectric turbidimeter
box (H) which is painted a dull flat black on the inside to reduce the stray light caused by internal reflections. I t then passes through an aperture (I) so that a beam about 3 in. in cross section enters the solution to be examined, the solution being contained in a glass cell (J). The position of the beam must be adjusted so that it passes through the center of the solution and does not hit the side of the cell. At right angles t o the cell and mounted on the outside of the thermostat is a lens (K) which serves to collect the scattered light from the sample and focus it onto the light-sensitive portion of the phototube (L). The output of the phototube is electronically amplified, and the current produced when light impinges
ASSOCIATIOS O F POLYMER .MOLECULES IS SOLUTIOS
39
on the tube is determined nith a sensitive galvanometer.5 The instrument, most sensitive t o wave lengths at the lower end of the spectrum, has a sensitivity of about 2 X foot candles per scale division in the blue region, and this may be increased tenfold by svitching out the shunt across the galvanometer. Since the galvanometer has 100 divisions and can be read to about one scale division, the precision depends t o a large extent on the portion of the scale used. The response of the instrument is linear, as shown in figure 5 . The data v-ere obtained in the same fashion as for the photronic cell. The relative positions of the lens, glass cell, and phototube are so arranged that light from only the center of the solution reaches the photocell. This eliminates reflected light from the sides or corners of the glass cell. For the
FIG.5 Linearity of response
of the phototube
same reason enough liquid must be put into the glass cell t o avoid ieflections from the meniscus. The cell containing the liquid is mounted in a metal housing (11)which fits into zi glass aquarium converted into a thermostated water bath (5'). The temperature may be raised to about 80°C.
Operation and calzbration The instrument n a s calibrated indirectly. A gel of 1 per cent polystyrene in tributyl acetyl citrate was measured in a Tisual turbidimeter (4) irhich had been calibrated absolutely by using solutions and pure liquids of known turbidity. The turbidity of the gel was found to be 2.68 X cm.-l, and the nen instrument was checked before every series of readings nith this secondary standard. This entire photometer unit vas purchased from the Photovolt Corporation, Kew York City.
40
PAUL DOTY, HER’\IAS WAGNER, AKD SEYMOUR SINGER
The absolute value of the scattering of this gel being known, the proportionality factor between absolute scattering and instrument reading was obtained and used for all the solutions measured that day. This procedure corrects for small day-to-day variations, such as dust on the lens or on the glass plates. To measure the turbidity of a solution, a glass cell is filled with a t least 35 ml. of solution and set in place in the thermostat. Sufficient time is allowed for the solution to come to the appropriate temperature. A stop is placed in the path of the light beam and the galvanometer is adjusted to read zero. The stop is removed and the galvanometer is read again. A third reading is now taken with the stop in place again. The two dark readings are taken to be sure the amplifier has not drifted appreciably while the reading was taken. These two dark readings, which should be near cero, are averaged, and the result is subtracted from the reading obtained with the solution. Usually three such readings are taken, there being nine observations in all. The photronic cell ammeter is also read, as described above. To calculate the absolute turbidity: Let p . equal the galvanometer reading for the unknown solution, c, equal the photronic cell reading when p , was measured, PO equal the galvanometer reading for the standard gel, co equal the photronic cell reading when p , was measured, and K equal the actual turbidity of cm.? Then the standard gel, 2.68 X
since the response of the phototube is linear. The scattering of the solvent must be subtracted from 7 0 , the scattering of the solution, to obtain the turbidity T, due to concentration fluctuations from which the molecular weight may be obtained. This is done by measuring r for various concentrations, plotting H c / r as a function of concentration, and setting the intercept equal to l / M w . It was found necessary to filter carefully all the solutions used, since any foreign particles would obviously give erroneous results. The most prevalent and frequent contaminant was dust. All vessels were carefully rinsed and then dried by evaporation of solvents to avoid lint from the towels. The solutions were then put through sintered-glass filters, first through one of coarse or medium pore size, and then through one of fine pore size. The solutions were usually filtered directly into the glass cell in which they were to be measured, thus eliminating an intermediate step which might have caused contamination. The solution was considered dust free when no particles could be seen at right angles to an incident mercury-lamp beam.
