1

Certification of the Relative Molecular Mass and the Intrinsic Viscosity of SRM 

2887, a Polyethylene of Narrow Molecular Mass Distribution 

C. M. Guttman, J. R. Maurey, W.R. Blair, and C.R. Schultheisz

Polymers Division

NIST

Gaithersburg, MD 20899

Certain commercial materials and equipment are identified in this paper in order to specify 

adequately the experimental procedure. In no case does such identification imply 

recommendation or endorsement by the National Institute of Standards and Technology, nor does 

it imply necessarily the best available for the purpose.

According to ISO 31-8, the term "Molecular Weight" has been replaced by Relative Molecular 

Mass, symbol Mr. Thus, if this nomenclature and notation were followed in this publication, one 

should write Mr,w instead of the historically conventional Mw for the weight average molecular 

weight with similar changes for Mn, Mz, and Mv. Mw would be called the "Mass Average 

Relative Molecular Mass." The conventional notation, rather than the ISO notation, has been 

used in this publication.

Final report prepared for the sponsors, the NIST Standard Reference Materials Program (SRMP).

NISTIR 6456
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ABSTRACT

The certification of a polyethylene standard reference material, SRM 2887, is described. The Mw

of SRM 2887 by light scattering was determined to be 196.4x10+3 g/mol with a sample standard 

deviation of 6.6 x10+3 g/mol. A combined expanded uncertainty for this light scattering Mw 

determination, including systematic and random uncertainties, was estimated to be 13.7 x10+3

g/mol. The intrinsic viscosity of SRM 2887, by solution viscosity, in

1,2, 4-trichlorobenzene was determined to be 276.9 mL/gwith a sample standard deviation of

2.5 mL/g.. A combined expanded uncertainty for this intrinsic viscosity determination was 3.1 

mL/g. The bottle-to-bottle variation of the SRM was checked by size exclusion chromatography 

(SEC) and found to be negligible.
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1.0 Introduction

This report describes the certification of the Mw by light scattering and intrinsic viscosity (often 

called the limiting viscosity number [1]) in 1,2,4-trichlorobenzene (TCB) at 130 °C of a linear 

polyethylene, SRM 2887. The material was obtained from fractionating SRM 1475, as described 

previously [2]. In the early 1970's, some of this fractionated material was used in the preparation 

of SRM 1482, SRM 1483, and SRM 1484. Other fractions from the separation had been stored in 

the Polymers Division in the intervening years. From this material three new narrow mass 

fraction SRMs are being certified. This reports describes the cleanup, the Mw by light scattering 

and the intrinsic viscosity measurements on one of these fractions, a moderate molecular mass 

polyethylene. Bottle-to-bottle homogeneity on the final packaged material was determined by 

size exclusion chromatography (SEC).

2.0 Preparation, Bottling, and Handling of SRM 2887 

2.1 Preparation of the SRM

The Mw standard, SRM 2887, is a fraction of polyethylene SRM 1475. The fractionation was 

described in reference [2]. Fractions of SRM 1475, originally identified as LEA-4 and LEA-7, 

that had nearly the same SEC trace, were combined. This provided sufficient material for 

producing SRM 2887. The fractions contained fine powders, larger aggregates and some dirt 

particles. Also evident was a slight yellowing of the polymer. It was evident that these fractions 

needed to be cleaned and purified by recrystallization from solution prior to certification. Details 

of the recrystallization procedure and apparatus are given in Appendix I of reference [3]. 

Subsequent to recrystallization from solution as fine powders, the dry material was sieved 

together through a sieve with 1.65 mm openings (C E Tyler, Mentor Ohio, 10 meshes to the inch) 

and then well mixed in a 30 cm x 50 cm stainless steel tray. SEC was performed on samples 

taken from different positions in this tray to confirm the adequacy of mixing. After SEC samples 

were removed, the contents of the tray were sent to the NIST Standard Reference Materials 

Program (SRMP) for packaging.

2.2 Bottling and Sampling of SRM 2887

Of the approximately 240 g of purified material approximately 180 g was packaged in about 590 

 vials containing about 0.3 g each. In the following report, the containers holding SRM 2887 will 

be referred to as vials. The additional polymer was divided into two lots designated division 1 

supply and division 2 supply. These large lot samples were used to supply some of the material 

used in the light scattering and intrinsic viscosity measurements. Prior to the use of material 

from these division supply lots, however, we showed that these samples were identical to the 

material in the vials. (See section 2.3).

