Viscosity and Cryoscopic Data on Polystyrene J
J
Discussion of Staudinger's Viscosity Rule A. R. BEMP AND H. PETERS Bell Telephone Laboratories, New York, N. Y. From cryoscopic and viscosity data, a Kcmvalue for polystyrene of 0.45 X 10' is established for use in the viscosity-molecular weight equation :
This value is less than one third that selected by Staudinger for polystyrene, ranging in molecular weight from 7000 to 13,000 determined by the cryoscopic method. Cryoscopic data at various concentrations are presented on narrow fractions of polystyrene ranging in molecular weight from about 300 to 3000. It is shown that solutions of polystyrene in benzene exhibit increasing deviation from Raoult's law as the molecular weight increases beyond about 1000. This fact shows why the present Kcm value,
LTHOUGH polystyrene has been known for about a century (6),it was not until recently that its use as a commercial molding plastic and electrical insulation became important. Since the physical properties of polystyrene depend upon its state of polymerization, it is desirable to have some reliable method to determine average molecular weights of different preparations, as well as of fractions which may be separated from them to determine polymer size distribution. Staudinger (6) and his students carried out extensive investigations of polystyrene in an attempt to show some constant relation between viscosity, concentration, and molecular weight. These results were not conclusive since variations in the Staudinger ICmvalue ranged from 7.4 X t o 1.7 X 10-4 in the polymeric range of average molecular weights from 500 to 13,000, respectively. When viscosity and osmotic molecular weight data were employed in the case of more highly polymerized styrene fractions, Staudinger ('7) obtained K , values ranging from about 1.2 x lO-'to 0.4 x as the temperature of polymerization increased from 20" t o 200" C. The explanation offered for this decrease in K , value with temperature was that branch chaining occurs as the result of increasing the temperature of polymerization. The effect of variations in polymer size distribution under different conditions of polymerization might also be used to esplain these changes, Similar studies (8) of polyindene and hydrogenated polyindene, ranging in molecular weight from 570 to 6000, led t o K , values from 12 X 10-4 t o 1.6 X respectively. From these results Staudinger selected a Kmvalue of 1.8 X 10-4 to calculate the average molecular weight of both polystyrene and polyindene by measuring the viscosity of their solutions in benzene or Tetralin. using his well-known equation;
A
based only on ideal solutions, is so much lower than Staudinger's value, based on higher polymers whose solutions deviate widely from Raoult's law. I t is confirmed that the well-known Staudinger viscosity-molecular weight rule cannot be applied to different polymers. The Km value based on the or more than 300 per present work is 5.6 X cent higher than Staudinger's widely used talue ofi.8 x 10-4. A new Kcm equivalent for one chain atom is calculated for various polymers, based on the number of chain atoms in the base molecule, the Kern value, and the weight proportion of chain atoms to the base molecular weight. A wide variety of linear polymers gives Kcn equivalents ranging from 2.2 X 10' to 4.8 X lo4, depending on influences of solvent, side groups, etc.