Results The first experiment consisted in measuring the light scattering of a 1 per cent solution (0.01 g. of polymer per cubic centimeter of solution) of fraction 7 in dioxane. The dioxane had been purified by refluxing over sodium and subsequent distillation. As the temperature of the solution was slowly raised, a sevenfold decrease in turbidity occurred between room temperature and 90°C.,
ASSOCIATION O F POLYMER MOLECULES I S SOLUTION
41
although there was relatively little change between room temperature and
40°C. These results are shown in figure 6. A curve of the same general character resulted for fraction 12, but fraction 20, a fraction of very low molecular weight, showed very little scattering (see table 3). I n every case the tempera-
FRACTION 7
TEMPERATURE
FIG.6. Change of
C/T
2.
with temperature for fraction 7 in dioxane
ture was increased slowly, so that equilibrium was attained before a measurement was taken. It was observed that the turbidity corresponding to the higher temperature was reached a t once when the solution was heated. However, when the solution mas cooled from a higher temperature back to a lower temperature, the turbidity increased very slowly and rf,qulred several weeks to
TABLE 3 Change of turbidity of polyvinyl chloride with temperature (a) 1 per cent solution of fraction 7 in dioxane; K C O / P O=* 181 X lo-' cm.-l; solvent = 1.08 X cm.-1 PHOTROTIC CELL
TEMPERATURE PI
__ "C
26 29 31.5 38 45 47.5 50.5 56.5 64.5 75.0 81.5 86.0 88.0
59.5 58.5 5i
55 46.5 38.5 30.8 23.3 15.8 15.5 13.2 11.0 10.5
94 91 89.5 88 87 86 86 S5
85 85 85 85 8.5
~
cm.-1
1
114 X 116.5 116 113 97 98 65 51.0 39.9 32.7 27.8 23.4 22.5
i i I
1 1
~
1 ~
~(p./cc.)cnt.
cm:i
113 X 10-6 115 115 112 ! 96 97 64 50 38.8 31.6 26.7 22.3 21.4 , ~
~
~
~
0.88 0.865 0 . S75 0.89 1.04
;:::
2.00 2.58 3.21 3.83 4.50 4.65
(b) 1 per cent solution of fraction 12 in dioxane; K c o / p o = 180 X 10-4 cm.-'; solvent = 1.08 X 10-4 cm.-'
I
PHOTOTUBE
-
1
Pa ~
.
"C
25 29 37 43 47.5 51 57 61.5 65 75.5
cm.-
48.5 46.5 43.5 37 28 23.5 20 19.5 18.5 16.5
95 89 87 87 86 86
92.5 X 10 95 91.5 78 59 49.5 43 41.7 39.9 36
85
84 83 82
(g./cc.)cm
Cm.?
91.5 94 90.5 77 58 48.5 42 40.7
x
10-4
1.1 1.07 1.12 1.3 1.75 2.m 2.41 2.60
(c) 1 per cent solution of fraction 20 in dioxane; K c o / p o = 180 X 10-4 cm.-'; solvent = 1.08 X lW4 cm.-'
cm.7
'C.
28 33 39 51 57.5 66
3.05 2.75 2.85 2.3 2.2 2.1
91 87 85 84 83 82
6 . 0 X lo-'
5.7 5.4 4.8 4.8 4.5
, ~
i
1 ' ~
~
* For an explanation of K c o / ~ see o , the section on aooaratus. 42
cm.7
(g /cr.)cm
4.8 X 4.5 4.2 3.6
3.6 3.3
I
20 22 24 28 28 30
43
ASSOCIATIOX O F POLYMER MOLECULES IS SOLUTIOS
reach the value previously exhibited at room temperature. The approach t o t h e room-temperature value appeared to be exponential. Turbidity !vas then studied as a function of concentration at 28"C., 4i°C., TABLE 4 Change of turbidity of p o l p i n y l chlorzde (fraction 7) wath Concentration
1. Temperature = 28.5"C.; K C O / P O= 166 X lo-' cm.-l 1
I
64 60.5
gromr/IOo mi.
88
86.5
3" 33
~
m.-1
1.00 0.833 0.714 0.526 0.430 0.296
89
f
x 104
(t./cc.)cm.
