The Characterization of Linear Polyethylene SRM 1475. VII. Differential Refractive Index of Polyethylene Solutions

Abstract

The value of dn/dc for polyethylene in 1-chloronaphthalene at 135 °C, required for the determination of molecular weight by light scattering, was found to vary with molecular weight. Similar changes were found in 1,2,4-trichlorobenzene, the gel permeation chromatograph solvent. The absolute value of dn/dc decreases by about 2 percent as the polymer molecular weight increases from 12,000 to 110,000.

1. Introduction

Since the change of refractive index with concentration, dn/dc (differential refractive index), enters as a squared term in the light scattering equation, its accuracy is of considerable importance for obtaining reliable values of molecular weight of polymers. The first determination of dn/dc of polyethylene in 1-chloronaphthalene (table 1) found in the literature was by Nichols and was reported by Billmeyer [1].¹ It was measured at 90 °C and 125 °C using a divided cell technique, giving values of −0.199 ml/g and −0.191 ml/g respectively. The latter value is the one most often quoted. Kobayashi, Chitale, and Frank [2], using an interferometer technique, obtained a somewhat lower value at 90°, namely −0.183. Nicholas [3] found a very low value (−0.257 at 125 °C) using a Rayleigh differential refractometer at concentrations of 0.15 to 0.7 g/100 ml. This result seems to be completely out of line with the other values reported and may be due to the greater errors incurred working at low concentrations. The use of such low concentrations would appear to be unnecessary inasmuch as dn/dc is found to be constant at the concentrations used in this work, which range from 0.5 g/100 ml to 4 g/100 ml.

Table 1.

Literature values of dn/dc for polyethylene in 1-chloronaphthalene

dn/dc in ml/g
Refs.	1	2	3	6	22	7	8	9
Temp. °C
90	−0.199	−0.183			−0.198
99.5							−0.1924
104.5							−1927
105				−0.188
109							−.1934
114							−.1927	−0.1957
120							−.1917
125	−.191		−0.257		−.195	−0.195	−.1911
127								−.1967
128								−.1955
135							−.190
139								−.1956
140						−.191		−.1961
145								−.1967

Most of the other literature values fall in the range of −0.188 to −0.199 [4,5,6]. The recent data are those of Drott and Mendelson [7], Chiang and Rhodes [8] and Benoit et al. [9]. Drott and Mendelson provide considerable detail about their procedure, which appears to be thorough and careful, and obtained a value of −0.191 at 140 °C and −0.195 at 125 °C. Chiang believes his values for a low molecular weight branched sample of −0.195 at 80 °C [10] are consistent with his values for higher molecular weights which range from −0.193 at 100 °C to −0.190 at 135 °C. Benoit et al. measured dn/dc between 141 °C and 150 °C finding values about $2\frac{1}{2}$ percent higher than those of Chiang and Billmeyer. The change in dn/dc with temperature is insignificant in this temperature range.

In view of the uncertainties described above and the importance of accurate values of dn/dc, it appeared necessary to make as accurate a determination as possible for the Standard Reference Materials Program. It soon became evident that dn/dc was to some extent a function of molecular weight. This may account for some of the discrepancies in the literature but these could not be readily resolved because in most cases no characterization is provided for the polyethylene used in the dn/dc measurement. It was also necessary to measure the variation with molecular weight in 1,2,4-trichlorobenzene since this solvent is used in gel permeation chromatography with the assumption that dn/dc is constant.

2. Experimental Procedure

The determination of the change of refractive index with concentration is most conveniently accomplished by a differential refractometer. The instrument employed here was the image displacement type, in which light passes through a cell consisting of two adjacent prismatic compartments, one containing solvent, the other dilute solution. It may be easily shown that in the limit as the difference Δn between the refractive index of solution and of solvent becomes small, the displacement Δd of the imaged light source from its position with pure solvent in both compartments of the cell becomes proportional to Δn, i.e.,

$$\Delta n=k\Delta d$$

where k is the proportionality constant and is determined by calibration with a substance of known refractive index.

