Solution Viscosity and Partial Specific Volume of Polystyrene EFFECT OF SOLVENT TYPE AND CONCENTRATION D. J. STREETER AND R . F . BOYER The Dow Chemical Go. Midland, Mich. T h i s paper is concerned with the solution viscosity and partial specific volume behavior of a single sample of poly= 370,000) dissolved in a range of solvents styrene from the very best ones for polystyrene, such as benzene and chloroform, to borderline solvents such as Decalin and ethyl laurate. Concentrations up to 12% were covered in some cases. The reduced specific viscosity, vsp/c, was ] ~a function of c, plotted on a linear chart of slope k ’ ~ [ 7 7as according to Huggins, and as a semilogarithmic plot, according to Martin. The slope in the former case, k ’ ~ [ q ] * , was exactly a linear function of [7]as suggested by Eirich and Riseman, with slope u. The reduced specific viscosity plots tend to cross over a t higher concentrations-i.e., those for Decalin aiid ethyl acetate cross a t about 5% concentration by weight, while those for Decalin and dioxane cross a t about 129’0 concentration. In the dilute region the qsp/c curves cross a t a concentration of -l/u. It is shown empirically t h a t the viscosity of a 10% solution of polystyrene in a range of solvents depends primarily on the product [7].70 where 70 is the viscosity of the solvent. This rule is shown to be a consequence of the Martin equation and the empirically found constancy of ~ k’.w is the slope of the Martin the product [ v ] k ’where equation. Finally, as densities w-ere available for all the solutions prepared, partial specific volumes of the polymer were calculated. The partial specific volume is a minimum in intermediate solvents such as methyl ethyl ketone aiid is higher i n the poorest and best solvents for polystjrene.
(aw
S
EVERAL years ago Janssen and Caldwell (12) pointed out, in the dilute-solution viscosity of polyvinyl chloride-acetate copolymers, that although a good solvent produced a greater intrinsic viscosity, the reduced specific viscosity versus concentration plots actually crossed over at higher concentrations, suggesting the presence of a structural type viscosity. Spurlin, Martin, and Tennent ( 1 9 ) later noted similar behavior for cellulose derivatives. Since, in each of these two cases, a highly polar polymer was involved, the existence of fairly specific interaction forces between polymer and solvent might be expected. On examination the existing literature did not contain sufficient data over a range of solvents and concentrations to show experimentally whether such crossover effects also exist for a nonpolar system involving polystyrene. The experimental data reported here were undertaken about 2 years ago. The data were considered from the point of view of the crossovers of the viscosity plots and from as many other points of view as possible. Accordingly the several currently used dilutesolution viscosity equations were checked as well as an equation that would be valid for higher concentrations. The authors also wanted to determine how intrinsic viscosity and the various constants in the viscosity equations depend on solvent type. Finally, as densities of the solutions would be available, partial specific volumes could be calculated to show whether these depended in any manner on the type solvent.
It is customary to plot dilute-solution viscosity data according to any one of three equations:
log
=
log [7lar t lzk
[qI’Mc
Equation 1 in its present form is due to Huggins ( 9 ) , and the slope constant in this equation k ’ signifies ~ that this is a Huggins equation. It is well lrnown (6,13) that intrinsic viscody is connected with molecular weight through the relation
where the numerical constant, a,ranges in value from 0.5 to 1; its exact vaIue depends on the structure of the polymer and on the nature of the solvent. For a polymer homologous series, IC$ in Equation 1 is truly a constant. However, when the same molecular weight polymer is used and a series of solvents is investigat’ed, k$ varies in a, systematic fashion with the effectiveness of the solvent. Alfrey, , Justice, and Nelson ( 1 ) and, more recently, Eirich and Ri,.-wnaii (7) demonstrated conclusively that t.he less effective the solvent the larger is the value of k’. In fact, Eirich and Riseman were led by general theoretical considerations to propose the following relationship which seemed t,o bo verified by their experimental data: k;i
[?I2
=
a
+
u
[a1
(5)
The work reported here indicated that intrinsic viscosity usually increases linearly with the quality of the solvent; thus a good correlation is established between ,ti and effectiveness of solvent,. Equation 2 is evidently an alt,ernutive form of Equation 1. Staudinger employed i t on some occasions and numerous workers have used i t since. Some prcf‘er it 011 t’he basis that this plot, has a smaller slope and hence allows extrapolation of the data t,o infinite dilut.ion with greater accuracy. Since Equations 1 and 2 have the same intercept it is now fairly common practice to plot the data in both forms, allowing determination of [ v ] with greater accuracy. Both equations evidently would contain higher order terms in the concentration, but as long as their use is limited t u 1% or less, depending on molecular weight, they will give coinparable results. In fact, in the limit of extremely small trations, the following intimate relationship b e h e e n th constants exists: ,kA = 0.50
-p
(6)
This relationship, which is only a first approximation, was oriyinally pointed out by Ewart (8). Equation 3, known in its present form as Martin’s equation (15) was designed to take care of the fact that there usually is
1790
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1951
some upward curvature in the experimental plots when Equation 1 is employed because of the neglect of higher order terms. The slope constant of this equation, written here as k;, should be related numerically t o the corresponding constant in Equation 1 through the relation
(7)
k;i = 2.303