The unsatisfactory nature of these and similar results on other polymers has been the basis for frequent adverse comment on the Staudinger viscosity method of determining molecular weights. I n fact, several investigators, including Staudinger, have recently placed increased emphasis on the osmotic method, since they are of the opinion that osmotic molecular weights are generally more reliable than those obtained from viscosity measurements, especially when applied to nonlinear polymers. One cannot subscribe t o this view, however, in the case of linear polymers, since numerous variables in the viscosity method have recently been cleared up (8), and the more reliable viscosity-molecular weight equation @),
based on the Arrhenius relation,
has been adopted. Futhermore, it is clear that the failure of solutions of high-molecular-weight polymers to obey Raoult's law results in osmotic molecular weight values which are inordinately high. For example, Staudinger and Fischer (9) obtained the value of 105,000 for the osmotic molecular weight of gutta-percha hydrocarbon in toluene. Their viscosity data, using the recently determined (2) K O , value of 0.75 X give an average molecular weight of 44,000, which checks our recent value for the same substance @). We have shown that gutta has a very narrow polymer size distribution; therefore, the values by the two methods can be directly compared. 1097
1098
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
Vol. 34, No. 9
The polystyrenes shown in Table I represent special fractions derived from liquid polystyrene % pf LOgl.. Cryoscopic A and therefore do not give complete distribution Original c In MOL Wt. in data, as all of the material is not represented. Polymer Material Benzene Benzene Method of Preparation A. liquid 100 0.127 .. Catalytic polymerization followed by The dimer content of AI was reduced to a small v a c w m dlatn. at 170' C . t o remove proportion by discarding the first alcohol extract, monomer and dimer AI liquid 14.6 0.093 292 Second cold CHaOH ext. from A leaving A I containing largely trimer. Az and As A* liquid 17.0 0.097 344 A dissolved in acetone CH30H added, represent trimer preparations containing increasfiltrate decanted frdm ppt., evapd.: ing amounts of tetramer. I n the case of Ac a washed with cold CHaOH very narrow fraction was obtained by first reAa liquid 12.7 0.10: 386 As rewashed with cold CHsOH moving the dimer and trimer by cold alcohol Aa solid 20 0.142 '08 3 2 ~ t ~ extraction m ~ and then ~ separating ~ ~an intermediate ~ ~ partially pptd. with CH80H. ppt: fraction, Ad, by fractional precipitation, which discarded: A4 pptd. b y addikon of more CHsOH was designed t o leave tetramer and pentamer in Aa solid 6 0.278 1200 A dissolved in acetone: higher po1ymt.r solution. The method of preparation and low fraction pptd. with CHaOH. percentage of Aj indicate that it has very narrow redissolved in acetone; p&dp\: addition of CHsOH distribution of polymer size. The present investigation indicates that material A consists largely of a mixture of polystyValues of 300,000 to 500,000 are usually reported for the rene homologs in the range of two t o twelve styrene molecules. osmotic molecular weight of crepe rubber in benzene or ' Material B4 is the second hot acetone extract which toluene, while the viscosity method gives a value of about followed two cold acetone extractions of a commercial lowmolecular-weight polystyrene &, Some data on these 105,000if based on the whole rubber ( 3 ) . The same situation exists in the case of other high polymers of the straight-chain extracts follow: type. L u .inBenzene Staudinger selected K , for polystyrene of 1.8 X Material based on cryoscopic measurements on polymers ranging in Commercial material B 3.01 molecular weight from 7000 to 13,000. It appears from our Bz (2nd cold acetone ext. of E1 2% e x t . ) 0.354 B4 (2nd hot acetone est. from dz residue, 3.5% ext.) 0.546 work on polyprenes ( 2 ) and polyisobutylene (4)that cryoscopic values for these polymers are likely to be too high due All materials were heated under high vacuum a t 100" C. to the probable failure of solutions of polystyrene in this t o constant weight to remove the last traces of solvent. I n molecular weight range to obey Raoult's law. Since Equation 2 will be used in the present investigation, the case of fractions Ai, Aa, and As, heating was a t 80" C. the K,, values ha.rrebeen calculated from Staudinger's data for until the loss in weight was a t a constant rate since these polystyrenein benzene and found to range from 0.34 X 104 to polymers had appreciable vapor pressures. 