Cryoscopic Determination of Number-Average Molecular Weight by Quartz Crystal Thermometry John S . Fok, John W. Robson, and Flora C. Youngken' Central Research Dept., Experimental Station, E. I . du Pont de Nemours and Company, Wilmington, Del. 19898 Application of a quartz thermometer to the cryoscopic determination of Mn,50-2000, has resulted in a simple, rapid method yielding results with a relative error of +2-3%. The sensitivity and high resolution (1 x 10-4 "C) features of this tool permit precise evaluation of freezing point by the steady-state technique applying exact procedural specifications. Design of an appropriate freezing point assembly is described. values are obtained from a test solution Accurate considerably less concentrated than ordinarily specified using a single charge of sample. Solvent interchange requires only a minor adjustment. Solvent purity and solution equilibria are evaluated, and unstable materials create no problems. Representative data substantiate the numerous advantages and analytical accuracy resulting from these innovations. The method is especially suitable where sample supply is limited and sample type random.
m,
QUARTZ CRYSTAL THERMOMETRY has been applied to the cryoscopic determination of number-average molecular weight Accurate values for the range, 50-2000, are obtained. Our apparatus has been in operation for approximately four years and an appreciation of its practicality and potential continues. A change in the cooling-bath temperature is the only minor adjustment necessary for quick solvent interchange. Our method is especially suited for evaluation of solvent purity and solution equilibria. It is geared to supply M,!values speedily for sample types submitted at random. Ordinarily, a satisfactory determination is accomplished by examination of one optimum solute concentration for M n
\&,
(1)
Under identical conditions, the of an unknown in the same Solvent is obtained. an= KaPDFP X wt of sample (mg) (2) AT X wt of solvent (g)
H.Rodehush. J. Phys. Chem., 32, 109 :9) Ref. 7, Chap. I, IV.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
39
EXPERIMENTAL
Apparatus. Details of the freezing point assembly are illustrated in Figure 2. It consists of the following: 2 airbath tubes ( A ) , one mounted permanently in the cooling bath and the other to hold the FP tube and accessories at standby (see Figure 1); FP tube ( B ) ; desiccant chamber (C); nitrogen vent attachment (D); stainless steel stirrer ( E ) ; three-hole split Teflon (DuPont) stopper with two guide pins to recombine the stopper and two W o n (DuPont) O-rings as fasteners ( F ) (G); Quartz Crystal Thermometer (QCT), H-P Model 2801A (H)along with Digital Recorder, Model M84562A (see Figure l), Dymec Division, Hewlett-Packard Co., Palo Alto, Calif. Mechanical stirring is accomplished by a Cenco stirring motor (Central Scientific Co., Chicago, Ill.) ( I ) attached by a two-way stopcock to a vacuum line permitting fast change from a stirring rate of one stroke per second prior to seeding to two-three strokes per second after seeding. Retooling of part ( J ) reduces vertical length of the stirring stroke by approximately inch to adapt stirring stroke to FP tube dimensions. Refrigerated and heated baths with circulators and thermoregulators designed to control bath temperature within less than 20.03 "C from approximately -18 to +50 "C in an ambient of 24 "C have fulfilled our needs (Forma-Temp. Jr., No. 2095, Forma Scientific Inc., Marietta, Ohio). Sample Handling. A Parr pellet press (Parr Instrument Co., Moline, Ill.) is used to produce pellets of a solid sample of lis- or 1/4-inch diameter. A sample of high viscosity is manipulated on a split half of a cover glass, approximately a/4 inch square. A liquid sample is transferred from a microdropping bottle or a microsyringe. Calibrated automatic pipets with Teflon stopcocks, 15 ml and 20 ml, are used for delivery of solvent. Routinely, the method calls for the use of 15 ml of solvent pipetted directly into the FP tube but optimum handling of an unstable sample could require final aliquoting from a previously prepared 20-ml volume of desired solute