REFRACTIVE INDEX INCREMENT OF POLYSTYRENE IN SOLUTION
Sept., 1959
1435
TEMPERATURE DEPEKDENCE OF THE REFRACTIVE INDEX INCREMENT OF POLYSTYRENE I N SOLUTION BY J. H. O’MARAAND DONALD MCINTYRE Nalional Bureau of Standards, Washington, D.C. Received February 11, lg6B
The refractive index increments of polystyrene in cyclohexane and in toluene have been determined interferometrically as a function of temperature. The experimental results have been found to be in good agreement with calculations based on the Gladstone-Dale rule when the liquidus state curves for the refractive index and specific volume of polyst rene are extraoolated below the glass transition and then used to calculate the refractive index increment for temperatures {elow this transition.
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Introduction
Experimental
An accurate evaluation of the refractive index increment, dn/dc, of polymer solutions a t various temperatures has become increasingly important for several reasons. The square of this quantity occurs in equations used to derive molecular weights and virial coefficients from light-scattering data. Experimental work is often conducted to test the predictions of polymer solution theories by determining the increase of the size of the molecule in a poor solvent while increasing the temperature. Also, an increasing amount of work is being conducted on new polymers a t higher temperatures where the refractive increments have not been determined. Furthermore, many workers are using relative instruments to determine these increments, and the optical constants of these instruments are not easily established as a function of temperature. The need to know the temperature dependence of dn/dc arose as a result of work to determine the virial coefficients of polystyrene in cyclohexane a t different temperatures. Earlier experimental work’ had indicated that there was no temperature variation, although a temperature dependence had been assumed and used by some investigator~.~,3Table I lists some calculated (c) and measured (M) values obtained by the previously-mentioned investigators and also by Outer, Carr and Zimm.4 These somewhat divergent results led us to examine another solvent, toluene, in addition to cyclohexane, over a wider temperature range because of its higher boiling point and its better solvent power. Both of these solvents are easy to handle, can be obtained “pure” and have well known physical constants. I n addition, they have a relatively large refractive index increment with polystyrene. Literature data on the temperature dependence of dn/dc for polystyrene-toluene are not available, although the actual dn/dc values reported in the literature vary from 0.118 to 0.108 at 436 mpbJ and 0.108 to 0.104at 546 mp4Jwave length of light near room temperature. Actually these values are in relatively good agreement as compared with the values reported for systems’ involving polar solvents and macromolecules.
Materials.-Two separate fractions of polystyrene8 were used in this investigation. Fraction I was prepared by thermal initiation and had a molecular weight of 34,500. Fraction I1 was prepared by benzoyl peroxide initiation with the aid of a mercaptan transfer agent and had a molecular weight of 50,000. When the olymers were dried above the glass temperature for several Rours they were found to contain less than 0.5% residual solvent from freeze drying. The solvents used were ACS reagent-grade samples of cyclohexane and toluene. Before use they were fractionally distilled in columns packed with glass helices. The toluene was distilled over sodium. The refractive indices of both solvents as measured with a dipping refractometer at 30’ checked with literature values. Interferometer.-A Hilger Rayleigh Interferometer was used to determine the refractive index increment. The instrument had been modified so as to contain a special thermostatting compartment which could accommodate not only the usual cells but also Rome special all-glass fused cells used for volatile liquids. The cell used in the present investigation was a 1-cm. cell provided by HilgerB which had fused glass joints throughout. When in use, the cell was covered by glass plugs to prevent evaporation. Originally, a 1-cm. cell was used that had been cemented together with polyvinyl alcohol, but the results obtained with toluene in this cell were erratic, probably because of pick up of water by the toluene from the polyvinyl alcohol. The monochromatic source of radiation was provided by an AH-3 mercury lamp manufactured by the General Electric Company. The monochromatic light was filtered by a Corning filter combination of No. 3484, 5120 and 4303 for the 546 mfi line and a combination of No. 3389 and 5113 for the 436 m s line. The white light was furnished by a 100watt projection bulb. Techniaue.-The achromatic band shift can came a problem with -organic materials where the dispersion of t6e organic solute is markedly different from that of the glass compensating plates. This problem is easily resolved, however, if enough time and care are taken to work with sufficiently dilute solutions so that the shift of one band is drastic enough to cause severe changes in the calculated refractive index increment. Once the location of the true refractive index increment is known, the accuracy of the determination may easily and judiciously be increased. The accuracy of the measurement reported here is =!=2 X 10-6 units of refractive index. I n other routine work in these laboratories, the location is often made by means of a differential refractometer. All solutions were prepared independently on a weightpercentage basis, and the concentration at each temperature waa determined in grama per deciliter by multiplying the weight concentration by the density of the solvent at the temperature in question. The concentrations ranged from 0.05 to 0.6 g./dl. Three to five solutions were measured at each temperature. In determining the temperature dependence of the dn/dc, the solvent and solut,ions were measured at one temperature, then the thermostat raised to a new temperature, and fresh samples of solvent and solutions measured. The temperatures in the cell were measured by means of a thermocouple. In one experiment the dn/dc of a 0.3 g./dl. solution
(1) W.