1.46 x l o 4 for molecular weights ranging from 500 to 13,000, HYDROGENATED POLYINDENE FRACTIONS. A colorless clear hydrogenated polyindene resin obtained from the respectively; the K,, for the previously mentioned indene polymers in benzene range from about 0.30 x 104 to 1.6 x 104. Neville Company was fractionated with the results shown in The authors' recent work (.2) showed that the high K,, value Table 11. A small amount of hydrogenated polycoumarin largely reflects the deviations in the cryoscopic measureis present, which cannot be over about 8 per cent as judged by the analysis given in Table 11. The presence of hydromerits with concentration, in the case of polymers with chain genated polycoumarin should have practically no effect on. lengths exceeding those which form ideal solutions. For example, in the case of a polyprene fraction, a cryoscopic the value of Kcm. molecular weight of 6000 was obtained a t 9 per cent concenDetermination of K O , $ration, whereas a t the usual 2 per cent concentration employed Staudinger' the was 149300' It 's then The viscosity and cryoscopic data for all polystyrene and readily Seen how Kc,, which is equal to M + (log w'c), polyindene fractions are given in Table 111. The cryoscop~c becomes inordinately high when it is based on such cryodata for polystyrene fraction at different concentrations in scopic measurements, made a t concentrations employed by benzene are plotted in Figure Deviation from Raoult'S Staudinger and his students. Since K , is calculated from lam is appreciable in the of fraction As, ( p P / C ) + M , it is also seen why it is too low when obtained in this fashion. I n view of this situation, the present investigation was undertaken to establish more reliable KC, values for polyTABLE 11. FRACTIOXATION OF HYDROQENATED POLYINDENE RESIN styrene and polyindene and t o determine the limit of molecular weight of polystyrene within which its solutions obey Log $I ;rl % of C Raoult's law. Solvent effects and fractionation methods FrgPt1 Treatment Benzene also constituted a part of this investigation. Only highly Original ......,..... 0.134 I 2.0 Cold alcohol ext. J3 extnQ 0.105 fractionated polymers were employed to determine the K,, I' 64.65 Residue from I dissolved in CaHa; 0.128 value on account of the large effect of polymer size distribufraction I11 separated b y pptn. with alcohol tion on cryoscopic results. I11 33.4a Precipitate from I 0.172 Materials ANALYSIS TABLE1. FRACTIONS FROM LIQUIDPOLYSTYRENE
g2i;$l
The starting polystyrene material, A , mas a liquid polymer obtained by catalytic polymerization; fractionation indicated that A consists largely of a mixture of polymers weight from about 300 to 1200' Data ranging in regarding the preparation and properties of various fractions prepared from this material are given in Table I.
Found fraction 11
~~~&$~$[~$~~,h
C
II
87.46 87.78
11.37 11.15 11.56
88.44
0 by Difference 1.17 1.07
..
Ratio,
H,'C 1.55
1.53
1.55
a Heated t o opnst+nt weight a t 150' C . under vacuum before using in cryoscopic and vlscoslty measurements.
~
0
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1942
1099
having a molecular weight somewhat in excess of 1000 and corresponding to a polymer chain of about twenty carbon atoms or one fourth the Concentration chain length causing deviation in the case of Base G./100 g. L x Cryoscopio Kern X polyprene (2) and polyisobutylene (3). CryoMol. Wt. 10-4 molal eolvent qr C A ? - Af Solvent scopic measurements on polymer fraction Bd were Polystyrene Fraction A I unsatisfactory when made in the usual manner, 0.32 0.95 ... ... 0.166 293 0.080 CsHe 1.92 0.333 295 0.32 0.159 since crystallization following supercooling re291 3.90 1:072 0:094 0.686 0.31 0.318 sulted in a temperature of more than 2' C. above 8.06 1.145 0.092 1.426 290 0.31 0.636 the freezing point of pure benzene. This also Polystyrene Fraction A2 occurred in the case of polyisobutylene polymer 0.94 .. . ... 