There are several equations which are pertinent to the question of crossover of viscosity plots-for example, equations of the type of Equation 1 will cross each other when the same polymer sample is studied in different solvents, in accordance with the relationship
However, the substitution of Equation 5 into 8 immediately leads to the simple result Cr
=
-1 U
(9)
This is a completely new and rather significant result. It would not have been anticipated prior to the development of Equation 5 by Eirich and Riseman. This statement about crossovers obviously will hold true only in the concentration region where Equation 1 applies. At somewhat higher concentrations where Equation 3 is preferable, the corresponding crossover equation is (10) where k ; and k i refer to the Martin equation slope constants. The product k h [ ~appearing ] in the denominator is not related simply to other quantities, although visual inspection of the data will show that it is approximately constant and actually increases slowly with [q]. Equation 10 thus allows, enipirically a t least, conditions for crossover. Equation 2 also leads to crossovers although there is no unique point, as with Equation 9. Instead, if Equation 6 applies cz
= LO.5
(h11 -
[~12)
- el-'
1791
The constant temperature bath was controlled to *0.001 O C. a8 read b y a Beckmann thermometer. This constant temperature was made possible by placing a 4-liter beaker of water on a platform in the center of a 12 X 12 inch jar of water and maintaining agitation in each. The outer bath was controlled to ~ 0 . 0 1 ' C. with a Magna-set thermoregulator and a Lo-Lag heater. The temperature of the inner bath was controlled by the outer bath, and the variation was not readable on the Beckmann thermometer. The entire setup was insulated against heat loss with Styrofoam on the sides and a Transite cover. It was further insulated against heat from variable light intensity by enclosing the apparatus in a large cardboard carton. A small fluorescent light was installed, giving a low heat, constant light source. The higher concentration of the sample was prepared by cai efully weighing into a 50-m]. volumetric flask and partially filling it with solvent. When the solution was complete the volunir was adjusted at 25' C. All other concentrations were made by dilution of this original sample at 25' C. This procedure for preparing solutions is more subject t o a systematic error than is the case where each Concentration is the result of an independent weighing. However, the excellcnt linearity of most density versus concentration plots confirms the correctness of the dilutions. T h e density of the solutions was obtained with a IO-ml. Gay-Lussac specific gravity bottle which gives results to *0.00005. Liyhtscattering molecular weight was 370,000. The numerical viscosity data are given in Table I. Section A includes solvents used in concentrations up to 2 grams per 100 ml. and section B the solvents used in concentrations up to 12 grams per 100 ml. Table I1 gives the various constants calculated from the viscosity plots. Table IIA is arranged in order of decreasing intrinsic viscosity, [ V ] H from a Huggins' plot. 2.3 k,' should equal h i , but it was consistently lower. In fact, 2.74 k,' was more nearly equal to h i . Table IIB, also arranged in order of decreasing intrinsic visrosity, is based entirely on Equation 3, used in the concentration region of 2 to 12 grams per 100 m]. The intrinsic viscosities are consistently higher than those of Table IIA, with the expeption of Decalin. Since the [VIM values are high, 2.3 k i would naturally be lower than the k i values of Table IIA, Dec@in again being an exception. The constancy of the product k M [TIM is evident in the last column of the table. Figure 1 illustrates the application of Equations 1 and 2 to the data up t o 1% concentration for the best, the average, and the poorest samples. I n general, Equations 1 and 2 work equally well for all solvents used with the possible exception of ethyl laurate. Ethyl Iaurate is such a borderline solvent that the authors
These crossovers are on the positive side and a study of the actual data agrees with this prediction. Soivents 8 to 14, inclusive (Table IIA), lead to a common crossover point at 4.3 grams per 100 ml., but this is presumably a coincidence. Since Equation 6 does not really hold, only pairs of solvents for which k , eauals 0.33 would meet in a comhon p.oint as given b y this expresTABLE I. SOLUTION VISCOSITYOF POLYSTYRENE sion. A.
EXYERIMENTAL METHODS AND DATA
Modified Ostwald viscometers, having capillaries sufficiently small in diameter to require time readings of at least 200 seconds, were used in this work. Thus, d r a i n a g e a n d kinetic energy errors, which are the major ones in using capillary instruments, were nearly eliminated. A carefully regulated Elgin stop watch was used to time the viscometers, and the same watch was used on all determinations. The time was read to 0.1 second. and an average of three readings was used.
c
Grams per 100 M1. 2.000 1.000 0.500 0.250 0.125 0.00
,
Chloroform 3.268 1.564 0.974 0.738 0.634 0.542
Tetralin 13.593 6.566 4.260 3.296 2.872 2.492
B. Grams per 100
DILUTESOLUTIONS TO 2% Centipoisea a t 25" C., z-Dichloros-ChloroMethyl s-diethylz-triethyln-amyl benzene benzene ketone 13.304 12.151 2.587 6.992 6.466 1.468 4.782 4.500 1.082 3.884 3.698 0.920 3.485 3.339 0.847 3.006 0.779 3.118
Carbon tetrachloride" 4.774 2.361 1,524 1 192 1.044 0.907
-
CONCENTRATED SOLUTIONS TO 12% 0-
Ethyl DichloroBenzene Toluene benzene Dioxane benzene 12.000 180.11 153.7 160.8 285.07 321.67 10.000 97.13 82.99 88.23 154.71 175.66 8.000 50.63 43.08 45.00 80.488 91.42 24.44 21.04 21.69 39.388 44.33 6.000 10.50 9.245 4.000 9.287 17.055 19.51 2.000 3.598 3.157 3.266 6.088 6.881 1.000 1,739 1.536 1.624 3.082 3.2872 0.500 1.088 0.970 1.063 2.018 2.1295 0.747 0.832 1.5728 1.66631 0.250 0.828 0.125 0.713 0.648 0.728 1.3766 1.4554 0.000 0.606 0.556 0.634 1.1992 1.2699 a Carbon tetraehloride was added after other solvents were calculated.
MI.