concentration. Standards. Benzil (analytical reagent, Eastman Organic Chemicals, Eastman Kodak Co., Rochester, N.Y.) is used with benzene, dimethyl sulfoxide (DMSO), p-dioxane, and 100% acetic acid. Anhydrous dextrose and ammonium sulfate (analytical reagent, Mallinckrodt Chemical Works, N.Y.) are used with water and 100% sulfuric acid, respectively. These reagents are prepared in appropriate size pellets, dried 1 hour in a vacuum oven at 60 "C, and stored in a desiccator over "Tel-Tale" silica gel. Solvents. Benzene (B & A, General Chemical Division, Allied Chemical Co., Morristown, N.J.) is purified by refluxing with excess phosphoric acid anhydride under nitrogen for 10-12 hours, Subsequent distillation under nitrogen yields solvent, FP 5.53 "C. Dimethyl sulfoxide (Chemical Packaging and Sales Co., Wilmington, Del,) is purified by shaking 2-3 hours with approximately 1 cm depth of basic, activity grade 1, aluminum oxide (Woelm, Eschwege, Germany) added to a pint bottle of the solvent as received from the vendor. It is then filtered by decanting into a fine sintered glass funnel containing an approximately 1-cm layer of Woelm neutral, activity grade 1, aluminum oxide reagent. The latter operation is performed under a dry nitrogen atmosphere. p-Dioxane (spectroquality, Matheson, Coleman and Bell, East Rutherford, N.J.), FP 11.7 "C, is used as received from the vendor. Procedure. The digital recorder is set to print every 15 seconds and a record of the latter phase of cooling, the seeding temperature, and a minimum of 19 readings after the maximum observed temperature after seeding are printed for each FP run. A specific FP is the numerical average of the SST series as previously defined. The following conditions are used for an R,determination in benzene. The cooling bath is maintained at 3.1 2 0.03 "C, 40
approximately 2.5" below the F P of this solvent. From numerous trial conditions, 4.40 + 0.01 "C (1.1" below the FP of benzene) was chosen as the optimum seeding point. Under a dry nitrogen atmosphere, a 15-ml aliquot of solvent is pipetted into the F P tube and the Teflon stopper and combined accessories are immediately seated in the tube. A source of nitrogen with flow sufficient to maintain a pressure equivalent to approximately 10 cm of mercury at the outgoing vent is attached. The FP tube is cooled rapidly to approximately 8 "C by immersion directly into the cooling bath. The outside of the FP tube is carefully dried and positioned in the air-bath tube. Stirring is maintained at one stroke per second with the Cenco motor until the seeding temperature is reached. The motor is then stopped. The screw holding the stirrer is loosened, and rapid, manual, vertical manipulation of the stirrer for 15 seconds produces seeding. Mechanical stirring is resumed at an increased rate of 2-3 strokes per second until sufficient temperature output data have been accumulated by the recorder. The stirrer is disconnected and the FP tube removed from the air-bath tube and placed intact in the storage tube. When possible, sample weight is selected to give approximately a 0.1 O FP depression. If the sample is a powder-type, it is now added as a pellet to this same aliquot of benzene. When dissolution is complete, the solution temperature is readjusted to approximately 8 "C, the F P tube is replaced in repeated to obtain the air-bath tube and the procedure isa F P value for the sample solution. M, is calculated by Equation 2 using a K,,, F~ value obtained for benzil by this identical procedure. RESULTS AND DISCUSSION
The K,,, F1> for benzil in purified benzene is 5.42 and the standard deviation (u) is 0.036. Respective values for DMSO are 4.42 and 0.063. In each case, these represent 20 calibrations with several different lots of purified solvents during a recent period of three months. Other representative Ka,, FP values are 3.7 for 100% acetic acid, 2.0 for water (dextrose), 5.2 for p-dioxane (benzil) and 4.8 for 100% sulfuric acid (ammonium sulfate). K,,, FP for (NH4)&04is calculated on the basis of four osmotically active ions. 2(NHi)zS04
+ (n + 2)H2S04 2(NH4)(HsSOJ,+
K,,,
FP
+ 2HSOa-
AT X 132.15 X wt of solvent (8) wt of (NH4)*S04(mg) X 4