0.137 352 0.36 0.079 CoHs 1.89 0,277 349 0.36 0.168 having a molecular weight of about 5000 (3). 1:072 0:096 0.582 3.86 338 0.35 0.315 Possible formation of a polymer-benzene complex 337 0.34 8.00 1.151 0.098 1.212 0.630 may explain this phenomenon. Although the Polystyrene Fraction As cryoscopic measurements in cyclohexane of frac393 0.95 ... . .. 0.124 0.38 0 080 C.Ho 0.36 1.92 0.260 379 0.159 tion B4did not show this effect, there was a slight 0.37 3.90 i:oie o:iO4 0.516 387 0.318 precipitation of the polymer on cooling which 0.37 8.06 1.167 0.105 1.069 386 0.636 may have influenced the results. The cryoscopic Polystyrene Fraction A4 measurements on benzene solutions of polyindene 0.95 ... ... 0,160 0.083 585 0.41 0,080 CnHe 615 0.43 0.160 1.92 behaved normally; and there appears t o be no 3.90 ilia7 o:i& 0.320 623 0.45 0.320 deviation in Raoult's law in this case up to a 8.06 1.240 0.146 0.881 607 0.42 0,640 molecular weight of about 1200, which was the 0.94 ... ... 0.301 633 0.44 0.070 CaHi2 1.89 0.594 644 0.45 0.140 highest polymer studied. 3.85 i:O95 o:iii 1.184 660 0.47 0.279 7.90 1.211 0,148 2.287 0.47 698 0.558 It is of interest to note that the K,, values of the lower polystyrene polymers agree with Polystyrene Fraction Aa similar data published by Staudinger (6) who 1.17 1.058 1300 0.51 0,254 0.046 0.097 CsHs 1220 2.35 1.123 0.260 0.194 0.099 0.47 obtained values for K,, of 0.34 X lo4 to 0.387 4.76 1.279 0.276 0.212 1150 0.42 0.280 0.471 9.92 1.649 1080 0.39 0.774 0.43 X lo4 for polymer fractions ranging in molecular weight from 438 to 595. Polystyrene Fraction B1 The data in Table I11 are plotted in Figure 2 0.94 1.105 0,546 0,015 3200a 0.080 0.59 CsHa 0.56 1.91 1.216 0.533 0,033 2960 0.159 to show the molecular weight dependency of 0.49 8.88 1.475 0.531 0.076 2610 0.317 8.03 2.148 0.524 0.178 0.44 2310 0.634 polystyrene fractions A1 to Ag, inclusive. 0.94 0.067 2830b 0.53C 0.070 CsHia Staudinger (6) accounted for the large devi1.89 1:iio o:iao 0.129 0.139 2960 0.56 ations in the K , values between the lower and 0.273 3.85 1.307 0.430 0.271 2870 0.54 0 555 7.90 1.772 0.446 0.504 3160 0.59 higher styrene polymers by the supposition that Hydrogenated Polyindene Fraction I1 an increase in chain length resulted from the end 1.17 0.089 672 0.50 CsHa phenyl group standing out in the direction of the 0 : 327 i:iog o:ih chain, which increased the chain length by two ib:io 1.247. 0.146 o:iia 750 0:51 0.664 benaene rings. It appears, however, from present Hydrogenated Polyindene Fraction I11 data on the effect of chain length on K,, that 1.15 . ... ... 0,052 ... 1130 CsHs 0.60 1190 2.32 0.100 0.63 this explanation of the increase in K,, with ... i:i& o:iii 0:321 molecular weight cannot be correct, since the 0:408 9.84 1.341 0.199 0.642 1Zio 0163 chain length of a trimer so constituted would Anomalous behavior; separate determinations varied as much a5 *15%. Rmults are average of several determinations. be more than twice that of a normal trimer b Solutions showed slight precipitation on aooling. Using average value for log w/C of CsHe solutions. where the phenyl groups stand out from the sides of the chain. DeBoer (1) presented evidence to show that the benzene rings in the polystyrene molecule take a perpendicular position with respect to the chain. The molecular weight dependency of K,,, shown in Figure 2, may be explained by the greater mobility of the lower polymers together with the increased influence of the end bonds with decreased chain length, thus increasing viscosity and reducing Kcm. If we assume the chain in a styrene trimer is I I I I I I I I I I TABLE111.
vISCOSITY-hCfOLECULAR W E I G H T OF POLYSTYRENE AND POLYINDENE FR.4CTIONS
0
0
Y
5 I I r
I
5
I
1
1
-- 1
-
J
.2 I
3
n
i
1 2 GRAMS
I
I
I
1
I
I
~
3
4
4
5
OF SOLUTE PER
7
0 7 8 9 10 100 GRAMS OF SOLVENT
FIGURE 1. EFFECTOF CONCENTRATION ON CRYOSCOPIC MoLECULAR WEIGHT OF POLYSTYRENE FRACTIONS I N BENZEKE 1. Fraction B4 2. Fraction As
3. Fraction A4 4. Fraction Ac
11
INDUSTRIAL AND ENGINEERING CHEMISTRY
1100. TSBLE
IV.