119 113 107 96 86 65
0.83 0.74 0.665
K3
1
35 24
18
I
87 86
0.979 0.815 0.700
;::"0
85 85
1
~
0.311
81.5 72.0 66.5 53.4 49.3 36.6
~
0.46
M w . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
0.449 0.366 0.322 0.240 0.210 0.173
~
'
I
....I
16,700,000
1.20 1.13 1.05 0.97 0.92 0.84
0.54 0.51 0.46 0.40 0.38 0.32
M,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27 24.5 22 18 15 11.5
-1
'
3. Temperature = 63°C.; Kcalp0 = 164 X lo-' cm.-l
90 87
E:
1
44.7 0.686 0.506 0.413 0.285
1
1
2.15
4,500,@33
1
0.86 0.81 0.68 0.65 0.60
28.2 20.7
M,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.,
2,040,000 ~~
* Concentrations must be corrected for the change in density as the temperature is increased. The density of dioxane a t 29", 48", 51", and 63°C. is 1.0218,0.9997,0.9964, and 0.9832 g./cc., respectively. t Corrections for dissymmetry a t 48°C. were obtained by an interpolation procedure, as explained in section D. and 63"C., to determine how the molecular weight varied with temperature. In tables 4 and 5 H c / r (corr.) indicates that r is corrected for dissymmetry. The term denoted by H in equation 1 must be evaluated. The refractiveindex increment, anlac, was determined by measuring the refractive-index differ-
44
PAUL DOTY, HERMAN WAGNER, AND SEYMOUR SINGER
ences between dioxane and a 1 per cent solution of fractions 7 and 12 in dioxane by means of a Pulfrich refractometer with a divided cell. For fractions 7 and 12 the refractive-index increment was found to be 0.0850 and 0.0865 (g./cc.)-*, respectively, at a wave length of 5461 A. The quantity H is evaluated : for fraction 7, H = 9.0 X lo-'; for fraction 12, H = 9.3 X lo-'. In figures 7 and 8 H c / r is plotted against c in accordance with equation 1.
pramrll00 nl.
44 41 39 32.5 28.5 22
25 22 20 15.5 13 9.9
19.5 16 13.5 11.5 8.9
cnL-1
(z.jcc.)cn.
82
1 .Ooo 0.833 0.714 0.526 0.430 0.296
87.6 x 10-4 84.0 79.8 67.2 58.8 46.2
1.16 0.99 0.89 0.78 0.73 0.64
0.593 0.498 0.425 0.34 0.30 0.236
92 89 88 86
0.977 0.814 0.698 0.514
84
0.m
83
0.289
48.0 X lo-' 43.2 39.3 30.6 27.0 20.1
2.07 1.87 1.78 1.67 1.55 1.43
0.97 0.905 0.805 0.721 0.644 0.578
92 90.5 89 88 87
0.962 0.686 0.506 0.413 0.285
37.8 X lo-' 31.2 26.1 22.8 17.4
2.55 2.22 1.93 1.82 1.65
1.03 0.98 0.834 0.79 0.71
87 85 85 84 84
M , . ...................................................................
1,780,Ooo
The values of 7 corrected for dissymmetry are used. It is noted that the intercepts, which are numerically equal to the reciprocal of the molecular weights, vary with temperature similarly t o the case of osmotic pressure. The molecular weights for these two samples a t the different temperatures are listed in table 6. By means of two minor approximations it is possible to transform the curve of 4 7 shown in figure 6 into a plot of molecular weight versus temperature,
45
ASSOCIATIOX OF POLYMER MOLECULES IN SOLUTIOS
First it must be assumed that the dissymmetry of a 1 per cent solution varies linearly with temperature above 40'C. but is constant below that temperature. Secondly, the approximation is made that the H c / r plot has a slope independent of temperature. On this basis we can immediately correct the turbidity for I
Ro. 7.