Ethyl laurate 8.235 4.954 3.857 3.398 3.186 2.999
Methyl Ethyl Ketone 59.31 30.88 15.45 7.395 3.222 1.247 0.7170 0.5293 0.4514 0,4162 0.3833
Ethyl Acetate 73.66 38.04 18.62 8.542 3.610 1.357 0.7844 0.5849 0.5031 0.4771 0.4318
Deoairn 583.25 268.90 118.49 49.475 19.213 7.015 4.138 3.155 2.747 2.562 2 3885
Vol. 43, No. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
1792
also seemed to agree. The plot failed completely for a POLYSTYREKE very high molecular weight A . DILUTESOLUTIONS (LESSTHAN 2%) polystyrene whose Equation 1 Solvent [?I% kka Bb k;, B k;j[?IH ki;Al& k,;C type plots were curved in all 0.101 0.416 0 467 0 30G 1 . 3 6 0.225 0.232 1. Benzene the solvents a t ly0 concentra0.126 0.591 0 494 0 458 1 , 2 9 0.363 0.141 2. Chloroform 0.124 0.527 0 426 0.491 1 . 2 4 0.345 0.146 3. Toluene tion and below. 0.129 0 412 0.477 0.499 1 . 1 6 0 . 3 5 5 0.144 4. Tetralin 0 . 11.8 Dilute solution data were 0.419 0 366 0 478 1 . 1 4 0.320 0.156 0. Ethylbenzene 0.130 0.457 0 403 0 504 1 . 1 3 0.356 0.148 6. Dioxane examined also in terms of 7. o-Dichloro3 23 0 322 0 384 0.140 0.477 0 517 0 430 1 . 1 1 0 387 0.130 benzene Martin's equation (Equation 3) 8. z-Dichlorodi0 430 3 25 0.157 0 361 0.340 0.540 0 383 ethylbenzene 0.898 0.427 0.113 for the representation of the 9. z-Chlorotri3 50 0 350 0 427 0.156 viscosity data as a function of 0.303 0 357 ethylbenzene 0.848 0.421 0 . 1 1 5 0.536 10. Methyl n-amyl roncentration. Historically an 6 00 0 400 0 477 0.174 0.210 0,552 0 311 0.675 0 . 4 6 1 0.091 ketone 11. Methyl ethyl equation of this type was used 5.50 0.412 0.490 0.179 0.209 0.558 0 315 0.663 0 . 4 7 5 0.083 ketone 0.545 7.50 0,458 0.199 0.580 0 326 0.201 0.616 0.529 0.051 12. Ethyl acetate by Bungenberg de Jong, Kruyt, 0.462 0.551 12.00 0.201 0 299 0.168 0.564 0 , 5 2 9 0,047 0.576 13. Decalin 0.520 0.619 -2.00 andLens ( 4 ) on a number of 0.226 0.140 0,299 0.596 0.502 0.596 0.000 14. Ethyl laurate polymers and later by StaudB. COYCEYTRATCD R O L U T I O X S ~ (ABOVE2 % ) inger and Heuer ($0) rather Solvent [?l,U k.; 2.3 k,;, k.); Ililhf extensively on p o l y s t y r e n e , 0.100 0.143 1.62 0,0620 Benzene 0.139 0,097 However, its current popu1.60 0.0606 Toluene 0.097 0.151 1.48 0.0657 o-Dichlorobenzene larity and present reincarna0.096 0.155 1.42 0.0675 Dioxane 0.102 0.174 1.35 0.0757 Ethylbenzene tion are due to Martin. This 0.104 0.334 Methyl ethyl ketone 0.72 0.14$ 0.111 0.380 0.165 equation has the obvious adEthyl acetate 0.67 0.135 0 , GO7 0.264 0 51 Decalin vantage of accounting for an Based on Equation 1. upward curvature which someb Based on Equation 2. Baaed on Equation 3. times a p p e a r s in reduced d Based on Equation 12; rallies caloulated by Weissbriig, Simha, and Rothman, Sational Bureau of Standards specific viscosity versus concentration plots. The data given in Table I were plotted .iz-ithlog q s o / c as a function of concent,ration,up to 1% concentrawere never completely certain that the samples were in solution, tion, The only curve that was significantly improved was that and the viscosity data usually exhibited some peculiar breaks. for benzene, which showed evidence of a definite upward curvaCertainly for Decalin, the nest poorest solvent, F>quations 1 and ture when plotted as suggest'ed by Equation 1. Aside from this 2 were still quite valid. question of curvature, most, of t,he other data plotted had good However, the simple relationship, Equation 6, between k; and straight lines, although there was some suggestion t'hat plots p does npt apply exactly, as shown in Figure 2 . The dotted which had been linear on the Huggins' equation were slightly curve shows Equation 6, which was expected from the simple thecurved in this logarithmic representat,ion. I n general, the intrinory. It is evident that the data do differ rather widely from this sic viscosities were the same by the two methods, when working but in a systematic fashion. If the theory is developed further to a t 1?& or less. take care of higher order terms in the expansion of (In qrei)/c, thp result is TABLE
11.