The entire set of SRM 2887 vials was divided into 14 subsets of 41 or 42 vials. One vial was 
4

randomly selected from each subset of SRM 2887 for homogeneity testing. The first and last 

bottled vials were also taken. These vials and the two division supply lots were used in the SEC 

homogeneity testing described below. All these materials were used in the light scattering 

determinations and intrinsic viscosity determinations described in later sections 

2.3 Homogeneity Testing

Homogeneity testing was accomplished using SEC. In this study, a Waters 150-C ALC/GPC 

Liquid Chromatograph (Waters Corp., Milford, MA) with a differential refractive index (DRI) 

detector and three Waters styragel columns, HT-6, HT-4, and HT-3, were used. The 

chromatograms were taken at a 0.8 mL/min solvent flow rate. The injector and column 

compartments of the Waters 150-C ALC/GPC were controlled at 130 oC for all measurements. 

The solvent, 1,2,4-trichlorobenzene (TCB), was obtained from Aldrich Chemical (1,2,4-

trichlorobenzene, 99+ %, spectrophotometric grade, Aldrich Chemical, Milwaukee, WI) and used 

as received. Santonox (5-tert-Butyl-4-hydroxy-2-methylphenyl sulfide), also obtained from 

Aldrich Chemical, was added to the solvent at about 0.1 g/L as an antioxidant. 

Vials of SRM 2887 were obtained from SRMP as described above. The polymer in the two 

division supply lots was also included in this test. A mass of 1.3 mg to 2.4 mg of the 

polyethylene was weighed into the Waters autosampler bottle along with 4 mL of solvent 

yielding a concentration of approximately 0.6 g/L. Hexadecane, at 0.03 mL/L, was added to the 

solutions of polymer and solvent as a marker to indicate the reproducibility of the solvent volume 

delivered by the SEC pump for all measurements. Each autosampler bottle was heated to 150 oC 

in an oven for about 1.5 h and the solution was shaken at frequent intervals to aid the dissolution. 

The autosampler bottles were placed in the Waters 150-C ALC/GPC injection compartment held 

at 130 oC . Chromatograms were then run with these solutions.

Solutions were prepared from each vial of SRM 2887 sample population and from each of the 

division supply lots. Two solutions were prepared from each vial selected from those received 

from SRMP and four solutions were prepared from each division supply lot. For SRM 2887, this 

resulted in 40 solutions to be tested. The order used to run the solutions was randomized 

following the method described in section 1-4 of the handbook by Natrella [4]. Two injections 

were made from each solution. All chromatographic data were obtained during a five-day period, 

with 10 solutions measured per day.

After baseline subtraction, the SEC chromatograms were normalized to unit peak height and 

compared initially by overlaying to determine if there were visible differences outside the noise. 

The chromatograms from different solutions all superimposed on each other. This preliminary 

comparison showed that polymer samples taken from all the vials produced identical 

chromatograms. Further statistical analysis of the chromatograms is discussed in Section 2.3.1
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2.3.1 Statistical Method to Compare Chromatograms 

2.3.1.1 Match Factor

In previous SEC studies on SRM homogeneity, the match factor was used to compare one 

chromatogram to all others [5]. The match factor is a correlation coefficient between one 

chromatogram and another. The match factor is defined by Huber[6] as

Match Factor = 103 {3x*y-(3x*3y)/p}2/[{3x

2

-3x*3x/p}{3y

2

-3y*3y/p}] (1)

The values x and y are the measured signal in the first and second chromatograms, respectively, 

at the same time in the chromatograms; p is the number of data points. The sums are taken over 

all data points. 

At the extremes, a match factor of zero indicates no match and 1000 indicates identical 

chromatograms. Generally, values above 990 indicate that the chromatograms are similar. 

Values between 900 and 990 indicate there is some similarity, but the result should be interpreted 

with care. All values below 900 are interpreted to mean that the chromatograms are different 

[6,7]. The method we describe here has been used previously [8]. We obtained the match factor 

of the entire set of chromatograms, which include two injections for each solution prepared, 

against the average chromatogram. In the following discussions we will compare chromatograms 

against the average chromatogram.

An ANOVA study, using OMNITAB [9], was made on the match factors obtained from the 

chromatograms. It indicated that the match factors for the chromatograms from the same vial 

were no different than those from different vials on a level of significance with α = 0.05 [10]. 

Moreover, the match factors of chromatograms from the two division supply lots and the vials 

were indistinguishable using the same significance level with α = 0.05. The samples were run in 

groups of 10 on different days. Using the match factor we found that chromatograms showed no 

day-to-day variation.

From this we conclude that there is no statistically significant difference between the contents of 

vials sampled from the SRMP supply of SRM 2887 and no difference between the SRMP supply 

and the two division supply lots.