R. Krigbsum and D. K.Carpenter, THISJOVRNAL,69, 1166
(1955).
H.-J. Cantow, 2. phyeik. Chem. (Frankfurt), 7, 68 (1956). (3) N. T. Notley and P. J. Debye, 3. Polymer Sci.. 17, 99 (1955). (4) P. Outer, C. I. Carr and B. H. Zimm, J. Chem. P h y s . , 18, 830 (1950). ( 5 ) W. R. Krigbaum and D. K. Carpenter, Ibid.. 24, 1041 (1956). (6) H. P. Frank and H. F. Mark, J . Polymev Sci., 17, 1 (1855). (7) C. I. J w e and A. B. Biawas, ibid., 27, 576 (1958). (2)
W.
(8) D. MoIntyre, J. H. O’Mara and B. C. Konouck, J . Am. Chem. Soe., 82, 3498 (1959). (9) E. Grunwald and B. J. Berkowits, Anal. Cham., 29,124 (1867).
J. H. O'MARAAND DONALD MCINTYRE
1436
Vol. 63
TABLE I REFRACTIVE INDEX DATAFOR POLYSTYRENE-CYCLOHEXANE SOLUTIONS 546 m p light (dn/dc)aoo
Ref.
(dn/dc)rao
1 2
0.173(c) .1695(M)
0.173(M) .174(c)
3 4
436 m light (dn/dcYd
(d/dl) (dn/dc)
(dn/dc)ao
OW)
0.183(c) .181(M)
2 . 8 X 10-4(c)
(d/dt) (dn/dc)
0.183(M) OW) .185(c) 3.0 x 10-4(~) 184(c) Av. 3 . 8 X lO-'(C)
.170(c)
of polystyrene in cyclohexane was determined from 30 to 55" after a separate determination of the solvent zero band position. The result,s in this case were identicnl with the others.
Results Table I1 summarizes the data obtained on refractive index increments for both the 546 and 436 mp wave lengths of light and for both fractions of polystyrene in cyclohexane and fraction I in toluene. The values for d/dt(dn/dc) represent the least squares slope and its standard error. Figure 1
TABLE I1 REFRACTIVEINDEX DATAFOR POLYSTYRENE SOLUTIONS Polystyrene-Cyclohexane I
Fraction Light, mp 28.9' dn/dc 34.0 38.6 53.5 (d/dt) (dn/dc)
546 0.1689 .1705 .I719 ,1765 (3.08f 0.04) x 10-4
I1 546 0.1693 .1703 .1715
436 0.1798 ,1810 .1823 .1884
(3.582= 0.29) x 10-4
2.3 X
10-4
Polystyreiie-Toluene 0 CYCLOHEXANE
01850
0.1800
0.1 150
dn. dc
Fraction Light, mp a1.20 dn/dc 28.9 38.6 58.0 79.4 (d/dt)(dn/dc)
I 546 0.1068 ,1089 ,1122 ,1185 ,1226 (2.89 =t0.14) x 10-4
0.1750
+
0.1100
R = W~RI WZR~ 0,1700
I
I
I
I
1
50
60
70
80
90
0.1650
OlOOOL
436 0.1109 ,1126 .1168 .1242 ,1280 (3.21 2= 0.25) x 10-4
' 20
I
I
30
40
I
T "C.