I
I
I
I
I
I
I
Plot of turbidity data for fraction 7 in dioxane at various temperatures
1
o
FIQ.8. Plot
aiI
I
01
I
03
I
I
a+ 0 CONSCI(M&u
I
Dd
*le
a?I
I
08
I
no
to
of turbidity data for fraction 12 in dioxane at various temperatures
dissymmetry and multiply the c / r value thus obtained by H . If the average increase of H C / Tin the concentration range 0-1 per cent in the plots in figure 7 is subtracted, ther,e is obtained a curve representing H c / r at zero concentration versus temperature. The reciprocal of this curve is the weight-average molecular
FPACIION
TEYPEPATURE
7. . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
'C . 28.5 48 63 28.5 51 62.5
YOLECULAP WEIOET
16,700,000 4,500,000 2,040,000 12,500,000 2,m,000
1,780,000
C. ULTRACER*TRIFUG.4L STUDIES
The ultracentrifuge is able to give sedimentation diagrams which are essentially plots of the concentration gradient in the solution versus distance from the axis of rotation. If there are two very different molecular-weight species in a solution, each will sediment with its own rate and create its own concentration gradient. The area under such a gradient curve is proportional to the concentration of that species in the original solution. Therefore, if there is a discontinuous distribution of molecular weights of fraction 7 in dioxane, the sedimentation diagrams should show two or more distinct maxima, and if association is the cause of the effects just described it is expected that the areas under the maxima should reflect the changes attendant upon heating the solution. Fortunately, in order to obtain sedimentation diagrams of the dioxane solutions of polyvinyl chloride at different temperatures, it is not necessary to operate the centrifuge at elevated temperatures for, as previously noted, the change in molecular w i g h t brought about by heating persists essentially unchanged for several hours after the solution is cooled. Thus if the solution is observed in the ultracentrifuge shortly after heating to a certain temperature for over 15 min., the results should not be significantly different from those obtained by actually operating the ultracentrifuge a t the elevated temperature.
47
ASSOCIATION OF POLYMER MOLECULES IN SOLUTION
The ultracentrifuge used in these experiments is an air-driven Beams-Pickels model; our installation is described in detail elsewhere (11). The optical method in use is the Philpot modification of the schlieren method which permits visual observation of the course of an experiment,
16
I4 I
I2
IO
f x
9 803 \
6
4
2
Mn
I 20
I
30
I
So TEMPERATURE ' C . 40
FIG.9 Number-average and weight-average molecular weights of fraction 7 in dioxane as a function of temperature.
Two runs on a 1 per cent solution of fraction 7 in dioxane, one at 25"C., the other at 25OC. after the solution had been heated at 76°C. for 1 hr., were performed. I n figure 10 t n o pictures taken at comparable times and speeds show the results obtained. Sedimentation is taking place from right to left, the species under the left peak being of larger molecular weights. A definite shift from the
48
PAUL DOTY, HERMAN WAGXER, AND SEYMOUR SINGER
larger t o the smaller molecular-weight species upon heating is evident. Measurement of the areas gave the results in table 7. The great asymmetry of the curve of the heavier species indicates considerable skewness in the molecularweight distribution of that group of components.
W
R b
a
FIG.10. Sedimentationdiagrams of fraction7 indioxane at (a) 25°C. and (b)76"C. Sedimentation proceeds toward the left. TABLE 7 Relative concentrations of the two molecular-weight species i n fraction 7 -dioxane and fraction 7-butanone solutions as a function of temperature TEKPSPATVXE
8OLvENT
'C
.
HEAYIEP COYPONENT
LIGErP.
CoxPomUI
per ccnl
per cent
Dioxane. . . . . . . . . . . . . . . . . .
25 76
62 41
38 69
Butanone. ................
25
11
89
76
9
91
a
b
FIG. 11. Sedimentation diagrams of fraction 7 in hutanone at (aj 25OC. and (b) 76°C. Sedimentation proceeds toward the left.