3.0 Estimation of Impurity Peaks and Polydispersity Index of SRM 2887

SEC measurements described in the Section 2.3 were used to estimate the polydispersity index 

(PD). We used the solvents as described in Section 2. Columns for this part of the work were two 

Waters Styragel HT-6E and one Waters Styragel HT-2 (Waters Corp., Milford, MA) .The 
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instrument used for this work was a Waters Alliance GPCV 2000 (Waters Corp., Milford, MA) . 

Columns were calibrated with SRM 1482, SRM 1483, SRM 1484, SRM 1475, SRM 2885, SRM 

2886, and SRM 2887. From the SEC curves for SRM 2887 we estimated the PD (PD = Mw /Mn)

to be 1.29. No effects of column broadening were taken into account in this measurement, so we 

expect the value of 1.3 to be an overestimate of the PD. 

In a separate calculation, we tried to take the effects of column broadening into account using the 

Waters Corporation Millennium Software (Waters Corp., Milford, MA) . Using their Axial 

Dispersion Calculation with peak compression, we found a PD of 1.23. 

SEC analysis of the chromatograms from SRM 2887 showed a minor peak at around 80 x 10+3

g/mol. We assume the minor peak arises from a small quantity of a lower molecular mass 

fraction that was not removed during fractionation. Analysis of chromatograms from four 

different vials yielded RI signals for the minor peak ranging from 2.0 % to 3.3 % of the main 

peak. We take 3.3 % as the upper fractional limit of the RI signal and, therefore, the maximum 

fractional mass in the minor peak. The Mw measured by light scattering will, of course, include 

the low mass fraction.

 Mw-LS = (1-f ) Mw-main peak + f Mw-minor peak

where Mw-LS is the mass averaged molecular mass from light scattering, Mw-main peak is the mass 

averaged molecular mass of the main SRM 2887 peak , Mw-minor peak is the mass averaged 

molecular mass of the minor peak, 80 x 103 g/mol, and f is the fraction of signal in the minor 

peak. We can then estimate the main peak Mw-main peak as

 Mw-main peak = (Mw-LS - f Mw-minor peak)/(1-f)

Using our estimate of Mw-minor peak and f we calculate the value of 

 Mw-main peak = 200,400 g/mol.

The maximum error in taking the measured light scattering mass average molecular mass, Mw-LS , 

as the estimation of the Mw-main peak is then 4000 g/mol, much less than our estimated overall 

uncertainty in the light scattering mass average molecular mass, Mw-LS .

 

4.0 Intrinsic Viscosity of SRM 2887 

4.1 Measurement of the Intrinsic Viscosity

 

Viscosity measurements were made with a Schott-Gerate Ubbelohde micro-viscometer (SchottGerate GMBH, Hofheim, Germany) with a Schott-Gerate constant temperature bath held at 
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130 oC. Flow times were measured by the Schott-Gerate AVS 400. The solvent, 1,2,4-

trichlorobenzene (TCB), was obtained from Aldrich Chemical (1,2,4-trichlorobenzene, 99+ %, 

spectrophotometric grade, Aldrich Chemical, Milwaukee, WI) and used as received. Butylated 

hydroxytolulene (2,6-Di-tert-butyl-4-methylphenol), also obtained from Aldrich Chemical, was 

added to the solvent at about 0.7 g/L as an antioxidant.

Solution concentrations ranging from 0.2 g/L to 1.0 g/L were prepared from independent 

weighing of polymer and solvent, rather than employing successive dilution techniques. 

Concentrations were calculated from densities and partial specific volumes determined earlier in 

this laboratory [11]. 

The polymer was dissolved by heating the mixture to 135 oC to 140 oC in a hot air oven with 

occasional stirring. Solutions were then transferred to a viscometer by filtering the solution 

though a syringe and syringe filter heated in the same oven. The syringe filter assembly used was 

a Swinny Stainless 25 mm (Millipore Corp., Bedford, MA) while the filter membrane was a PallGelman Sciences ZEFLOUR all Teflon 0.5 μm pore size 25 mm diameter membrane (Pall Corp., 

Port Washington, NY).

For each polymer concentration, flow times were measured for both solvent and solutions. The 

AVS 400 is designed to perform a number of preconditioning runs to insure that the solution or 

solvent comes to temperature equilibrium before the actual measurements were made and 

recorded. The operation of the AVS 400 took about 2 min to 2.5 min for each of the five 

preconditioning runs. Five flow times were measured on each aliquot of the solvent or the 

solution. Flow times measured in this viscometer ranged from 40 s to 60 s.

At the beginning of an overall measurement on a solution, the viscometer was flushed with at 

least three solvent aliquots. Then, at least two aliquots of solvent were introduced for flow time 

measurements. Three aliquots of solution were used to flush the viscometer. Three aliquots of 

solution were then measured. Three aliquots of solvent were used to flush the viscometer. 