Fig. 1.-Refractive index increments at 546 mp wave length of light for polystyrene fraction I in cyclohexane and in toluene a t various temperatures.
shows these data in graphical form for fraction I in toluene and in cyclohexane for light of 546 mp wavelength. From observations in this work using simple glass cell covers it appears that any measurements of the refractive index increments that are made without adequate closure of the compartments to prevent creep or volatilization should be viewed with skepticism. In addition, solvents that have been thoroughly dried during preparation can give very misleading results because they are prone to pick up water during the course of the measurements when the cells are not thoroughly closed.
Discussion The specific refraction of the mixture of two liquids may be successfully represented in many cases by the sum of their respective specific refractivities.IO The representation of the specific reactivity R of a material by the expression (n - l ) / p , where n and p are the refractive index and the density, respectively, is known as the Gladstone-Dale expression. If the summation of these refractivities is to be made on the basis of the volumes occupied, or mathematically on the basis of their weight fractions w, then the Gladstone-Dale rule for the refractivity of a mixture may be represented by the equation (10) J. R. Partington, "An Advanced Treatiae on Physioal Chemistry," Vol. I V , Longman, Green and Co., London, 1953.
(1)
If the specific volume v of a binary mixture is also considered to be a n additive sum of the weighted specific volumes of its pure components, then a n expression can be derived for the refractive index of the dilute solution in terms of the concentration of the solute species, c, as n
- 1 = (1 - c / P ~ ) P ~+R ICRZ
(2)
Since the refractivities are not functions of the concentration of the solute, the refractive index and its temperature variation may be expressed as in equations 3 and 4 dnldc = RZ - (pdpdR1 = ( n ~ nd/p2 (3) (d/dt)(dn/dc) = vz d(n2
- nJ/dt
+ (n2 - nl)(dvddt)
(4)
If (I) the data for the specific volume of polystyrene taken from Fox and Flory,l' both above and below the glass transition temperature (-go"), (2) the refractive index data for polystyrene from Jencke1,I2 both above and below the glass trapition temperature, for light of wave length 5890 A; and (3) the data for the refractive index of cyclohexane and toluene from Timmermans13 are used to calculate the dn/dc a t 30" and the temperature dependence from equations 3 and 4, results are obtained that are shown in Table 111, columns 1, 4, 5 and 8. The results listed as glassy values in the table were obtained by assuming that the true glassy state refractive index and specific volume values obtained from the data below the glass temperature were the correct ones to use in the above equations. The second set of values were derived from the assumption that the proper values to be used in these equations are from the liquidus, derived by extrapolating the (11) T. G.Fox and P. J. Flory, J . A p p l . P h w , 21, 581 (1950). (12) E. Jenckel and R. Heusch, Xolloid-Z., 180,89 (1953). (13) J. Timmermsns, "Physioo-Chemical Conatanta of Pure Organio Compounds," Elaevier Publiehing Co., New York, N. Y., 1950.
KINETICSOF REACTIONS OF MERCURIC SALTSWITH OLEFINS
Sept., 1959
TABLE 111 CALCULATED AND MEASURED VALUESOF dnldc AND (dldt) (dnldc) AT 30” Cyclohexane Toluene dnldc dnldc (dldt) (dnldc) 1 2 3 4 5 6 7 589 546 436 589 589 546 436 0.159 0.162 0.174 4.2 X 0.0931 0.0935 0.0976 .166 .170 ,183 2 . 8 x 10-4 ,102 ,1025 ,1070 ... .1693 ,1800 . . ...... .... ,1096 .1134
Column no. Wave length, mp Glassy Ex trapd . Measured
curve above the glass temperature to lower temperatures. This makes the calculation more closely approximate the mixing of two liquids. Unfortunately, the light-scattering measurements are conducted a t 546 and 436 mp rather than a t the sodium-D line, so that the measurements of dn/dc cannot be directly compared with the above calculations using Jenckel’s data. The dispersion curve for glassy polystyrene has been given14 and fits a Cauchy relation. Similarly the dispersion of the solvents is known so that the dn/dc for glassy polystyrene can be calculated directly. The dispersion effects would be expected to be similar both above and below the glass temperature since it is directly a function of the internal molecular structure; therefore, the values for the dispersion dn/dc of the (14) R. M. Boundy and R. F. Boyer, “Styrene, Its Polymers, Copolymers, and Derivatives,” Reinhold Publ. Corp.. New York, N. y., 1952.