2.1. Optical System

The optical system, consisting of the elements shown in figure 1, is mounted on an optical bench 125 cm long. Light from an air cooled mercury lamp passes through a combination of filters which transmits green monochromatic light at 5460 Å. This light enters a slit, passes through the collimating lens, L₁, then through the cell, where the deviation due to the refractive index difference takes place. The displaced slit, imaged by the lens, L₂, is observed with a micrometer eyepiece having a 10 mm scale and a drum divided to 0.01 mm. The entire optical system is carefully aligned so that the collimated beam is normal to the face of the cell. The system was stable in that once the optical components were fixed the reading did not change over a period of several days with a given solvent in both compartments of the cell.

Figure 1.

Optical system, schematic.

2.2. Glass Cell

The sample cell, supplied commercially [11]² is a sinter fused Pyrex optical cell 15 mm square with plane parallel windows. The partition is set at such an angle that the light beam forms an angle of incidence of approximately 69° with the normal to the surface of the partition. This cell is provided with a fused top with openings which are closed by Teflon stoppers, thus eliminating the problem of evaporation which in the past has caused troublesome temperature gradients at high temperatures.

2.3. Cell Holder

In order to achieve temperature stability over long periods of time and to keep the temperature difference between the two compartments of the cell down to a few hundredths of a degree, considerable care was necessary in the design of the cell holder. As in the apparatus discussed by Benoit et al. [9], the cell is set into a rectangular opening in the center of a cylindrical aluminum block, 4 in in diameter and 5 in high (fig. 2) containing a ⅜ in hole for passage of the light beam. Aluminum 1100 was used because of its superior heat conductivity. The aluminum block is positioned by three bakelite pins inside a ⅓ in thick brass shell of 5 in diameter, leaving a half inch air space to minimize heat loss. Both the aluminum block and the brass shell are heated by coils of wire embedded in silicone rubber. Additional heat is supplied by means of four rod heaters inserted into holes in the block and by another coil heater, also embedded in silicone rubber, underneath the brass shell. The temperature of the cell holder is maintained by a thermistor temperature controller. The entire assembly is insulated by a laminate composed of eight layers of balsa wood alternating with aluminum foil. Short term temperature fluctuations of the aluminum block were of the order of 0.001 °C. Drift during a set of measurements was no greater than 0.01 °C.

Figure 2.

Heating block for cell.

(1) Divided cell, (2) aluminum cylinder, (3) cartridge heaters, (4) brass shell, (5) balsa wood-aluminum foil laminate, (6) opening for light path, (7) heaters embedded in silicone rubber, (8) balsa wood cap, (9) air space, (10) bakelite positioning pins, (11) thermistor.

Brice [12] recommends that the temperature difference between solvent and solution should be no greater than 0.01 °C. Attempts to measure this difference by simply inserting thermocouples into each compartment were unsuccessful, probably because of heat loss through the openings for the thermocouple leads and through the leads themselves. In view of the construction described above it is doubtful that a significant difference existed. In any case the effect of such a difference would be cancelled since measurements were made first with solution on one side and solvent on the other and again with solution and solvent reversed.

3. Materials

3.1. Solvents

Reagent grade 1-chloronaphthalene was double distilled, center cuts being taken each time. Observable impurities were less than 0.05 percent by gas liquid chromatography. The 1,2,4-trichlorobenzene, technical grade, was not further purified and 0.05 percent Ionol (2,6-di-tert.-butyl-4-methylphenol) was added as an antioxidant in order to use the same material used in the gel permeation apparatus [13]. Gas liquid chromatography revealed only a single major peak containing at least 99 percent of the material.

3.2. Polymers

Measurements of dn/dc were made on several polyethylenes. They are: (1) SRM 1475, the linear polyethylene standard reference material described previously [14]; (2) fractions of SRM 1475 obtained by column extraction of this polyethylene [15]; (3) SRM 1476, the branched polyethylene standard reference material. The available data are provided in the certificate for this material. Additional details will be given in a forthcoming publication; (4) fraction R 1201–7 is a linear polyethylene supplied by the Monsanto Chemical Company; (5) AC–6 is a polyethylene wax obtained from the Allied Chemical Corporation.