Finally, flow time measurements were made on three aliquots of solvent.

4.2 Results of Solution Viscosity

The solution viscosity, η(c), may be expanded as a power series in solution concentration, c, [12] 

η(c) = η(0) (1+ a1 c+a2 c

2

 + ...) (2)

where η(0) is the solvent viscosity.

The viscosity number is defined as

(η(c) - η(0))/( η(0) c) = a1 + a2 c (3)
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The intrinsic viscosity, [η] = a1, is the zero concentration limit of the viscosity number.

 

For a properly designed capillary viscometer, the solution viscosity is almost proportional to the 

product of the solution density and the measured flow time. The deviation from proportionality 

is due to a combination of kinetic energy effects and hydrodynamic effects at the end of the 

capillary. The manufacturer of the viscometer gives tables to correct the measured times for each 

viscometer. These corrections, designated by the manufacturer as the Hagenbach correction [13], 

are approximately of the form 1/tm

2

, where tm is the measured time. The manufacturer’s 

corrections were fitted to this form to interpolate their correction data. This correction is applied 

to each average flow time for solvent or solution yielding t(c) where the c refers to the 

concentration of the solution being measured.

From eq. 2 then

K ρ(c)t(c)= K ρ(0)t(0)(1+ a1 c + a2 c

2

.....) (4)

where the solvent viscosity is 

η(0) = K ρ(0)t(0) (5)

and K is the viscometer constant.

Finally, we do not need to know K since the quantity of interest is the limiting value of 

[η] = (η(c)- η(0))/(η(0) c) = a1 (6) 

Thus we may rewrite eq. 4 as 

ρ(c)t(c) = ρ(0)t(0) (1 + a1 c + a2 c

2

...) (7)

On any given day measurements on only one concentration and related solvents as described 

above were practical. As viscometers became dirty, they were taken out of service and similar, 

but not identical, clean ones used in their place. Thus, the ratio, T(c), is expected to be invariant 

at any concentration where T(c) is

T(c) = (ρ(c)t(c)- ρ(0)t(0))/(ρ(0)t(0)) (8)

Following the normal definition of [η] as the zero concentration limit of T(c)/c , we fit T(c)/c 

to the expression 
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 T(c)/c = a1 + a2 c. (9)

The value of a1 so obtained was 276.9 mL/g with a standard deviation of 2.5 mL/g. For our study 

of uncertainty, we consider the value of the standard deviation reported above to be the expanded 

uncertainty in the repeatability of the measurement. This is reported in Table 1 with other 

contributions to the reported uncertainty of this measurement.

The coefficient a2 is related to the Huggins constant [14] as 

k H = a2/(a1)

2

. (10)

We obtain the value of kH of 0.45 g/mL. 

Earlier, Wagner and Verdier [12] studied other fractions of the same base material, SRM 1475, 

certified as SRM 1482, SRM 1483 and SRM 1484. They measured and reported limiting 

viscosities in TCB on these materials. Fitting their data for the limiting viscosities, [η], of SRM 

1482, SRM 1483 and SRM 1484, we obtain

lne{ [η]w } = 0.7312 lne{Mw}- 3.247 (11)

where [η]w is their measured intrinsic viscosity.

Using the Mw of our polymer obtained in Section 5, we estimate [η]w from eq. 11 for SRM 2887 

to be 289 mL/g, in good agreement with our measured value considering the fact that the [η]w is 

an extrapolated value. Furthermore, extrapolating their kH, we estimate kH for this molecular 

mass as 0.48 g/mL, again in good agreement with our value. 

4.3 Estimating Uncertainties in the Intrinsic Viscosity Measurement

 

The likely sources of uncertainty are discussed in the following subsections and the table referred 

to herein. For this analysis, we largely follow the paper of Wagner and Verdier [12]. 

4.3.1 Shear Rate Dependence of Viscosity 

Low molecular mass polymers in dilute solution are expected to show little, or no shear rate 

dependence. Wagner and Verdier [2] were unable to detect shear rate dependence, even for SRM 

1484, a linear polyethylene with an Mw of 114,000 g/mol. The capillary in their viscometer had a 

smaller diameter than that in the Schotte-Gerate viscometer used in the present measurements. 