1437
(d/dt) (dnldc) 8 589 4.14 X 2 . 4 6 X lo-‘
..........
extrapolated liquidus state of polystyrene may also be calculated. These values appear in columns 2,3, 6 and 7 of Table 111. The temperature dependence of the refractive index of polystyrene and the solvents changes very little with wave length so the calculated value a t 589 mp can be directly compared with the measured values in Table 11. The excellent agreement of the calculated and experimental values for the dn/dc using the polystyrene constants extrapolated from the liquidus state is indeed encouraging, although the calculated temperature dependence of dnldc in blue light does not seem to fit the measured values regardless of the choice of state. However, it is to be reemphasized that there is a sizable temperature dependence of dn/dc and it must be taken into account in experimental measurements performed a t different temperatures.
THERMODYNAMICS AND KINETICS OF THE REACTION OF MERCURIC SALTS WITH OLEFINS. PART I. THE REACTION FWI” MERCURIC CHLORIDE BY E. R. ALLEN,J. CARTLIDGE, M. M. TAYLOR AND C. F. H. TIPPER Dept. of Inorganic and Physical Chem., The University, Liverpool, England Received February 18,1969
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The equilibrium constant of the reaction HgC12 CzHr HzO $ ClHgC2HIOH HC1 has been measured a t 25” a proaching the equilibrium position from both sides. The values are in agreement within the experimental error. TI; constant has also been determined a t other temperatures between 15 and 40” commencing with mercuric chloride and ethylene and thus the heat content and entropy changes of the reaction have been calculated. The kinetics do not correspond to a first-order reaction opposed by one of the second order. Added sodium chloride had a marked retarding effect. The results are discussed and it is considered that they lend strong support to the hypothesis that the reaction proceeds by an ionic mechanism.
Introduction The interaction of mercuric salts with olefins has been studied for many years. Many mercurials have been prepared and their reactions studied, but relatively little work has been reported on the thermodynamics and kinetics of these systems and the mechanism of the processes involved is still not c1ear.l Sand and Breest2 investigated the equilibrium (1) and obtained values of the equilibrium
simple one, and so the physical chemistry of the reaction of mercuric chloride and simple olefins has been reinvestigated by more direct methods.
Experimental
The uptake of ethylene or propylene by mercuric chloride solutions (volume 20 or 25 cc.) was followed a t a constant pressure by conventional means. The 100-ml. reactio: vessel was immersed in a thermostat, constant to + O . l , and shaken about 350 times per minute. The rate of absorption was independent of shaking rate. The air in the HgClz CZHd HzO )r ClHgCZHdOH HC1 (1) flask had previously been swept out by the olefin, and the volume absorbed was determined by means of a thermoconstant approaching the equilibrium position from stated gas buret connected to the flask by wide capillary both sides. Their work has been c r i t i c i ~ e d , ~tubing and polythene tubing. Before an experiment the and certainly their method of calculating K is vessel was washed with concentrated nitric acid, distilled water and acetone, and dried over a flame. The solubility of incorrect. However, this system is a relatively the gas in water was determined in the same way. It was found in all the experiments that no uptake occurred until (1) J. Chatt, Chem. Revs., 48, 7 (1951). (2) J. Sand and F. Breest, 2. physik. Chsm., 69, 424 (1907). the solution was shaken. The equilibrium was approached from the opposite direo(8) PhBrandt and 0. Plum, Acta Chem. Scond., ‘7, 97 (1958).
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