The number average molecular weights of these materials were obtained in various ways, as indicated in tables 2 and 3. Some were obtained by direct measurement by osmometry [16]; others were determined by gel permeation chromatography (G.P.C.) [13]. The number average molecular weights of fractions 12x and 7y were estimated from molecular weight measurements made on other fractions prepared by the same process. For three of the samples (AC–6, R 1201–7, and SRM 1476), the values supplied by the manufacturer were used.

Table 2.

dn/dc of Polyethylenes in 1-Chloronaphthalene at 135 °C

Sample	Mn	dn/dc, ml/g	Stand, dev. of dn/dc,e ml/g	No. of points e
SRM 1475	a 18,310	−0.1932	0.00016	5
SRM 1476	b 25,200	−.1916	.00028	5
Fraction R 1201–7	b 12,300	−.1931	.00042	3
Fraction PE 15	c 13,500	−.1929	.00035	3
Fraction 12x	d 110,000	−.1883	.00088	2
Fraction PE 120	c 112,200	−.1879	.00059	4

^aValue obtained from Gel Permeation Chromatography [13].

^bValue provided by manufacturer.

^cDetermined by osmometry [16].

^dEstimated as described in text.

^eThe estimated standard deviation of the slope, calculated by linear regression of the refractive index difference, Δn, on the concentration c, assuming a zero intercept. The number of points in each regression line is shown in column 5.

For convenience all standard deviations are given to two significant figures, with no implication that such precision is warranted.

Table 3.

dn/dc of Polyethylenes in 1,2,4-Trichlorobenzene at 135 °C

Sample	Mn	dn/dc, ml/g	Stand, dev. of dn/dc,d ml/g	No. of points d
AC-6	b 2,000	−0.1085	0.00028	3
SRM 1475	a 18,310	−.1085	.00015	5
Fraction 12 AC	a 34,800	−.1082	.00019	3
Fraction 7y	c 77,000	−.1073	.00038	3
Fraction 12x	c 110,000	−.1063	.00014	4

^aValue obtained from Gel Permeation Chromatography [13].

^bApproximate value, supplied by manufacturer.

^cEstimated as described in text.

^dThe estimated standard deviation of the slope, calculated by linear regression of the refractive index difference, Δn, on the concentration c, assuming a zero intercept. The number of points in each regression line is shown in column 5.

For convenience all standard deviations are given to two significant figures, with no implication that such precision is warranted.

4. Procedure

For each concentration two readings of the displacement of the light beam were made. The first was taken with the solvent on one side and solution on the other and another reading was taken with these reversed. One-half the difference between the two readings multiplied by the calibration constant gave the value of the refractive index difference Δn. This is similar to the procedure of Brice and Halwer [12] except that since it is not possible, as in their apparatus, to rotate our cell housing because of its large bulk, the cell is kept fixed and the contents reversed. Readings with solvent on both sides were made occasionally to make certain that the beam’s position through the center of the cell had not shifted.

Solutions were made up by weight, and concentrations were calculated from measurements of solvent densities and partial specific volumes. The densities at 135 °C of 1-chloronaphthalene and 1,2,4-trichlorobenzene were found to be 1.095 g/ml and 1.315 g/ml respectively. The partial specific volumes were approximated from measurements of the change in density on dissolving the polymer to specified concentrations. The values obtained were 1.29 ml/g in 1-chloronaphthalene at a concentration of 0.03 g/ml and 1.30 ml/g in 1,2,4-trichlorobenzene at a concentration of 0.01 g/ml. It was assumed that at the low concentrations employed here the partial specific volume is constant, so that the volume increase on dissolving polymer is equal to the weight of the polymer multiplied by this approximate partial specific volume. The polymer was dissolved in the solvent at 140 °C and about 1.5 ml was transferred by a heated hypodermic syringe to the cell. The compartment was not cleaned and dried when its content was changed but was thoroughly rinsed beforehand with solvent and solution of the new concentration. A period of at least 15 min was allowed after transfer for temperature equilibration before readings were taken. The standard error (15 readings) was about 2 × 10⁻⁶ in Δn or about 0.2 percent. The least square slopes computed from these data show a standard deviation of the slope of from 0.1 to 0.5 percent, as shown in tables 2 and 3. The standard deviation of the slope for the standard reference sample is about 0.1 percent.