A 0.53 per cent solution of fraction 7 in butanone was studied under similar circumstances and showed no eignificant change in the relative amounts of the two species with heating; moreover, amuch smaller amount of associated polymer exists in butanone than in dioxane (figure 11). It should be emphasized that
ASSOCIATION OF POLYMER MOLECULES IN SOLUTION
49
the observed number-average molecular weights prohibit the identification of the two peaks in the butanone diagram with those in the dioxane diagram. The quantity of the large-molecular-weight component in dioxane at 76°C. appears to be much larger than in butanone, yet at approximately these temperatures the number-average molecular lyeight in dioxane is 86,500 whereas in butanone it is 120,000. These sedimentation experiment? thus confirm the hypothesis that in dioxane some of the molecules are associated into clusters which break up somewhat on heating and re-form slowly when cooled. The remaining portion of the investigation is concerned with obtaining some information concerning the nature of the clusters. D. DISSYMMETRY OF THE RADIATION EKVELOPE
(3, 10, 14)
If the largest average dimension of a dissolved particle exceeds a few hundred Angstroms, the intensity of the light scattered from it will not be symmetrical about 90' (from the incident beam) because of the destructive interference of light scattered from different portions of the same molecule. This effect is conveniently characterized by the ratio of the intensities of the light scattered forxard and backward at two angles symmetrical about 90". This ratio is the dissymmetry at the given angles and serves as a useful measurement of particle or molecular size when evaluated by extrapolation to infinite dilution. The dissymmetry can also be used to determine the amount by which the 90' scattering has been diminished by the interference effect. Consequently, the observed turbidity can be augmented to that which would have been observed if the molecules had been compact enough to give symmetrical Rayleigh scattering. I t is in this manner that the turbidities in section B have been corrected for use in equation 1. The dissymmetry of dioxane solutions of fraction 7 was determined for a number of concentrations a t 25°C. and after heating to 64°C. for a few minutes. The results are plotted in figure 12. For the correction of turbidities observed at 48OC. an interpolation is made (dotted line). The limiting dissymmetry for the unheated sample is 2.63, compared with 2.02 for the heated sample. This shows that the average molecular size is smaller after heating. An indication of how much smaller may be gained from the following considerations. First, since the dissymmetry is a weight-average effect, the observed change does not seem t o be of the same order of magnitude as the chfnge in weight-average molecular weight that was observed. Secondly, the variation of dissymmetry with a characteristic dimension has been worked out for models such as spheres, rods, and random coils (4, 6, 14). The latter model is probably the nearest approximation for our purpose. In terms of a model random coil a dissymmetry of 2.03 (for a wave length in air of 5461 A.) corresponds to a value of 1700 A. for the root-mean-square separation of the ends of the coil; a dissymmetry of 2.63 corresponds to 2150 A. It thus appears that the average molecular or cluster size does not greatly diminish upon heating. From another point of view, consider the difference in molecular weight be-
50
PAUL DOTY, HERMAN WAGNER, AND SEYMOUR SINGER
tween two random coils exhibiting the observed dissymmetries. The molecular weight is proportional to the mean-square separation of the ends for a random coil. Consequently, the molecular weight of a random coil with a dissymmetry of 2.62 is 60 per cent greater than of one with a dissymmetry of 2.03. Since
FIR 12. Dissymmetry of fraction 7 in dioxane at various temperatures. The values at 48%. are interpolated.
the observed change in weight-average molecular weight between 25°C. and G 3 O C . was found to be about eightfold, we can conclude that the small difference in dissymmetry observed at these two temperatures indicates that the cluster and the individual molecules are of about the same size, that is, have the same
51
ASSOCIATIOX O F POLYMER MOLECULES I N SOLUTION
average extent in space. This would require that the cluster be considerably more closely coiled than the individual molecule. E. VISCOSITY
Additional evidence favoring the view that the cluster is approximately the same size and hence more densely coiled than the individual molecule is obtained from an examination of the variation of specific viscosity with temperature. The specific viscosity of both fraction 7 and the unfractionated polymer in dioxane mas determined a t 26°C. and at 60°C. The solutions measured a t 26°C. had, of course, been stored a t this temperature for the previous month. The results of the measurements are shown in figure 13, where q a P / cis plotted against concentration. It is a t once apparent that the specific viscosity is practically unchanged when the temperature is increased from 25°C. t o 60"C.,
t
-1
J
0.0 0
02.5
0.50
I
1.00
0.75
I
I.25
96
~NCEMTRATION
FIG.13. Viscosity of fraction 7 in dioxane
a6
two remperatures
whereas the same increase in temperature produces an eightfold decrease in the weight-average molecular weight. In fact, the change in the specific viscosity and the intrinsic yiscosity is fractionally less in the case of the diosane soiution than in the case of cyclohexanone or butanone solutions. The unlikely possibility that the clusters were broken up in the shear field of the capillary tube was elirninated by demonstrating that the turbidity of a solution was the same before and after passage through a thin capillary. The view is taken that the fact that the specific viscosity is essentially unchanged when the amount of association is altered is coincidental and nor particularly significant. The important feature is that the observed viscosity is very considerably less than would have been predicted if the configuration of the molecules in the cluster were nearly identical with the configuration of the individual molecule except for the effect of molecular weight. For example, if the association were of the end-to-end t'ype, then the viscosity Fvould surely
52
PAUL DOTY, HERMAS WAGNER, AND SEYMOUR SINQER
have been decreased several fold when the associated molecules were broken up. Here in the viscosity measurements there is evidence that the cluster must be of about the same size as the individual molecules, for it is the largest average dimension more than any other factor which determines the specific viscosity. Consequently, it appears that the molecules are so highly coiled and packed in the cluster that the viscosity is greatly reduced and by coincidence is nearly equal to that of the unassociatcd molecules a t the same weight concentration. F. DEPOLARIZATION OF SCATTERED LIGH?