(3) (4)
The method of Gillespie et al. (10) for the preparation of 100% sulfuric acid is accomplished efficiently. The literature value of FP 10.35 "C is confirmed by the QCT. The advantage of observing actual temperatures with a QCT applies equally to the evaluation of 100% acetic acid, FP 16.60 "C. A detailed study of the behavior of benzil in benzene yielded the results in Table I. These data project a composite appraisal of the capabilities of our method. The validity of establishing a F P from the SST series, justification for our specification for an optimum AT, the small amount of material required, the numerical effect on and K results with concentration, and the precise control and reproducibility of the F P of solvent are projected. The widening in range of the temperatures in the SST series coincidental with increase in concentration realistically demonstrates departure from "ideality." (10) R. J. Gillespie, E. D. Hughes, and C. K. Ingold, J. Chem. Soc., 1950,2473-92.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
Table I. K Results for Benzil in Benzene with Cross-Check of M,, Values for Benzil Bemil MW, 210.22 Cooling-bath temp, 3 . 1 =t0 . 0 3 "C Benzene 15 ml = 12.94 grams Seeding temp, 4.40 4~ 0.01 "C Incremerit,
(4
Wti
mg
ZWti -_
Concn
81
ATi
K*PPFP-
ZATi
"C x 10-2
g
SST drift,a
ATi
ZATi
...
"C X
zrl (K # 1 and
ATi) 1 2 3
48.98 47.94 18.12
1 2 3 4
95.64 16.24 18.96 22.28
...
96.92 115.04
3.79 7.49 8.89
9.82 9.52 3.70
19.34 23.04
5.45 5.40 5.55
11'1'.88 130.84 153.12
7.39 8.65 10.11 11.83
19.14 3.35 4.01 4.91
22:49 26.50 31.41
5.44 5.61 5.75 5.99
-
M" (K # 1
Re1 error,
Re1 error,
and
z
z
ZATi)
...
,..
...
...
5.43 5.45
1.5 2.8 6.7
212.1 206.3
+0.89 -1.88
211.1 210.3
+0.40 $0.03
3.4 5.8 12.8 28.5
...
...
...
5.47 5.51 5.62
203:8 198.8 190.8
-3.05 -5.44 -9.25
209.1 207.6 204.9
-0.51 -1.26 -2.51
Difference between highest and lowest temperature of SST series.
Table 11. Dextrose MW, 180.16 DMSO 15 ml = 16.36 grams Total Wt. Wt. mg
..
Benzil 1. Dextrose 2. Dextrose 3. Dextrose . . . Dextrose a See footnote, Table I. ,
... ...
91.05 72.48 28.56 23.83 147.06
101.04 124.87
...
E,, Results for Dextrose in DMSO Cooling-bath temp, 1 5 . 1 =k 0.03 "C Seeding temp, 17.64 + 0 . 0 2 "C AT "C x 10-2 11.72 10.85 16.52 21.30 23.41
The use of DMSO is restricted to samples which cannot be examined in any other solvent or by another M, method. We have found no better purification procedure than the one previously described. Table I1 illustrates the behavior of dextrose in this solvent. This example indicates the possible consequences with its indiscriminate use. With a freshly prepared dextrose solution yielding a AT (0.1 "C) of the same magnitude as for the benzil standard, an M,,very close to theory was obtained. Successive additions of sample to this original solution produced nonlinear values. Also, a freshly prepared dextrose solution, estimated to yield a AT double the amount that previously was satisfactory, yielded a result outside the accuracy limits we assign to our method. With DMSO, it is essential to duplicate AT values for unknown and standard within a much narrower range than is necessary with benzene. These data indicate degradation in DMSO relative to time as well as demonstrate evidence of a more pronounced molecular activity in a DMSO system than has been noted with benzene. Table 111 lists representative results. Compounds at various M, levels, different cryometric solvents, and various standards are presented in these data. Most values agree within 2-3 of theory, and each is the result of a single determination for Mn. Recognition of the influence of impurity, water and/or extraneous solvent on an M n result must be emphasized. These effects become more acute with increase in molecular weight. With polymers, the presence of small amounts in terms of weight per cent of low molecular weight molecules can completely dominate an M, value (11). Solvents degassed by a series of freeze-evacuate-thaw cycles are used when samples are unusually sensitive. The following
a,&
(11) I. M. Kolthoff et al., "Treatise on Analytical Chemistry," Interscience,New York, N. Y., 1968, Part 1, Vol. 8, p 5022.