VISCOsrTY O F POLYSTYRESE FR.4Cl.IONS I N
Val. 34, No. 9
DIFFERENT SOLVENTS A S COMPARED WITH BENZENE Solvent
Fraction Unfractionated low polymer
Mol. Wt. 500
Ai polymer
GOO
Bd polymer
2,400
Commercial polystyrene
18,600
Commercial polystyrene
53,500
Polystyrene fraction
93,100
Polystyrene fraction
98,100
Solvent Benzene Chloroform CClr Benzene Cyclohexane Benzene Cyclohexane Benzene Chloroform CClr Benzene Chloroform
CClr
Benzene Chloroform CCla Tetralin Benzene Chloroform CCla Tetralin
made effectively longer by end bonds equal in effective length to the distance between two chain atoms, then K,, of the trimer would be 6/7 X 0.45 X lo* or 0.35 X lo4. which agrees with the experimental results. From the results of Staudinger and his eo-vorkers (8). K,, values were calculated for polyindene and hydrogenated polyindene up to molecular weights of 1600 and found to lie between 0.58 X lo4and 0.70 X lo4. I n the case of fractions with molecular weights between 2800 and 6000, the values rose from 1.2 X lo4 to 1.6 X lo4, respectively; probably this result was due to the failure of the higher polymer solutions to obey Raoult's law, thereby giving cryoscopic molecular weights which were too high. The K,, value selected for use for styrene polymers higher than the octamer is 0.45 X lo4. I n the case of the polyindene, a K,, value of 0.6 X lo4was selected as the result of analysis of the present data. Polyindene is believed to polymerize, at least in part, in large rings; therefore, one would expect its ICcm value to exceed that for polystyrene. The difference, however, is small and may be due to structural differences in the two 17ydrocarbons. If the molecular weight of the highest polymeric fraction of styrene described by Staudinger (6) is calculated using Equation 2 and a K,, value of 0.45 X lo4, the result is 180,000 instead of 660,000, calculated by the use of the Staudinger Equation 1and a K,, value of 1.8 X The value of molecular weight obtained from viscosity data is based on the assumption that only linear polymers are involved, whereas branch chaining and cross linking may result from certain polymerization reactions. Since viscosity measures the over-all polymer length rather than molecular weight, a K,, value established for linear polymers will yield molecular weights which are too low when applied to cross-linked or branched-chain polymers of the same base molecule.
Concn., Base Molal 0,800 0.800 0,800 0,640
0.558 0.317 0,273 0.0500 0.0504 0.0504 0.015 0.015 0.016 0.010 0,010 0,010 0.010 0.010 0.010 0,010 0.010
77
1 238 1.245 1.30i 1.240 1.211 1.475 1.307 1,606 1.600 1.561 1.509 1.480 1.419
1,612 1.560 1.492 1,577 1.651 1.613 1.531 1.GOO
C 0.116 0,119 0.145 0.146 0.149 0.531 0.426 4.13 4.05 3.84 11.9 11.3 10.1 20.7 19.3 17 f 19., 21.8 20.7 18.5 20.4
100 103 125
100 102 100 81
100 98 93 100 95 85 100 93 84 95
100 95 85 94
Staudinger and Heuer (10) studied numerous solvents to determine the relative viscosities of two polystyrenes having molecular weights of 1'7,500 and 43,300, using K,, of 0.45 X lo4. The ratio of the log q./C values to that for the benzene solution taken as 100, ranged from 90 to 105; as a whole, this indicated a remarkable freedom from solvent effects of any magnitude. The authors selected benzene as the most suitable solvent based on the data in Table IV, especially those data on highmolecular styrene fractions prepared by precipitation from commercial polystyrene having a n average molecular weight of 54,000.
Fractionation of Migh--Molecular Polystyrene High molecular polystyrene dissolved in benzene is not precipitated by the addition of acetone until a large proportion is added. Methyl alcohol, however, is a much stronger precipitating agent. I n Yiew of this fact, a mixture of equal volumes of acetone and alcohol was first employed to precipitate all but the lolvest molecular portion. The higher fractions were thrown out of solution by adding acetone in a quantity only sufficient for partial precipitation. Data regarding this fractionation are given in Table V. TABLE v. FRACTIOXATIOX O F HIGHPOLYMERIC
SPYRENE B Y
PARTIAL PRECIPITATIOX
L-,
% pf 111 Original Average Material Benzene h101. Wt.6 Polymer Original 100 12.0 54,000 Unpptd. materialb 0 2.85 12,000 Fraction I 57 14.1 63,500 Fraction IAC 15 20.7 98,000 Fraction 1A:C 11 21.8 98,000 a M = (log q r x 0.45 x I O ~ ) / C . b Fraction obtained by adding excess Precipitating agent following first partial precipitation of fraction I ; precipitate diaoarded and solvent evaporated t o obtain unprecipitated portion. 0 IA obtained bv Dartial nrecinitation of fractiun I: 1.41 obtained from IA in same mannei..