A study of the depolarization of light scattered laterally from polymer solutions, using both polarized and unpolarized incident light, has been shown t o yield useful qualitative information on the shape of dissolved molecules. The only feature of this type of investigation (7) which we have used here is that of measuring the depolarization ratio when the incident light is vertically polarized. The depolarization ratio in this case is a measure of the anisotropy of the
FIQ.14. Depolarization ratio for vertically polarized and unpolarized light as a function uf temperature for fraction 7 in dioxane.
molecule. In figure 14 the ratio of the horizontal t o the vertical component, that is, the depolarization ratio pu, of the light scattered from a 1 per cent solution of fraction 7 in dioxane is plotted as a function of increasing temperature. We note that in the vicinity of 40-50'C. pu increases significantly. This reflects an increase in the anisotropy of the scattered particles. Since the number of individual molecules has increased over this temperature range, it appears that the individual molecules exhibit greater anisotropy than the cluster. This behavior is consistent with the picture that the clusters are more closely packed, homogeneous particles than ?re the individual molecules. That is, if a cluster of molecules is of about the same size as a chain-like molecule, it is t o be expected that the single molecule is more anisotropic. The evidence from depolarization supports this view. 6
The-authors are:indebted to Mr. S. J. Stein for these measurements.
ASSOCIATION OF POLYMER MOLECULES IN SOLUTION
53
G . DISCUSSION
Investigation of the forces holding the molecules together in the cluster has not been carried out. However, in view of the observations described above, certain explanations of the phenomenon can be eliminated and a self-consistent description can be postulated. Is it possible to explain the observed behavior by assuming that there is a dynamic equilibrium between individual molecules and a cluster composed of a number of molecules? Such an explanation is fundamentally incompatible with two observations. First, it was noted both with osmotic pressure and turbidity that the equilibrium value of either of these quantities was obtained a t once upon heating but, upon cooling, a very long time was required for the return of either of these properties to its equilibrium value at the lower temperature. This microscopic irreversibility cannot result from a dynamic equilibrium where individual molecules would be associating and clusters would be breaking up a t a reasonably fast rate. The second objection to the hypothesis of dynamic equilibrium is found in the straight lines obtained in the osmotic-pressure plots at any temperature measurement, for if this association resulted from a dynamic equilibrium the equilibrium constant, being defined in terms of the concentrations, would demand that the apparent molecular weight would vary enormously with the concentration. This would lead to strongly curved lines of T / C v e t - 8 ~ 8c. The alternative explanation requires that the equilibrium be of the static type, and that the temperature dependence of the amount of association result from the presence of secondary bonds of many different strengths. In other words, if the points of binding in the cluster are of different strengths, then upon heating the dioxane solution to, say, 45OC., about the weakest 15 per cent of the secondary bonds would be broken and a certain number of individual molecules set free. Upon heating to a higher temperature, the weakest fraction of the secondary bonds remaining would be broken and more individual molecules would result. When the solution cooled, the individual molecules would return to clusters only when the portions of the molecule in which the secondary binding could arise diffuse together. Such a diffusion-controlled reaction would, of course, be very slow. The spectrum of secondary bond strengths required in this description may perhaps arise from a cooperative phenomenon, in which regions of varying length of the polymer chains could fit together in such a sterically favorable pattern as to enhance greatly the dipole-dipole interaction or hydrogen bonding. The strength of such an attachment would depend upon the length of the chains participating a t the region of binding. It thus appears that qualitatively the observations on polyvinyl chloride solutions can be explained if the association originates in secondary bonds of varying degrees of strength. From the sedimentation diagrams it would appear that a significant critical number of molecules are necessary to form a cluster, because there is always a large gap between the two peaks, indicating the absence of clusters of intermedi-
54
PAUL DOTY, HERMAN WAGNER, AND SEYMOUR SINGER
ate size. There is some basis for further speculation, but in view of t h e complexity of the phenomenon it would scarcely serve a useful purpose.