Thus, we expect little shear rate dependence of the intrinsic viscosity of SRM 2887, even though 

SRM 2887 is of higher molecular mass than SRM 1484.
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To confirm the above assertion, we estimate the ratio of the intrinsic viscosity at zero shear rate, 

[η]0, to the shear rate,

.

g , of the viscometer, [η]ã . Booij, Schoffeleers and Haex [15] examined 

the shear rate dependence of the limiting viscosity of high molecular mass polyethylene with 

broad polydispersity. They suggested that their viscosity data were best described by an equation 

that reduces, for polymers of narrow polydisperty and at low shear rates, to

[η]ã/[η]0 = 1- (

.

g ôm)

2 

 (12)

where 

ôm= (A0 ηS [η]w Mw

(1+r) ) /RT (13)

and [η]ã is the limiting viscosity at shear rate 

.

g , [η]0 is the limiting viscosity at zero shear rate, 

ηS is the viscosity of the solvent, R is the Boltzmann constant, T is the temperature, and A0 is a 

constant O(1). They find the exponent r = -0.7 from their data. We estimate 

.

g ôm ≈2x10-6 for 

shear rates of 2000 s-1 estimated from the manufacturer’s specifications for our viscometers. We 

can make a much more conservative estimate of 

.

g ôm using the characteristic relaxation time 

estimated from a Rouse Zimm like model, see references in [15]. For the latter model, with r =0 

and A0 = 1, we obtain 

.

g ôm ≈ 0.016. This yields a fractional correction of 0.03 % to the 

limiting viscosity. We thus assume no correction for the shear rate dependence of the limiting 

viscosity. 

 

4.3.2 Solution Concentration and Density

According to Wagner and Verdier [12], their reported value of ρ(0) has an estimated relative 

expanded uncertainty of 0.2 % and their reported value of the specific volume of the polymer in 

solution, vavg , has an expanded uncertainty of 0.04 mL/g. We used their values ρ(0) and vavg in 

our calculations. The solvent density uncertainty leads to 0. 6 mL/g expanded uncertainty in 

intrinsic viscosity and the vavg uncertainty Wagner and Verdier report leads to 0.04 mL/g 

expanded uncertainty in intrinsic viscosity (see Section 4.3.3). 

Wagner and Verdier [12] estimated a relative standard uncertainty 0.03 % in intrinsic viscosity 

due to the disregard of the buoyancy correction. Since we corrected for buoyancy, we take this 

uncertainty to be less than 0.01 %, or negligible. 

All solutions were prepared so that at least 50 mg SRM 2887 was used. We estimated that the 

balance used for this measurement had an expanded uncertainty of less than 0.1 mg. For those 

solutions where at least 50 mg was used, we estimate a 0.1 mg expanded uncertainty due to 

weighing would lead to an expanded uncertainty of 0.5 mL/g. 
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Solvent masses were measured with an expanded uncertainty of 0.01 g. A minimum of 30 g of 

solvent was used. This uncertainty had negligible effect on the results and so was taken to be 

zero.

4.3.3 Specific Volume of the Polymer

The intrinsic viscosity, [η], is the limit of

[η] = L {(ρ(c)t(c)- ρ(0)t(0))/(ρ(0)t(0)c)} (14)

where L { } is taken to mean the limit at zero concentration. Following Wagner and Verdier 

[12] using the fact that the limit of the product is the product of the limit, they find

[η] = ρ(0)-1(1+2K'/tm(0)+3)/(1-K'/tm(0)+3) * L {(tm(c)-tm(0))/(tm(0)w)}+ρ(0)-1-vavg

 (15)

where w is the mass fraction of solute in the solution and K' is the kinetic energy term derived 

from corrections given by the viscometer manufacturer [13].

This formula corrects a typographical error in their formula 11. The formula shows that the 

intrinsic viscosity as made up of two terms if we disregard the kinetic energy (KE) corrections of 

the viscometer. Assuming these KE corrections are zero we get then

[η] = ñ(0)-1 L{(tm(c)- tm(0))/( tm(0)w)} + ñ(0)-1-vavg (16)

The last two terms are the difference between the specific volume of the solvent, ρ(0)-1 , and the 

specific volume of the polymer in solution, vavg. This difference is small, about a few tenths of 

an mL/g, compared to an overall intrinsic viscosity of 276.9 mL/g for this polymer. Since vavg 

was determined on other fractions of this polymer previously [11,12], we estimate that our value 

of vavg has an uncertainty of no more than 0.04 mL/g. Thus, we take 0.04 mL/g to be the 

uncertainty in intrinsic viscosity from this contribution.

4.3.4 Timer Uncertainties

Individual flow times were recorded to 0.01 s. We take this to be the expanded uncertainty of the 

timer measurements. Since the intrinsic viscosity is the ratio of the time differences over a time, 

only the uncertainty in the time in the denominator is important. Since total flow times were 
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between 40 s and 60 s, a 0.01 s timer uncertainty would cause an expanded uncertainty of no 

more than 0.1 mL/g. 