OC
SST
-
drifta
M, Found
x 10-3 11 .o 12.8 20.3 36.4 42.1
KSPPFP
z
...
4.43
... ... ... ...
Relative error,
180.89 165.62 158.74 170.10
+ 0.41 -
8.07 -11.89 - 5.58
procedure permits evaluation of air- and/or moisture-sensitive compounds and samples otherwise unstable under optimum conditions using degassed solvent when oxygen- or carbon dioxide-sensitivity is recognized. One can assume that the established F P for a solvent and its appropriate K value are precisely reproducible. Solutions of samples of these types are prepared in an appropriate concentration in a container other than the F P tube in a dry box. In these cases, operations are performed in a more sophisticated type of dry box than is routine equipment in most laboratories as for instance, Dri Train (HE-193-2), Vacuum Atmospheres Corp., 7356 Greenbush Ave., North Hollywood, Calif. Later, still in the dry box, an aliquot can be sealed in the FP tube with the QCT and accessories in place. This procedure is equally advantageous for a sample that is slowly soluble or highly colored where a safety margin of time is required to assure complete dissolution in an ordinary dry box, if the sample is an inert type. With foresight, an analyst can continue operation of the equipment with other determinations while awaiting resolution of problems of solubility. Polymers at low degrees of polymerization are the most frequently encountered sample type for the M,,range, 10005000. N o problems have been attributed to our referencing all unknowns in the range applicable to this method, to standards around the 200 molecular weight level. Nevertheless, for purposes of evaluation and coordination of all molecular weight determinations based on colligative properties, we have investigated the possibilities of verifying standards of higher molecular weight, particularly materials representative of polymeric behavior. M,,results for three polystyrene samples (designated as standards) by our subject method and by our ebullioscopic (BP) and vapor pressure osmometric (VPO) procedures are listed for comparison in Table IV.
a,,
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
41
Table 111. Representative
E,,Results by Cryoscopy
-
M,
Solvent
Sample
Theory
Standard
(“a)zS04
H2O
Dextrose
CF3COOH
100%
(“4)2SOa
132.15 2 114
CaH6
Benzil
C6He
Benzil
mo-r
(12)
Found
Relative error, %
63.52
-3.87
116
+1.75
150
152
$1.33
224
221
-1.34
~
0-CH,
S
C6HsCHz-S-P
II/
Fa
\
F Pd(CH3COO)z 100% CHaCOOH Benzil 225 227 -0.88 BioHioSCOCsHs* CeH6 Benzil 274 272 -0.73 274 215 +0.36 BioHioSCoCsHb* DMSO Bend 288 294 +2.08 Benzil C~&bzSz~ (13) c6H6 410 417 $1.71 Benzil (COCuOOCCF3)z‘ C6He [CH3(CHz)3CHzlaPb (14) C6H6 Benzil 491 489 -0.41 Ethyl ester of Kel-F acid 8114” Benzil 508 501 -1.38 p-dioxane Benzil 629 618 -1.75 [(ceH d3PlzC~B3Hd CeH6 Benzil 723 698 -3.46 H2Fe[P(OC2H&14 (15, 16) c6H6 N~[P(O-O-C~H~CH~)~]~Bc6Hs Bemil 1116 1145 +2.60 a , b , d , f , Compounds ~ synthesized in these laboratories by H. W. Roesky, W. R. Hertler, C. W. Alegranti, F. Klanberg, and L. W. Gosser respectively. 1,IO-Dithiocyclooctadecane was prepared by R. T. Uyeda. e Kel-F acid 8114,ClCF2CFClCFzCFC1CF2CFC1CFzCOOH, The M. W. Kellogg Co., Chem. Manufacturing Division, Jersey City, N. J. Ethyl ester was prepared by T. A. Ford.