11. ASSOCIATION IN POOR SOLVENT MEDIA It is natural to inquire whether or not the association which is so marked in solutions of polyvinyl chloride in dioxane might be a general phenomenon, especially in poor solvents or solvent-non-solvent mixtures. The striking opalescence of some polymer solutions when near the phase-separation point (as, for example, in fractionation by precipitation) suggests the possibility of association. On the basis of the experiments described in Part I , it is clear that the phenomenon is greatly enhanced if the solution near the precipitation point is allowed to remain at a low temperature (for example, room temperature)
10
I2
14
16
18
TME(HOURS)
FIG.15. Relative turbidity as a function of time for a polyvinyl chloride-acetate copolymer in butanone. The sharp minimum in turbidity occurred upon heating the solution to 70°C.for 3 min.
for sweral weeks preceding investigation. On this basis, association has been observed in several solutions other than those of polyvinyl chloride. An investigation of association in polystyrene solutions (8) will be described in a forthcoming publication. Here we shall describe qualitative experiments with polyvinyl chloride-acetate copolymer and cellulose acetate. A solution of polyvinyl chloride-acetate copolymer containing 5 per cent of polyvinyl acetate was dissolved in butanone to make a 1 per cent solu ion. Methanol was added until the solution was very close to the phase-separation point. I t was then heated to about 60°C. for several minutes and stored in a 27°C. thermostat for 2 weeks. After this time its relative turbidity was observed; it was then heated to 70°C. for 3 min. and cooled to 30°C. Its relative turbidity was followed throughout these manipulations and for some time after cooling. The results are summarized in figure 15. The relative turbidity
ASSOCIATIOX OF POLYMER MOLECULES IN SOLUTION
55
diminished about threefold upon heating and upon cooling returned exponentially t o its original value. These results are qualitatively the same as those observed in solutions of polyvinyl chloride in dioxane, except that the return to the original turbidity value was rather slow. Other polyvinyl chloride-acetate copolymers behaved qualitatively in the same manner when treated similarly. It is perhaps of interest to record what happened when an acetone solution of cellulose acetate was treated in this manner. A solution of a fraction of cellulose acetate with molecular might of about 100,000was dissolved in a 10: 23 acetonemethanol mixture to give a concentration of 0.15 per cent and after heating was stored in a thermostat at 27°C. for 10 days. At the end of this time there was no apparent phase separation, yet the observed absolute turbidity and dissymmetry indicated a molecular weight of several million. The solution was slowly heated in the turbidimeter, whereupon its turbidity gradually diminished t o 60 per cent of its room-temperature value when the temperature of the solution had reached 52°C. Cpon cooling to 30"C., the turbidity had returned to 85 per cent of its original value and 10 min. later the turbidity had completely returned to its original value. Thus, the association was not greatly broken up by heating. Acetone was then added to the solution in order to adjust the acetonemethanol ratio t o 10:20. The solution was then heated and stored in a thermostat at 27°C. for 10 days. After this time it was observed that the absolute turbidity was not significantly different from what it was previously, but upon heating and cooling the turbidity was reduced threefold and returned to its room-temperature value very slowly, exhibiting behavior quite similar to that shown in figure 15. These experiments tend to emphasize that near the phase-separation region there can be stable association of the molecules. The existence of association probably plays an important r61e in fractionation procedures. The very narrow asymmetric distribution curves obtained for polyvinyl chloride