I N T R I N S I C 171SCOSITY, SLOPE CONSTANTS, AND CALCULATED COSSTANTS FOR
+
kk
+P
=
'/z
IF;, - '/all?7lc
(11)
This equation predich, the essential features of Figure 2 : the sum is close to when k H is 0.33, is greater than l/z for the poorer solvents, (large k i ) , and less for the very best solvents such as benzene. Actually the plot in Figure 2 ignores the factor [ q ] whose variation is opposite that of k i . The concentration is somewhat ambiguous but presumably refers t'o the average value used over the range of linearity of Equations 1 and 2. A value of 0.5 gram per 100 ml. checks with the data of Figure 2 rather well. Equation 11 obviously reduces to Equatiqn 6 as the concentrations become small and especially when k , is around 1/3, which is a common value,for many good solvent's. Figure 3 is a plot of kH [ q ] 2 as a funct'ion of 171 as suggested by Eirich and Riseman and is according to Equation 5. The data follow this relationship extremely well considering the wide variety of solvents employed. Benzene and ethylbenzene lie farthest from the curve. Since the slope of this straight line is 0.53, a crossover of the reduced specific viscosity plots at a concentration of -1.89 grams per 100 ml. could be predicted from Equation 9. Figure 4 shows the plot,s of Equation 1 where the lines are extrapolated to the crossover point. Many of the solvents were omitted in this plot to avoid confusion. Ethylbenzene, not shown, failed rather badly, but other lines do tend to meet in this common point. However, this plot was found to hold good on another set of data involving a different sample of polystyrene; ethylbenzene agreed but dioxane did not. Isophorone
2.0
I k i = .273
I .5
BENZENE k/n=.427
/3 = . I 6 7
I .o
BENZENE
/3=.113
,125 . 2 5
1.00
.50 G R A M S PER
100 m l
Figure 1. Plot of Reduced Specific Viscosity US. Concentration in Dilute Range (Equations 1 and 2) Characteristic behavior patterne on going from good to average t o poor solvent
August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
a/?
I
300
-
.400
-
1793
I. BENZENE 2. CHLOROFORM 3. TOLUENE ’ 4. TETRALIN 5. ETHYL BENZENE 6.DIOXANE Z 0-DICHLOR BENZENE
k;r[d2,
/
.300
VISCOSITY PLOTS AT HIGHER CONCENTRATIONS
Martin intended Equation 3 to provide improved curve-fitting possibilities for use in the very dilute solution range. Spencer and William (18)found this equation to hold for polystyrene in isopropylbenzene up to 12% concentration and possibly as high as 20%. The possibility of working at these higher concentrations in an industrial laboratory is of considerable importance from the viewpoint of increased speed and accuracy in determining intrinsic viscosities. The authors hoped that this equation would be generally applicable and would permit an extrapolation to the intrinsic viscosity from several measurements made in the range of 4 to 12% polymer by weight. Figure 5 shows some representative plots of the data of Table IB where the semilogarithmic representation is used. The top curves for benzene and o-dichlorobenzene show definite departures from linearity in the region below 2%. These plots for the intermediate and poorer solvents become reasonably straight again. However, the intrinsic viscosities obtained from these high concentration extrapolations do not agree well with those from the Huggins’ plot. Also, the slope constants do not agree. Figure 6 is a plot of intrinsic viscosity from the Martin equation at high concentrations versus intrinsic viscosity from the Huggins’ equation at low concentrations. These agree reasonably well only for very poor solvents. I n general, the Martin plot would give a high value of the intrinsic viscosity. The behavior of the slope constants is shown in Table IIB. Figure 5 indicates that crossover effects begin to show up a t these higher concentrations. The curves for methyl ethyl ketone, ethyl acetate, and Decalin cross each other at about 5% concentration. The curve for Decalin crosses the dioxane curve at about 12% concentration and will presumably cross the curves for o-dichlorobenzene and benzene at slightly higher concentrations. Thus, Decalin, which has the lowest limiting value of qap/c, eventually surpasses even the best solvents at the higher concentrations. The general interpretation of this type behavior has already been suggested by Janssen and Caldwell ( l a )as well as by Spurlin, Martin, and Tennent (19). The intrinsic viscosity, for an isolated polymer molecule, measures both the volume i t occupies in space and to what extent the interior of the molecule is shielded from solvent flow by the outer portions of the coil (6). The intrinsic viscosity is, therefore, something that is characteristic of an isolated polymer coil in a given solvent. However, by the time concentrations of even 1% are reached most polymeric solutions are already crowded and these coils must be starting to overlap (3). Under these crowded conditions, polymer-polymer contacts begin to become possible. In an excellent solvent each polymer chain is still well solvated, and the polymer will tend t o contact solvent rather than other polymer molecules. A poor solvent, such as Decalin, however, will tend to promote polymer-polymer
.zoo
.loa
8 . X-DICHLOR X- IETHYL
BENZENI 9. X-CHLOR TRII rHYL BENZEN IO. METHYL R - A M Y L KETONE It. METHYL ETHYL KETONE 12. ETHYL ACETATE 13. DECALIN 14. ETHYL LAURATE
-
0
0.4
I
I
0.8
1.2
Inl
I 16
Figure 3. Test of Eirich and Riseman Relationship of Equation 5 Correlating Slopes of Equation 1 with Intercept Intercept, a, is - 0.12; slope, is 0.53 (T,
contacts a t these higher concentrations. Hence i t is understandable that a type of structural viscosity or very weak three-dimensional dynamic network occurs and accounts for the higher viscosity. The general conditions for crossover of the Martin type plots are already giv:n as Equation 10. Table IIB gives the values for the product k,[.rl]~. This product is reasonably constant at a value of 0.1. To the extent that this product is almost constant the denominator in Equation 10 will tend to be small. There2.0
1.5
b P c
1.0
0.5
0
I
- 2.0
1 -1.0
I I I I I I 0
.4
.8
1.2
ml Figure 4. Test Plot for Equations 8 and 9 CONCENTRATION, G I 1 0 0
Huggins’ type plot (Equation 1) for series of solvents on givcn polymer intersect in common point t o left of origin
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1794
TABLE111.
nENsITIEs FOR SOLUTIONS AT
25/4" c.
4. DILUTE^ Grams per 100
Mi.
Chloro-
2.0000 1.0000
0.5000
0.2500 0,1250 0 0000
form
Tetrulin
1.4648 1.4681 1.4698 1.4707 1.4711 1.4715
0.9847 0.9834 0.9827 0.9824 0.9822 0.9820
Carbon Tetrachlorideb 1.5765 1.5803 1,5822 1.5832 1.5837 1.5842
B.