4.3.5 Kinetic Energy or Hagenbach Corrections

As noted above, kinetic energy, or Hagenbach, corrections were estimated from tables given by 

the viscometer manufacturer [13] and obey a G/t(c)2 law. The value of G estimated from the 

manufacturer’s table is 412 s3 for our viscometer. We take our value of G to have a relative 

expanded uncertainty of 20 %, twice that assumed by Wagner and Verdier [12] for their value of 

G. This leads to an expanded uncertainty of 0.8 mL/g in the intrinsic viscosity of SRM 2887.

We may estimate this correction in a different way. If we do not consider kinetic energy 

corrections to the measured data, we compute an apparent intrinsic viscosity that differs from the 

value estimated by 4.8 mL/g. If we take 20 % of this difference as a measure of the uncertainty, 

we estimate 1.0 mL/g is consistent with the expanded uncertainty estimated above. We take 1.0 

mL/g as the expanded uncertainty from any error in the kinetic energy correction.

4.3.6 Uncertainties Arising from Temperature Uncertainties

Wagner and Verdier [12] estimate the relative temperature dependence of the intrinsic viscosity 

of polyethylene to be no more than 0.2 %/ oC for polyethylene in theta solvents. The temperature 

dependence is expected to be less in TCB, which is a good solvent for polyethylene. Following 

Wagner and Verdier, we take 1 %/ oC as the outside limit of the temperature dependence of 

intrinsic viscosity. We believe the Schott-Gerate constant temperature bath controls the 

temperature much better than 0.3 oC, including effects of temperature gradients. This conclusion 

arises partly because we have a reproducibility of better than 0.10 s out of about 41 s for the 

solvent flow times taken over a period of weeks. Further, we found a 1 oC change in temperature 

altered the measured flow time of the solvent by 0.32 s. Thus, we take 0.8 mL/g as the expanded 

uncertainty from the temperature.

4.3.7 Estimated Combined Expanded Uncertainty

In Table 1, the estimated expanded uncertainties from all sources are listed. Following NIST 

guidelines [16] we obtain the combined expanded uncertainties as the root sum of squares of 

these quantities. 

5.0 Determination of Mw of SRM 2887 by Light Scattering 
13

5.1 Solvent Preparation for Light Scattering and for Specific Refractive Index Increment

The light scattering solvent, 1-chloronaphthalene, was purchased from Aldrich Chemical 

(Aldrich Chemical, Milwaukee, WI). According to the supplier, this 1-chloronaphthalene was 90 

% pure with 2-chloronaphthalene as the only detectable impurity. A two-step purification 

method, described in Appendix II of reference [3], involved crystallizing out the 2-

chloronaphthalene followed by vacuum distillation of the 1-chloronaphthalene.

The antioxidant Santonox, 3-tert-Butyl-4-hydroxy-2-methylphenyl sulfide (Aldrich Chemical, 

Milwaukee, WI), was added to the purified 1-chloronaphthalene in order to protect the 

polyethylene from oxidative degradation during the high temperature light scattering experiments 

and differential refractive index determinations. The antioxidant was dissolved in the 1-

chloronaphthalene at a concentration of 0.1 g/L at 130 °C.

The 1-chloronaphthalene was sparged with dry nitrogen gas for a few hours immediately before 

adding solvent to polymer samples in preparing solutions to conduct experiments. The nitrogen 

sparging was used to minimize residual oxygen content in the solvent. 

Solvent recovered from light scattering experiments was recycled. After the solutions had been 

allowed to cool and the polymer had separated out, the recovered material was drained through a 

filter. The collected solvent was redistilled by the process described in Appendix II of reference 

[3]. Since the 2-chloronaphthalene impurities had already been removed exhaustively from such 

recovered solvent earlier, the preparatory refluxing process to remove the isomer was omitted. 

 

5.2 Determination of Specific Refractive Index Increment

5.2.1 Instrumentation 

The specific refractive index increment (dn/dc) for SRM 2887 was determined using a 

Chromatix KMX-16 (Thermo-Separation Products, Sunnyvale, CA) differential refractometer. 

The refractometer light source was a helium-neon (He-Ne) laser operating at a wavelength of 

632.8 nm. For room temperature calibration, the measurement cell was controlled at 25 °C. The 

measurement cell was heated to 130 °C for the solution and solvent measurements.