Solvent Effects The results in Table IV show that polystyrene up to 98,000 molecular weight is remarkably free from solvent effects and that numerous solvents can be used to determine its viscositymolecular weight. Cyclohexane is a poor solvent, probably accounting for the decrease in viscosity as molecular weight increases. Carbon tetrachloride shows this same effect to a lesser degree but forms solutions of low-polymer styrene having high relative viscosity when compared with benzene.
Staudinger's Viscosity-Molecular Weight Rule Staudinger (6) presented data on several polymeric hydrocarbons showing that, when their K , constants were divided by the number of chain atoms in their base molecules, a socalled K , equivalent constant varying from 0.75 X lov4 to 0.90 X was obtained. From these results he formulated a rule which stated, in effect,that the specific viscosity
INDUSTRIAL A N D ENGINEERING CHEMISTRY
September, 1942
of equal base molecular concentrations of different hydrocarbons of the same molecular weight is proportional to the chain length of the molecule. Using our data, which are relatively free from cryoscopic deviations, concentration effects, and solvent influences, the Km equivalent values in Table VI were computed and are compared with those based on Staudinger's data. TABLE VI.
which compares with the authors' value of 3.2 X lop4 for polystyrene given in Table VI. If the K,, equivalent to one carbon atom in the chain is calculated for various linear polymers, the following are some of the factors which need to be considered as influencing the results: 1. Molecular size distribution 2. Molecular weight level 3. Viscosity level
CALCULATED K , EQUIVALENT ON VARIOUS POLYMERIC HYDROCARBONS c---Km x 10-' '--Keg, x 104--Staudinger
Authors"
Staudinger
1101
4. 5.
Concentration effects Solvent effects
6. Number of chain atoms in the base molecules 7. Weight percentage of chain atoms t o total base molecular
Authorso
weight 8. K,, value of polymer in question 9. Distance between chain atoms 10. Structure of the base molecule (side-group effects) E
b c
Benzene used as solvent. Data for CzsHas. Km = 6.4 x 10-4 when molecular weight of polymer was 350.
It is seen, therefore, that our data do not support this Staudinger rule, and that if a fundamental basis for the viscosity-molecular weight relation exists, i t must be stated in some different way. Staudinger and Leupold (11) state that "chain-equivalent solutions of different hydrocarbons with fiber molecules of the same molecular weight in the same solvent have the same specific viscosity". If we compare chain-equivalent solutions of normal paraffin and polystyrene in benzene, each having a molecular weight of 14,000, the specific viscosities in the two cases are calculated to be 2.83 and 34.9, respectively, using a K,, of 2.4 X lo4 determined for octacosane and 0.45 X lo4 for polystyrene. The chain-equivalent concentrations are 14 and 52 grams per liter, respectively. It is obvious from these results that t h k rule does not apply or even approach compliance. TABLE VII. Polymer Tetradecane to octacosanea SameQ Paraffins .with side groupsb Squaleneb Polyprene Polyisobutylene
Same CzoH41 to CiaHe4
(CsHs)n
Polyethylene oxide dihydrateb Cellulose acetateb
H(CaH4O)nH
Cellulose nitrateb
[CeHiOs(NOz)s]n
a
Data to be published.