900-Special
Table IV. M, Values for Polystyrenes Standard, benzil. Solvents, benzene, toluene* Cryoscopy M, Supplier“ Concn MI% data sheet by wt Found 1050 f 105 1.79% 1030 1.77
2030-12a
2050 i 170
4ooO-1la
3690 f 365
1045
1.64% 2.54 3.27 4.91 2.46% 3.27 4.91 7.37
1525 1540 1425 1525 2693 2634 2513 2464 2900
concn
VPOb
Ebullioscopy - concn
-
concn
M*-o Found
M, d Found
1270 1240 1270* 1777 1856 1920 1950* 4160
1130 1110
o
1640 1590
3465
-0
a
Pressure Chemical Co., Pittsburgh, Pa., Data Sheet No. 107/108,109jll0, March 1966-M, reported as an average.
* Hewlett-Packard Model 302 Vapor Pressure Osmometer at 37 “C.
Each BP @, value is based on data from six successive sample additions to solvent not exceeding a final solute concentration of 5 % by weight, extrapolated to infinite dilution. Each VPO result is based on four separately pre-
(12) H. E. Simmons and T. Fukunaga, J . Amer. Chem. Soc., 89, 5214 (1967). (13) A. Muller, E. Funder-Fritzsche, W. Konar, and E. Rintersbacher-Wlasak, Monatsch, 84, 1207 (1953). (14) G. Singh, J. Orgunometal. Chem., 11, 140 (1968). (15) F. N. Tebbe, P. Meakin, J. P. Jesson, and E. L. Muetterties, J . Amer. Chem. Soc., 92, 1069 (1970). (16) P. Meakin, L. J. Guggenberger, J. P. Jesson, D. H. Gerlach, F. N. Tebbe, W. G. Peet, and E. L. Muetterties, ibid., p 3482. 42
0
pared solutions, also with highest concentration not exceeding 5 % by weight and all data extrapolated to infinite dilution. Each cryoscopic R, result for the 900-Special polystyrene represents a single charge of sample. Freezing points were established by our routine SST procedure. For the two higher molecular weight polystyrenes, freezing points were considered the maximum temperature after seeding and R, was calculated individually for each solution of the strength specified. In these cases, concentrations were obviously beyond proportions where calculation from our SST series could be justified. For the polystyrene 2030, within the concentration range examined, %, values did not appear to be concentration dependent. The value for extrapolation of all data to infinite dilution for the polystyrene 4000 is included.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
Screaton and Seemann (17) reported detailed studies on polystyrenes from this same source while searching for reliable standards for gel permeation chromatography. Their data indicated that the nominal molecular weight values of this supplier might be incorrect in some instances. Their fractionation studies of individual polystyrenes and molecular weight results from these fractions, as well as their detection of a range in glass transitions within a given sample, showed the dissimilar composition of their material. This evidence could possibly explain our discrepancies in reproducing M n values among our subject methods. Our results appear to indicate increases in M, values with rise in the level of solvent temperature germane to the particular method, and an association effect appears to be demonstrated. These data illustrate the dilemma of an individual researcher facing the uncomfortable choice of which R, value to apply to each standard
when evaluating his own particular method. At this level of molecular weight, there is grave need for dependable calibration standards, particularly materials of narrow molecular weight composition. The overall result of our adaptation of a QCT to this determination is a well standardized procedure with specifications for apparatus and technique easily duplicated. Not only is demand on sample supply minimal but, since routine determinations are accomplished with a single concentration, analysis time is greatly reduced. Precise, accurate values can be obtained without resort to intricate calculations. The fortuitous achievement of a substantial reduction of solute concentration produces with a single charge of sample, an M, value comparable to one from the results of a multiple concentration study, extrapolated to infinite dilution.