mentioned previously can probably be traced to the association which was always taking place in varying amounts as the fractionation proceeded. All errors produced in this manner would of course tend to give a distribution curve that was too narrow. It would appear that in fractionation carried out by phase-separation procedures the length of time during which the two phases are allowed to be in contact should be a compromise between the time required for the attainment of equilibrium and the time in which a significant amount of association will take place. In the course of investigations of cellulose acetate fractions in various solvent media, it was discovered that in methyl cellosolve association existed. Osmoticpressure measurements on fraction 9 in acetone gave a molecular weight of 53,000 (9). When the same fraction was studied in methyl cellosolve, a numberaverage molecular weight of 71,400 was obtained. These osmotic data are illustrated in figure 16. Further indication of association in this solvent was given by the ultracentrifuge. In figure l i b diagrams of this fraction sedimenting in acetone at a speed of 720 R.P.S are recorded. It is to be noticed that the peak remains relatively sharp over an hour of sedimentation; in figure 17a we have
56
PAUL DOTY, HERMAN WAQXER, AND SEYMOUR SINQER
ACETATE FRACTION 9
CELLULOSE 6.0
-
4.0
-
-
n
10
-
-
I
I
I
I
n 17 a
b FIQ.17. Sedimentation diagrams of the cellulose acetate fraction of figure 16, a t 0.3 per cent concentration in (a) methyl cellosolve and (b) acetone. I n each pair, the diagram at the right is the earlier one, and sedimentation is taking place towards the left.
ASSOCIATION OF POLYMER MOLECULES IX SOLUTION
57
represented the same fraction sedimenting in methyl cellosolve. Here the rapid spread of the curve in 18 min. of sedimentation at 500 R.P.S. indicates considerable polymolecularity as well as increased molecular weights. Somewhat similar association appears to be present in ethyl cellulose dissolved in pure hydrocarbon solvents, according to the osmotic-pressure data of Steurer (12).
SUMMARY Association of polyvinyl chloride molecules in dilute dioxane solution is demonstrated by osmotic-pressure, light-scattering, and ultracentrifugal meaeurements. The association persists in butanone solution and is characterized by a rapid partial dissociation upon heating and a slow (diffusion-controlled) return to equilibrium association after cooling. Dissymmetry, depolarization, and viscosity measurements indicate that the molecular clusters are composed of many molecules but are much more densely packed, so that the sizes of the cluster and of the individual molecule are of the same order of magnitude. Some of the requirements of the binding forces are discussed. Qualitative experiments indicate that cluster formation occurs in varying degrees in other polymersolvent systems, especially near the phase-separation regions. Association in polyvinyl chloride-acetate copolymers and cellulose acetate is described, and the significance of this evidence for fractionation procedures is mentioned. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
AWERBACA, V.: Ph.D. Thesis, Polytechnic Institute of Brooklyn, 1945. CAMPELL, N . R . , AND FREETK, M. K.: J. Sci. Instruments 11, 125 (1934). DEBYE,P . : J. Applied Phys. 16, 456 (1944). DEBYE,P.: Lecture, Polytechnic Institute of Brooklyn, November 21, 1944. DOTY,P., AND MISAWCK, E . : J. Am. Chem. SOC.,in press. DOTY,P., AFFENS,W. A., AND ZIMM,B. H.: Trans. Faraday SOC.,in press. DOTY,P., AND KAWFMAN, H. S.: J. Phys. Chem. 49, 583 (1945). EDELSON, D . : B. S. Thesis, Polytechnic Institute of Brooklyn, 1946. SOOKNE, A,, A N D HARRIS,M.: Ind. Eng. Chem. 37, 475 (1945). STEIN,R . S., AND DOTY,P.: J. Am. Chem. SOC.88, 159 (1946). STERN,K. G., SINGER, S., AND DAVIS,S.: Polymer Bull. 1 , 3 1 (1945). STEWRER, E . : Z. physik Chem. AlW, 1,16 (1941). WOOD,L.A.: Rev. Sci. Instruments 7, 157 (1936). ZIMM, B., STEIN,R . s., AND DOTY,P.:Polymer Bull. 1, 90 (1945).