2-Chloro-
x-Dichlorox-diethylbenzene I . 1633 1.1641 1.1645 1.1647 1.1648 1.1649
triethylbenzene 0.9996 0.9989 0.9986 0.9985 0,9984 0.9983
c
Ethyl Lauratr 0.8635 0.8614 0.8604 0.8599 0.8597 0,8594
(14) Methvl Ethyi Ketone 0.8325 0.8272 0,8218 0.8161 0,8109 0.8062 0.802%5 0.8010 0.8004 0.8001 0.7997
Ethyl DichloroEtli>i Grams per Benzene Toluene benzene Dioxane benzene Acetate Decalin 100 hll. 0.8873 0.8865 I . 0335 1.2736 0.9159 0.9008 0.8969 12,0000 0.8831 0.8826 1.2777 0.9126 0.8971 1.0327 0.8930 10.0000 1.0319 0.8791 0.8782 1.2820 0.9088 0,8938 0.8890 8.0000 0.8750 1.0311 0.8742 1.2862 0.9052 0.8903 0,8852 6. 0000 0.8710 1.0303 0.8702 1.2901 0.9014 0.8888 0.8815 4.0000 0.8667 1.2942 0.8979 0.8834 1.0296 0.8658 0.8773 2.0000 0.8640 0,8960 0.8647 1.2962 0.8814 1.0291 0.8756 1.0000 0.8637 0.8628 1.0289 0.8951 0.880i 1.2973 0,8745 0.5000 0.8803 1.0288 0.8632 0.8947 1.2981 0.8623 0.8740 0,2500 0.8620 0.8801 1,0288 0.8629 0.8945 1,2984 0,8737 0,1260 n- 8735 0.8618 0.8799 0.8627 0,8943 1.2988 1.0287 0.0000 S'olume of pycnometer (except CCh) a t 25' C. = 10.0174 ml. i' 1 added after other solr-cnts n e i oaloulated. Volume of pyonometer for CCln a t 25' C. = 10.2431 ml.; CCl Volume of pycnometer a t 25' C. = 10.0174 ml.
TABLEIv.
PARTIAL SPECIFIC \'OLCnlES
O F POLYSTYREENE IS \T.iRIOUS
Molar
SOLVENTS
[TI
Partial Concri. Volume of Sp. T'ol., Range.. Solvent. hIl./G." (>./IO0 311.6 uc Vi JIl./Molr t0dd 0.956 .... ... >-\om 0.905 0:45 1.36 0- 1 88.9 R ,3 Benzene 0.908 0.43 0- 2 80 8.4 1.29 Chloroform 0.44 0.914 0- 4 106 1.24 5.6 Toluene 0.43 0-20 0.885 117.6 1. lG 5.9 Tetralin 122 1.14 0.42 0-12 0.921 6.2 Ethylbenzene 0.48 85.5 0.933 1.13 1-12 4.1 Dioxane 0.42 112.c 2-12 1.11 0.928 7.4 n-Dichlorobenzene .. 0.931 0.898 0- 2 ,,.. 3:- Dichlorodiethylbenzene 0- 2 0.952 0.848 J:-Clllorotriethylbenzene .... o:i1 0.906 0- 2 0.676 139 -0.43 Methyl n-amyl ketone 0-10 0.909 0.663 0 . 5 3 8Y,6 3.3 Methyl ethyl ketone 0.616 0- 0 . 5 0.940 0.55 97.8 -6.1 Ethyl acetate 08 0 . 5 5 0.564 0.939 187 3 .2 Decalin 0.923 0.502 0- 2 0.57 282 -2.6 Ethyl laurate Reciprocal of bulk density (1.045 g./ml.) of polystyrene and is listed for comparative purposes. b There was no evidence for any systematic dependence of partial specific volume on concentration range, with the possible exception of benzene which showed a higher value (0.92) in the region of 2 to 12%. The concentration range chosen was based on linearity of plot of density against concentration to avoid individual points outside the range which were seemingly i n error,.. c Vrom Boyer and Spencer (2). 1 his is FIuggins' polymer-solvent interaction constant usually obtained f r o m osmotic pressure measurements but derived in this work from equilibrium swelling measurements on slightly crosslinked polystyrene d Quantity shouid be proportional to osmotic slope constant, B , of Equation 14. The density of t,he polymer has been ignored. [?I
I
Dl./C.
Solvent
shown by expansion of ]!:quation 3 and by recognizing that the product of k$[71.v is approximately a constant. On rarrying through the calculations the equation for the viscosity of a 12% solution of polystyrene is ~(12% solut,ion) = 190 70[77]
CONCFNTRATED~ 0-
ii
Meths 1 n-Am> 1 Ketone 0,8210 0.8183 0.8170 0.8164 0.8161 0.8158
Vol. 43, No. 8
...
.
I
.
.
I
.
.
N I e n the 12% solution viscosities are actually plotted against the product [ 7 7 ] ~ 0 , the fit is improved except for Decalin which now lies far above the line. The slope of this experimental line is 185;it agrees well with the numerical value of Equation 14, and the line passes through the origin. The straight line of Figure 7 is really fortuitous and results largely from the anomalous character of Decalin a3 a solvent. These considerations have some bearing on the question of crossovers such as the ones shown in Figure 5, especially for methyl ethyl ketone, ethyl acetate, and Decalin. When all three solvents lead to about the same intrinsic viscosity then, according to Equation 14, the concentrated solution viscosity will be greater in the solvent of higher viscosity. It does not appear necessary to invoke any special consiticrations of structural viscosity to explain these crossovers, unless these structural aspeck are hidden behind the rmpirical Equation 14.