5.2.2 Calibration of Instrument at Room Temperature

The differential refractometer was calibrated with aqueous NaCl solutions at 25 °C. Refractive 

increments versus concentration for several aqueous electrolyte solutions at several wavelengths 

of light had been reported by Kruis [17]. Refractive increments for the same solutions at the HeNe laser wavelength, 632.8 nm, have been determined from interpolation of the data in the Kruis 
14

tables [17,18]. A cubic equation for these refractive increments as a function of NaCl 

concentration in aqueous solution at 25 °C is given in the instrument manual, and was used to 

compute the refractive increments of the aqueous NaCl solutions prepared as standards for 

calibrating the differential refractometer.

Analytical reagent NaCl (Baker and Adamson, Allied Chemical and Dye Corp, New York, NY) 

was dried in a hot air oven for approximately 18 h at a temperature of 140 °C in preparation to be 

used as a calibrant. Distilled water was degassed by boiling and left to cool to ambient 

temperature overnight in storage bottles tightly capped with zero headspace. The storage bottles 

had been leached out with several changes of boiling distilled water before being used to contain 

the degassed distilled water. Both salt and water components of each solution were measured 

gravimetrically, and atmospheric buoyancy corrections were applied to compute the 

concentrations as g NaCl/100 g H2O.

Following instructions in the instrument instruction manual [19] calibration measurements for 

the differential refractometer were conducted on four NaCl solutions ranging in concentration 

from 0.5 g NaCl/100 g H2O to 2.0 g NaCl/100g H2O in intervals of 0.5 g NaCl/100 g H2O. The 

calculated refractive increments of the solutions were fitted to their average image displacements 

to generate a linear calibration equation of refractive increment versus image displacement, 

dn/dc. The instrument calibration was found to be insignificantly changed from calibrations 

made many years earlier indicating that we were simply verifying an earlier calibration. In fact, 

the plot of the calibration verification points, when overlaid on an earlier instrument calibration 

plot, produced a graph in which the two data sets were indistinguishable.

5.2.3 Solution Preparation and Handling

Polymer solutions were prepared using 1-chloronaphthalene solvents with a mass fraction

0.01 % Santonox (Aldrich, Milwaukee, WI) antioxidant. The 1-chloronaphthalene (Aldrich, 

Milwaukee, WI) was purified by distillation before use as described in Appendix II of reference 

[3]. Solution concentrations in ranges described in Section 5.6.7 were made directly by weighing, 

without employing successive dilution techniques. Concentrations were calculated from densities 

and partial specific volumes determined earlier in this laboratory [11]. A general-purpose 

laboratory convection oven set at a temperature of approximately 145 °C was used to dissolve the 

polymer solutions. Glass bottles with ground glass necks and caps were used as dissolution 

vessels for the polymer samples. Experiments conducted earlier (private communication, R.C. 

Christensen) demonstrated that solvent loss at 130 °C through the ground glass joint was 

negligible.

Transfer of the polymer solutions from the glass dissolution vessels into the refractometer 

measurement cell was accomplished with a specially constructed glass funnel/valve assembly 

heated to approximately 145 °C. A 6.8 cm diameter Pyrex glass powder funnel was modified by

having the barrel of a 5 mL glass luer lock syringe attached to the funnel stem. An on-off valve 

(Popper & Sons, Inc., New Hyde Park, NY) was attached to the luer fitting and a shortened 20-
15

gage needle attached to the valve. The funnel was placed in a heating mantle (Glas-Col, Terre 

Haute, IN) and a flexible electric heating tape (Barnstead/Thermolyne, Dubuque, IA) was 

wrapped around the stem, valve and needle that protruded below the heating mantle. The funnel 

assembly was supported by a three-jaw clamp attached to the funnel stem and an adjustable 

height rack and pinion post (Edmund Industrial Optics, Barrington, NJ). The rack and pinion 

post was lowered to position the needle in the sample cell for filling the cell with polymer 

solution and raised above the cell to provide access to the cell by suction tubing, which was used 

to empty the cell. Heating mantle and heat tape temperature were measured with a digital 

thermocouple thermometer (John Fluke Mfg. Co., Palatine, IL) and adjusted by Variac 

autotransformers (General Radio Co., Cambridge, MA). Dissolved polymer solutions were 

removed from the oven and poured from the dissolution bottle into the heated funnel. Using the 

on-off valve on the funnel stem, the refractometer measurement cell was filled with hot polymer 

solution. Following the instrument instruction manual [19], the cell was filled and emptied five 

times before measurements were made on the solution. 