CALCULATED K,, EQUIVALENT OF VARIOUS LINEARPOLYMERS
Formula Cl4H80 to C2eHas
Polystyrene
ICeH7Os (CHsCO)a In
b
Table VI1 was prepared to evaluate some of these factors from our own data and certain data selected from Staudinger's work which appears to be most reliable. The effect of distance between chain atoms in the different polymers is in most cases relatively small and was therefore not considered. With the exception of the paraffins, the calculated K,, equivalent lies between 3.1 and 4.8. This is rather remarkable in view of the numerous variables which may influence the results. The average K,, equivalent per chain atom, not including the lower polyisobutylene or polystyrene polymers, is about 4 X 104. I n our series of measurements of normal para& hydrocarbons in benzene ranging from ClaH34 to C18H58given in Table VII, the K,, equivalent values decrease from 4.0 to 2.8, respectively, whereas the hexane solutions give a constant K,, value as the chain length increases. Judging from the K,, equivalent values in Table VI1 for the paraffins and polyisobutylenes in n-hexane, it is indicated
Mol. Wt. 198 to 394 Same 282 to 647
Solvent Benzene
Benzene Benzene Benzene n-Hexane n-Hexane n-Hexane Benzene Benzene Benzene Benzene
1485 to 106,000
Butyl acetate
5 Kcm
x 104 to 2.38 X 10 1.83 X 10' 2.44 x 104 to 2 . 6 4 X 104 0.66 X 10' 0.75 x 1 0 4 0 . 9 5 x 104 0.6G X 1 0 4 0.71 x 104 0.75 x 1 0 4 0.36 X 104 0.43 X 10' 0 . 4 5 x 104 1.1 x 1 0 4 0 . 2 1 x 10' 0 . 1 9 x 104 4.05
n-Hexane Benzene
410 1200 1080 358 456 1080 350 GOO 1180 800 to 1200 1150 to
3 ~ x 1 _"""
A No. Chain Atoms in Base Mol.
4 4 2
2
Dioxane 5
c
Wt Proportion,
Chain Atoms in Base Mol. 0.85 0 68 to
0.81
0.70 0.71 0.43 0.43 0.43 0.43
0.23
K c , Equivalent, (A X B)/C 4 7 x 101 to 2 . 8 X 10% 2 . 2 x 104
3.1 x
104 t o
3.3 8 X 6 X 10'10' 4 . 2 X 10: 4 4 x 1 0 3.1 X 10' 3 . 3 x 10' 3 . 15 x 104
3.7 x
0.23 0.23 0 91
3 . 9 x 104 3 6 X 104
0.22
4 . 8 X 104
0.21
4.5
x
10'
104
Staudinger's data.
Relation between IC,, Constants of Linear Polymers Since K,, is caloulated from the base molal concentration, the proportional weight of chain atoms to total base molecular weight of different polymers must be considered if some equivalent factor common to all linear hydrocarbon polymers is to be calculated. For example, paraffin has a base molecular weight of 14; therefore, each base molecule places 12/14 or 0.86 of its weight of carbon in its chain, whereas styrene has a base molecular weight of 104 and one base molecule places only 24/104 or 0.23 of its weight of carbon in the chain. On this basis alone the Staudinger K , equivalent for polystyrene would be (1.0 X 0.86) /0.23 = 3.7 X 10-4,
that polymers with side groups which increase the width of the molecule give higher K c , equivalents. The decrease in the K,, values for the normal paraffins in benzene as chain length increases was also in evidence in the case of polyisobutylene in the same molecular weight range. This is a special solvent effect and is discussed in connection with polyisobutylene (4). Staudinger's K O , values for polyprene, polyisobutylene, and polystyrene give KO, equivalent values of 5.2 X lo4, 6.5 X lo4, and 12,2 X lo4, respectively. These high values are mainly due t o the fact that the cryoscopic molecular weight data employed by Staudinger were obtained on polymer solutions which deviated widely from Raoult's law.
1102
INDUSTRIAL AND ENGINEERING CHEMISTRY
The agreement in the K,, equivalents lends considerable weight to the view that the viscosity method for determining the molecular weight of linear polymers is quite reliable when suitable solvents are selected and a reliable K,, value is employed. There still remains, however, a lack of certainty that in some cases a true molecular dispersion of the polymer exists in solution. I n the case of polystyrene, however, the fact that the same viscosity is obtained using different solvents is evidence that complete molecular dispersion probably is obtained. The question as to the reliability of the osmotic method as compared to the viscosity method for molecular weight determination cannot be finally settled a t this time. This is because the viscosity method is well established for the lower polymeric range, but its application must be assumed in the higher range of molecular weights where reliable independent methods are not available. Due t o experimental complications the osmotic method cannot readily be employed in the case of the lower polymers, and since the higher polymer solutions deviate widely from Raoult’s law, the results by the osmotic method are believed to be inordinately high. Outside the range of ideal solutions the molecular weight values obtained by the cryoscopic method are also too high, as shown in previous work ( 2 ) by the increase in the K,, value as the molecular weight increases.