No refractive index data at 135 °C are available for calibration of differential refractometers. We therefore calibrated our instrument with aqueous solutions of NBS sucrose at 25 °C and assumed the calibration did not change with temperature. The most likely cause for a change in calibration would be a change in the angle of the glass partition of the cell. Measurements in a cell similar to ours by Benoit et al. [9] of sodium chloride solutions up to 70 °C did not reveal any changes with temperature.

The partial specific volume of sucrose in water was taken as 0.618 ml/g at 25 °C [19]. The value of 0.1429 ml/g for dn/dc at 5460 Å at 25 °C, obtained by Norberg and Sundeloff [18], was employed in the calibration of the apparatus. This value agrees very well with the results of other authors [19–21]. Bodmann [21] has shown that dn/dc is constant up to concentrations of at least 0.025 g/ml. We found that the displacement Δd of the light beam is linear with concentration for concentrations as high as 0.04 g/ml and displacements up to 5 mm, the limit of our instrument scale. The calibration constant k for our instrument was found to be 1.1417 × 10⁻³ refractive index units per mm deflection, with a standard deviation of 0.1 percent.

5. Results and Discussion

The values of dn/dc for various polyethylenes in 1-chloronaphthalene are listed in table 2. The value for the linear sample, SRM 1475 at 135 °C is −0.193 ml/g and for the branched sample, SRM 1476, is −0.192. The numbers fall into two groups: values of −0.192 to −0.193 for low number average molecular weights (11,000–25,000) and a decidedly higher value, −0.188 for the higher molecular weights. In order to obtain a better idea of the molecular weight dependence and to determine whether gel permeation chromatography intensities need to be corrected for molecular weight, dn/dc was measured in 1,2,4-trichlorobenzene over a range of molecular weights. These are enumerated in table 3 and a plot of these values against 1/M_n is shown in figure 3. The change in dn/dc in going from an M_n of 12,000 to 110,000 is about the same in both solvents, a decrease of about 2 percent in absolute value. Several factors contribute to the belief that this is a real change. It is outside the limits of error of the determination, for which the standard deviation is of the order of 0.5 percent. Different fractions of the same molecular weight, such as 12x and PE 120 in one case, and R 1201–7 and PE 15 for another, the latter two coming from different starting polymers, have the same values of dn/dc. The infrared spectra of the whole polymer SRM 1475 and a high molecular weight fraction, showing a smaller dn/dc, are similar, indicating the absence of some chemical group which might account for the difference in dn/dc.

Figure 3.

Differential refractive index in 1,2,4-trichlorobenzene.

Unfortunately it was not possible to measure dn/dc for fractions of M_n greater than 110,000 because of the difficulties of handling the extremely high viscosities of these fractions at the concentrations needed to give meaningful results. For most determinations concentrations ran between 0.5 to 4 g/100 ml but were limited to no greater than 2 g/100 ml for the high molecular weight samples.

6. Conclusion

Because dn/dc changes with molecular weight, it is necessary to use the correct value of dn/dc in light scattering work, as is done in Paper VIII of this series [23]. Although 1-chloronaphthalene measurements were not made for the intermediate molecular weight range, the measurements in trichlorobenzene are extensive enough to show that dn/dc changes continually so that interpolation should provide sufficiently precise values for the former solvent. No data are available, however, at number averages greater than 110,000, and since it can not be assumed that the absolute value of dn/dc decreases without limit, the value at high molecular weights is taken, for the present, as constant at −0.188 ml/g in 1-chloronaphthalene.