Cole C, will occur at high values of concentration, and, in general, crossovers would not be expected in the concentration range up to 10%. The fact that crossovers do o w i r implies some unusual values of the slope constant. In Decalin, where the product IC; [779ni is the highest-namely 0.135-the greatest numbel. of cr'rossovers are evident at these lower concentrations. The authors did not attempt a systematic fitting of their data by any other equation designed for use at higher concentrations. ltobert Simha and coworkers at the National Bureau of Standards have tested these data against the. Raker equation ?rei
= (1
+ [ill c/nY
(12)
where TL 1s a constant. They found the equation to satisfy all concentration data of the authors. Values of the exponent n are given in column 10 of Table I I A ; n is related to the RIartin cquation slope constant through n = 1!(0.5
-
(13)
There is one other interesting and important roilsequence that comeS from these concentrated solution data. For example, in Figure 7 , the viscosity of a 1291, solution of polystyrene is approximately a linear function of the viscosity of the solvent used to make up the 12% solution. A similar linear relationship holds alcro for 10, 8, and 6% solutions. The accuracy of this result is
f c 0.5
7 0-DICHLOR BENZENE I I . M E T H Y L E T H Y L KETONE 12. E T H Y L A C E T A T E 13.DECALIN
F 0
2
4 6 8 GRAMS PER 100 rnt
IO
I2
Figitre 5. Semilogarithmic Plot of gsp/c as function
of c Plot carried t o higher concentration range t o test linearity of Equation 3 and tendency for crossovers at higher concentrations
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1951 2.0
I
-
119s
700 I 3. 5. 6 7
BENZENE TOLUENE ETHYL BENZENE #
I
600
/
DIOXANE 0-DICHLOR BENZENE
I
12 E T H Y L A C E T A T E
/
VISCOSITY IN CPS. OF 12% SOLUTION OF POLYSTYRENE IN INDICATED SOLVENTS
8 /
500
13. D E C A L I N
DECALIN
Q
/
1.0 -
400
3 00
0.5
200
IO0
I
0
0.5
Figure 6.
I O
@
Intrinsic Viscosities
0
0
Correlation of intrinsic viscosities, [VI Mi obtained by logarithmic Equation 3, using high concentrations, with the intrinsic , the data up to 1% concenviscosities of Equation 1 [ q ] ~using tration of polymer
inodynamic type of measurement (IO), and current practice is to relate it to the osmotic slope constant, B, in the followirig equation:
P = - R 2’ c M
+
Bc
The general nature of B has been evaluated in some detail by Huggins (11). Osmotic slope constants are not available for all solvents used in this study. However, most of them had been used in a series of swelling measurements by Boyer and Spencer ( 8 )who calculated the so-called Huggins p constant (11). This is intimately related to B in that the quantity - p ) / V , is directly proportional to B. Table IV is a list of the solvents in order of decreasing intrinsic viscosity. The values of p for the poorer solvents are probably in error on the side of being too high. 1.4 BENZENE@
1 - w 1dm -7 z]
12
where Vl = partial specific volume of polymer and wl = weight fraction of polymer. V = v / m where m is the mass of liquid in a pycnometer of volume v. The slope dm/dwl was usually based on two points which lay exactly on a smooth straight line of the density-concentration plot. The authors ureferred to calculate the Dartial sDecific volume below 1 % concentration, but this was not always possible because of seeming discrepancies in the data. In Decalin, however, the density-concentration plot was strictly linear to 20% concentration. These densities and, therefore, partial specific volumes, are not
2 5
Essentially a test of Equation 12
In order to obtain the absolute viscosities of polystyrene solutions needed t o calculate intrinsic viscosities it was necessary to measure the density of each solution. Measured densities are listed in Table 111. A knowledge of density versus concentration of polymer permits calculation of the partial specific volume of polystyrene. Polystyrene in a good solvent has a value of about 0.9 ml./gram. The reciprocal of this number-namely, 1.1-is the effective density of the polystyrene in solution. This is appreciably greater than the bulk density of polystyrene-namely, 1.045. The reason for this discrepancy presumably is that the bulk polymer contains “holes” caused by imperfect packing. The solvent molecules can fill these holes, thus leading to a more efficient over-all packing. Methods of calculating partial specific volumes have been reviewed by Kraemer (14). Numerical values for polystyrene were given first by Signer and Gross (16). The values obtained in this study are listed in Table IV. Also given is the concentration range over which the value holds. The equation used in t,he calculations, as given by Kraemer, is
v [l
0.5 1.0 1.5 2.0 V I S C O S I T Y IN CPS. OF SOLVENT
Figure 7. Correlation of Actual Measured Viscosity of 129‘0 Solution of Polystyrene with Viscosity of Solvent Used to Make Solution
PARTIAL SPECIFIC VOLUME
VI =
ETHYL ACETATE
1‘5
10
OB
-
TOLUENE e
00-Dl CH LOR
-M
BENZENE
oMEK
O M E T H Y L - r r AMYLKETONE
*
0.4
QETHYL-LAURATE
[w]
x 104
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1796
However, these I.L values do arrange the solvents in approximately the correct thermodynamic order. Simha ( 1 7 ) has shown, from various considerations, that the following relationship between the intrinsic viscosity and the osmotic slope constant, B, can be expected:
‘The second term on the right is the partial specific volume of the )polymer which can usually be neglected in comparison to the first term on the right. Figure 8 is a plot of the Simha relationship using the authors’ data. The solvents are divided into two groups-the good ones and the poor ones--a ith only dichlorodiethyl and chlorotriethylbenzenes in the intermediate zone. However, both these solvents contain mixtures of isomers and hence are not well characterized. They have not yet been studied for swelling power. “ ETHYL ACETATE
’
QOECALIN
Q
PARTIAL SPECIFIC VOLUME OF
OIOXANE
BENZENE
BENZENE
.89