Summary 1. The cryoscopic method is not satisfactory for polystyrenes containing more than twelve styrene units in the chain on account of the failure of their solutions to obey Raoult’s law.
Vol. 34, No. 9
2. The present work has established a new K,, value of 0.45 X IO4 for benzene solutions of polystyrene to be used in the equation,
A K,, value of 0.6 X lo4 has been similarly established for benzene solutions of polyindene. 3. Increased confidence in the viscosity-molecular weight procedure is derived from the data presented for the nenK,,equivalent covering a wide range of different polymers.
Literature Cited DeBoer, J H . , Trans. Faraday SOC.,32, 30 (1936). Kemp, A. R., and Peters, H., IND. ENQ.CHEM.,33, 1263 (1941) Ihid., 3 3 , 1391 (1941). Kemp, A. R. and Peters, H., unpublished work. Mark, H., and Raff, R., “High Polymeric Reactions”, Historical Discussion, New York, Interscience Publishers, 1941. Staudinger, H., “Die hochmolekularen organischen Verbindungen”, Berlin, Julius Springer, 1932. Staudinger, H., Trans. Faraday SOC.,32, 97 (1936). Staudinger, H., Ashdown, A. A., Brunner, M., Bruson, H. A. and Wehrli, S., Helu. Chim. Acta, 12, 934 (1929). Staudinger, H., and Fischer, K., J . prakt. Chem., 157, 19 (1940). Staudinger, H., and Heuer, W., 2. physik. Chem., A171, 129 (1935).
Staudinger, H., and Leupold, E. O., Helv. Chim. Acta, 15, 221 (1932). PRBBENTED before the Division of Paint, Varnish, and Plastics Chemistry at the 103rd Meeting of t h e AMBRICANCHEMICAL SOCIETY, Rlemphis, Tenn.
LEACHING CALCULATIONS A Note on the Graphical Method GILBERT FORD BINNEY Pratt Institute, Brooklyn, N . Y.
It is possible to transform triangular coordinates as used in leaching calculations to ordinary rectilinear coordinates, retaining the advantages of the triangular diagram and at the same time making the plot more flexible. The methods of calculation remain unchanged; the same straight line relations and material balances hold. The use of ordinary graph paper permits selection of scales more suitable for many calculations, particularly those for which extraction is nearly complete.
ROBABLY the most straightforward calculation of various leaching operations is the graphical method of Elgin (Z), related to similar methods for liquid-liquid extraction (3, 4). A triangular diagram is used, with the advantage that each region, path, and point has physical significance easily grasped. Material balances are indicated by lengths of the various line segments, and processes and changes are easily followed and visualized. These are all
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real advantages, particularly for the occasional user. A simple triangular diagram with calculations of a stepwise countercurrent extraction is shown in Figure 1. The graphical method of calculation in this particular case is seen to be somewhat unsatisfactory. The compositions and quantities give points and lines that are crowded together into a small area. Really precise graphical construction and evaluation become difficult. This same situation occurs in almost all cases where leaching is nearly complete and the solid product contains but little extractable matter. It has been pointed out that the crowding difficulty observed here and in similar cases can be partly overcome by working on an enlarged scale. Expansion of the scales on a triangular diagram is not without difficulty, however, for the diagram is inflexible by nature. For example, if a tenfold expansion of each coordinate were required (a not unusual case) and if the enlarged diagram were made from standard triangles pasted together, ten squared or one hundred triangles must be cut out and properly aligned. This is hardly a convenient procedure. The equilateral triangular diagram is but an adaptation of oblique coordinates for a particular purpose. Two independent variables only are involved, for the third quantity can always be found if the other two are known. Since oblique