(17) R. M. Screaton and R. W. Seemann, Appl. Polym. Symp. 8 , 8 1-1 10, (1969).
RECEIVED for review August 26, 1970. Accepted October 1, 1970.
a,
Accuracy of Analysis by Electrical Detection in Spark Source Mass Spectrometry R. A. Bingham and R. M. Elliott AEI ScientiJic Apparatus Limited, Barton Dock Road, Manchester, England The precision and accuracy of Spark Source Mass Spectrometry using electrical detection of the resolved ion beams has been critically examined. Rapid scanning of the spectrum using a logarithmic ratio amplifier system gives a survey of all elements present in the sample within a few minutes. The precision achieved in this rapid survey is shown to be better than 35% for concentrations down to below the 1ppm atomic level. Precision of 2% for any chosen elements is achieved using the more accurate peak switching technique down to 1 ppm. The limits of detection are 0.001 ppm atomic for the peak switching technique and 0.01 ppm for scanning. Automatic spark discharge control has been developed permitting unattended operation for long periods and giving improved reproducibility. The absolute accuracy of the peak switching technique has been assessed using standard steel samples. The mean difference between the observed and quoted values was 4.2% for impurities in the 5002500 ppm range.
SPARKSOURCE MASS SPECTROMETRY has been for some time an established technique for the chemical analysis of impurities where trace concentrations are involved or for a survey analysis of all possible impurities ( I ) . The combination of extremely high sensitivity and overall element coverage makes it unique among analytical methods. In this paper significant advances in the precision and accuracy of the technique are reported. The most widely used detector in the past has been the ion sensitive photographic plate, which effectively integrates the fluctuating ion currents produced by the spark discharge; in addition it can record all the elements from mass 7 to 240 (1) A. J. Ahearn, “Mass Spectrometric Analysis of Solids,” Elsevier, Amsterdam, 1966, p 5.
in a single exposure. These features made the photographic plate a natural choice initially. However, its use is timeconsuming and far from convenient, its linear range is only about 30 to 1 , and its precision is limited. The basic precision of the emulsion itself is usually estimated to be of the order of 3 - 6 z ; Franzen and Schuy (2) have obtained relative standard deviations of 2z but under a strictly defined routine of exposure, development, and measurement. By contrast the electron multiplier is routinely used for isotopic abundance measurements to 0.1 precision, and the output is immediately accessible in convenient electrical form. Thus, it was natural to investigate the possibility of using the electron multiplier as detector for spark source mass spectrometry; it offered not only improved precision and greater speed and convenience of analysis but also the opportunity for much easier investigation of the other remaining causes of irreproducibility. Factors such as spark parameters and accelerating voltage had been shown by Halliday et al. (3) to affect precision, and both Bingham et al. ( 4 ) and Svec et a[. ( 5 ) have shown that electrode position was critical. Once these factors were recognized and controlled, the reproducibility improved and analysis could be made with a precision of 5-20z:. Removal
z
(2) J. Franzen and K. D. Schuy, Z . Anal. Chem., 225,295 (1967). (3) J. S. Halliday, P. Swift, and W. A. Wolstenholme, “Advances in Mass Spectrometry,” Vol. 3, E. W. Mead, Ed., Institute of Petroleum, London, 1966, p 143. (4) R. A. Bingham, R. Brown, J. S. Halliday, P. Powers, and P. G. T. Vossen, International Conference on the Characterization of
Materials, Pennsylvania State University, University Park, Pa., November 1966. ( 5 ) H. J. Svec, R. J. Conzemius, and G. D. Flesch, 15th Annual Conference on Mass Spectrometry, ASTM E14, Denver, CO~O., May 1967.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
43