cosity will remain finite and, of course, ~villbe much larger than the specific volume. If viscosity data are expressed in the same units as specific volume the [?I value.: in Table I must be multiplied by 100. Hence there must be an additive constant in Equation 14, and presumably the nature of this constant is responsible for the behavior of [ q ]in very poor solvents. In Figure 9, the results may have the following qualitative explanation : I n a very poor solvent such as ethyl acctate or Decalin, polymer-polymer contacts are favored, and the conditions of the solution approximate somewhat those in the bulk polymer. Hence partial specific volume approaches the reciprocal density value for bulk polystyrene. As somewhat better solvents are approached these polymer-polymer contacts, which are rather inefficient from a packing standpoint, are replaced more and more by polymer-solvent contacts. This condition favors a more efficient utilization of the space, and the partial specific volume decreases, On going up the other side of the curve in the region of the very good solvents, these good solvents cause the polymer coils to expand and swell. This tends to cause a crowding in the solution and polymer-polymer contacts. As previously noted, in connection with viscosity behavior a t higher concentrations, polymerpolymer contacts were most numerous, or at least most firm, in the very poor solvents. In order t o reconcile these two points of view, the authors suggest that in the very good solvents polymerpolymer contacts tend to exist because of the crowding effect and that such contacts are really present in a static sense-that is, an equilibrium sense. Thus, a thermodynamic measurement, such as the partial specific volume, will show the existence of these polymer-polymer contacts and consequently the poor packing. However, because the solvents are very good the moment any shear is placed on the solution these polymer-polymer contacts are immediately broken in favor of a temporary polymer-solvent contact. The authors admit that this is a rather ad hoc explanation of the data suggpsted largely on the basis of the U-shaped curve of Figure 9. However? preliminary indications such as Figure 9 seem to indicate the importance of further study and correlations between partial specific volume and solvent type. As an alternative explanation for the increase of partial specific volume in good solvents Eirich (6) has suggested that the effect may be traced to a change in the specific volume of the solvent. ACKNOWLEDGMENT
1
The authors wish to thank 11. Simha and coworkers for their assistance and for the values of n shown in column 10 of Table IIA. NOMENCL4TURE
oTETRALIN
=
qo
.88
-a
Vol. 43, No. 8
-4
0
4
8
I2
qsp
Figure 9. Correlation of Partial Specific Volu m e of Polystyrene i n Range of Solvents with “Goodness” of Solvent
c
Large, positive values of abscissas represent best solvents. Dioxane and Tetralin are closest i n density t o that of polystyrene and hence partial specific volume values for t h e m are most subject to error
p k.,: JI
= = -
k;,
n
K Table IV shows that there is a general tendency for the partial specific volume to increase with decreasing intrinsic viscosities. However, there are many exceptions to this rule. I n the series of solvents, chlorotriethylbenzene, dioxane, o-dichlorobenzene, ethylbenzene, toluene, chloroform, and benzene, there is an exact linear relationship whereby the partial specific volume decreases with increasing intrinsic viscosities, but all other solvents lie rather widely off this straight line. It is possible that they may belong to other families of straight lines although the data are not sufficiently good or extensive to permit further generalization. Figure 0 is a plot of partial specific volume against the quantity - p ) / B 1 . There is a definite tendency for the curve to go through a minimum about in the region where the abscissa is zero. Dioxane and Tetralin obviously are far off the curve. Equation 14 cannot hold exactly because the osmotic slope constant, B , can be zero or even negative, and the intrinsic vis-
=
qrei =
a
= =
= = = = =
cz
= =
n
=
VI w1
B
= = = = = =
p
=
Q
T
R
T
solution viscosity solvent viscosity relative viscosit,y = v / o vrel - 1 = specific viscosity concentration of polymer in g./100 ml. I)/c = reduced specific viscopity; [ q ] = intrinsic viscoEity = limit ( v s , / c ) as c --+ 0 slope of vsp/c 2)s. c plot,s, Equation 1 slope of (In qrel)/c us. cplots, Equation 2 slope of loglo(v3p/c)vs. c plots, Equation 3 molecular weight constant, an exponent in Equation 4 const’ant in Equat,ion 4 constant, intercept of Equation 5 const’ant,slope of Equation 5 concentration a t which qyn/c us. c plots cross for two solvent,s const,ant,exponent. in Equation 12 partial specific volume of polymer weight fraction of polymer in solution osmotic pressure of a polymer solution gasconstant absolute temperature osniot>icslope constant, Equation 16; B = (0.5 - p ) / V L solvent-polymer interaction constant LITERATURE CITED
(1) Alfrey, T., Justice, J. D., and Nelson, S. J., Trans. Faraday Soc.. B42,50 (1946) [see also Alfrey, T., Goldberg, A. I., and Price, J. A , J . Colloid Sci., 5, 251 (195011. (2) Boyer, R.F., and Spencer, R. S., J . Polymer Sci., 1, 90 (1946). (3) Ihid., 5 , 375 (1950).
August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
(4) Bungenberg, de Jong, H. G., Kruyt, H. R., and Lens, J., KoLZoidBeihefte, 36, 461 (1932). (5) Debye, P., and Bueche, A. M., J. Chem. Phys., 16, 573 (1948). (6) Eirich, F., private communication. (7) Eirich, F., and Riseman, J., J. Polymer Sci., 4, 417- (1949). (8) Ewart, R. H., “Advances in Colloid Science,” Vol. 11, p. 211, New York, Interscience Publishers, 1946. (9) Huggins, M. L., J . Am. Chem. Soc., 64, 2716 (1942). (10) Huggins, M. L., J . Applied Phys., 14, 246 (1943). (11) Huggins, M. L., Proc. N . Y . Acad. Sei., 44, 431 (1943). (12) Janssen, A. G., and Caldwell, B. P., Polymer BUZZ.,1, 120 (1945). (13) Kirkwood, J. G.9 and Riseman, J . (%?m. PhWs 16, 565 (1948). (14) Kraemer, E. O., “The Ultracentrifuge,” edited by T. Svedberg J.3
and K. Pedersen,
p. 57,
1191 Oxford, Oxford University Press,
1940.
(15) Martin, A. F., presented before the AMERIC.4N CHEMICAL SOCIETY, Memphis, Tenn. (April 23, 1942). (16) Signer, R., and Gross, H., Helv. Chhim. Ada, 17, 335 (1934). (17) Simha, R., ”High Polymer Physics,” edited by H. A. Robinson, p. 410, Brooklyn, N. Y., Chemical Publishing Co., 1948. (18) Spencer, R. S., and Williams, J. L., J . Colloid Sei., 2, 117 (1947). (19) Spurlin, H. M., Martin, A. E’., and Tennent, H. G., J. Polymer Sci., 1, 63 (1946). (20) Staudinger, H., and Heuer, A . , 2. PhUsih. Chem., 171, 165 (1934). RB:CEIVED January 19, 1951. Presenthd as part of the High Polymer Forum before the Division of Physical and Inorganic Chemistry, 117th Meeting of the AMERICAN CHEMICAL SOCIETY, Detroit, Mioh.
EEect of Fluorine Carriers on Crops and Drainage Waters W. H . MACINTIRE, S. H. WINTERBERG, L. B. CLEMENTS, L. S. JONES, AND BROOKS ROBINSON The University of Tennessee Agricultural Experiment Station, Knoxville 16, Temn.
Because of the increased use of fluoric materials as insecticides and as fertilizers, and because of the distinctive reactivities of various fluoric materials after their incorporation into soils, it seemed imperative to determine the effects that incorporations of various solid carriers exert upon fluorine content in vegetation and in drainage waters. Until experimental inputs were at rates far greater than those to be expected in practice, no carrier induced significant enhancement in the fluorine content of either crops or drainage waters. The fluorine of rock phosphate was virtually inert. Incorporated at abnormal rate, sodium combinationsyielded fluorine leachingsbeyond those
that passed from magnesium fluoride and cumulative inputs of sodium proved more harmful to soil structure. Rational-rate incorporations of fluorides of sodium and magnesium, and cryolite, can be used without adverse effect upon plant growth, upon uptake of fluorine, and without causing harmful concentrationof fluorides in the soil drainage. Those effects hold in particular for incorporations of rock phosphate, without restriction as to rates. In making heavy-rate incorporations for insecticidal effects in the soil, it was demonstrated that the several industrial fluorides possess distinctive pmperties that should govern choice, quantity, and mode of input.
T
and ( 6 ) the occurrence of fluorine in the rain water leaching8 therefrom, under cropping and from fallow, in parallel. Because fluorine does not and cannot occur in elemental state in nature, the word fluorine in the text connotes the presence of that element as a component.
HE meager incidence of fluorine in cultivated soils has been
augmented through incorporations of phosphatic fertilizers, by dustings of fluoric insecticides, and also by the nugatory increments t h a t are brought by rain waters (6). Provision for determination of the fluorine content of soils was not included in the methods for soil analyses and few findings for such content have been recorded ( 1 , 4, 13, 18, 20, S I ) . Only recently was i t established that the fluorine content of a limed analytical charge of soil may be dispelled completely when the charge is calcined as a step preliminary to distillation from perchloric acid (10,1 1 ) . I n recent years, however, attention has been directed to the effects that additive fluoric materials may induce in the soil (8, 10, 13, 18) and upon plant uptake of fluorine therefrom (26l r , 19). Question arose as to whether the “reveision” that component fluorides induce in the processing of phosphatic fertilizers (6-8) ensues also after their incorporation into the soil (9, 11 ). One contribution dealt with the fate of barium silicofluoride incorporations ( 1 3 ) . Recent findings revealed that the nature of the additive carriers governs the leachability of the fluorine ion from its combination with calcium in the soil (12, I d ) , and also the migration of that ion from soil into vegetation (16, 17 j. The effects that additive fluorides exert upon uptake of fluorine from nutrient solutions ( 3 ) and from additives of sodium fluoride were dealt with in recent papers from the New Jersey Station ( l a ) . The present paper reports ( a ) the extent to which incidence of fluorine in three successive crops was affected by separate equivalent incorporations of four fluoric solids, and by rock phosphate on two representative soils that were limestoned at rational rates,
EXPERIMENTAL
FLUORINE CARRIERS. Cryolite (Na3AIF6), magnesium fluoride ( MgFZ), sodium fluoride (NaF), sodium silicofluoride (.Na2SiFG), and rock phosphate were incorporated to supply identical inpu$ of fluorine. Carrier content of fluorine and its occurrence in the crops and in the lysimeter leachings were determined b y means of the Willard and Winter titration technique on the respective distillates (39). SOILS. Clarksville silt loam and the Hartsells h e sandy loam were used. Their properties are given in Table I. The initial pH values of 5.9 and 5.2 were raised to final values of 6.1 and 5.9 as the respective effects from the full-depth incorporations of 3 tons and 4.5 tons of high-calcic limestone per 3,000,000pounds of soil. Both soils reccived full-depth inputs of potassium eulfate
TABLE I. PROPERTIES OF THE SOILSUSED Determinations k:change capacitya me. Exchangeable Ca +’Mg, me. Exchangeable H, me. Fluorine, p.p.m. a By means of ammonium acetate.
Clarksville Silt Loam 5.9 5.6 2.8 2.8 160
Hartsells Fins; Sandy Loam 5.2 10.2 1.0 9.2 169