5.2.4 Measurement of (dn/dc) at 130 °C 

Refractive index increments between solvent and solutions of polyethylene in 1-

chloronaphthalene were determined on solutions that had been prepared on the morning of the 

day the measurements were made. Six solutions with concentrations between 2.7 g/L to 6.0 g/L 

of SRM 2887 were prepared by the procedure describe in Section 5.2.2. For each solution two 

repeated image displacement measurements were conducted on these solutions of SRM 2887 

following methods as outlined in KMX 16 manual. Solvent-versus-solvent measurements were 

made before and after each solution-versus-solvent measurement. The incremental image 

displacement by each solution was obtained by subtracting the mean of the bracketing solvent 

average image displacements from the average image displacement by the solution. The 

refractive index increment of each solution was computed by application of the calibration 

equation to the incremental image displacement of the solution. The specific refractive index 

increments were obtained by dividing the refractive index by the concentration of the solution. 

The average value of the specific refractive index increment of the solutions was found to be, 

dn/dc = -0.1798 mL/g, for SRM 2887 in 1-chloronaphthalene at 130 °C with a standard 

uncertainty in the fit of 0.0029 mL/g. This issue of uncertainty and fit of this measurement will 

be discussed in Section 5.10.3.

Previous reports of the differential refractive index at 632.8 nm for other comparable 

polyethylenes in 1-chloronaphthalene gave values ranging from -0.178 mL/g to -0.183 mL/g at 

135 oC. Our value is well in the range of these reported values [21,22]. However, the value we 

obtained for SRM 2886 is slightly more negative than this value. Normally, the dn/dc for these 

high molecular mass polyethylenes would be expected to be the same. However, for 

polyethylene, Wagner and Hoeve [20] report molecular mass dependence of dn/dc, even at high 

molecular masses. 
16

5.3 Refractive Indices of Solvent and Calibrant 

The primary standard for this measurement is benzene; other standards are derived from it. The 

refractive index of the benzene primary standard at 23 oC and 632.8 nm is taken to be 

1.4941[23,24]. 

G. B. Arrowsmith, G. H. Jeffrey, and A. I. Vogel [25] tabulated the refractive index at the 

Sodium D line nD=1.63315 at 20 oC and a density at 20 oC of 1.1932 g/mL for 1-

chloronaphthalene. Christensen [11] reported the density of 1-chloronaphthalene as

1.098 g/cm3at 130 oC and Wagner [26] reported the density of 1-chloronaphthalene as 1.098 

g/cm3at 135 oC. The Lorentz-Lorenz molar refraction relation is used to estimate the refractive 

index for 1-chloronaphthalene at 130 oC from the densities at 20 oC and130 oC and the refractive 

index at 20 oC. Since the refractive index of 1-chloronaphthalene at 130 oC, nD=1.5772, is only 

used in the reflection correction to the Mw the limited accuracy of this value is acceptable. 

Dow Corning 705 silicone oil is used as the vat fluid. The Lorentz-Lorenz molar refraction 

relation was applied to the refractive index at 632.8 nm at 25 oC, and the density at various 

temperatures (Dow technical consultant Gary McIntyre) to estimate the refractive index of the 

Dow Corning 705 silicone oil at 130 oC as nD = 1.516. Since the refractive index of Dow Corning 

705 silicone oil 130 oC is only used in the reflection correction to the Mw the limited accuracy of 

this value is acceptable.

 

5.4 Design of Light Scattering Instrument

Dr. Charles Han of the NIST Polymers Division designed and constructed the light scattering 

apparatus. We review here some of the details of the instrument. A Universal circular dividing 

table (Universal Vise & Tool Co.), with a center bore design, is used as the goniometer. This 

goniometer is mounted on a rigid optical table (Newport Research Corporation). A beam of 

vertically polarized incident light (wavelength = 632.8 nm) is provided by a 10 mW He-Ne laser 

(Melles-Griot) also mounted.

The goniometric axis is defined by the center of the goniometer and aligned with a tapered center 

bore in the goniometer. The vat housing, which contains the sample cell, is mounted on an 

aligning rod with a precision-machined taper to engage the complementary taper of the center 

bore of the goniometer. The receptacle hole for the sample cell is machined at the cylindrical 

axis in the top flange plate of the vat housing. By this arrangement, the center axis of the 

cylindrical cell and the vat housing are held coincident with the goniometric axis. The intensity 

of light scattered at varied angles from the sample cell is measured by a photomultiplier in the 

receiving optics mounted on a rigid beam attached to the goniometer. 

The vat is thermostatted by a copper cylinder, which is built onto the underside of the vat housing 

cover plate, and extends down into the vat fluid. The vat temperature is controlled and indicated 

by a PID temperature controlling system, a copper constant current supplier, a four wire RTD and 
17

a voltage comparitor. The controlling system receives a voltage imbalance signal from a fourwired platium resistance temperature probe in the thermostatting cylinder and the voltage 

comparitor, and sends energy to cartridge heaters in the thermostatting cylinder. When working 

at high temperatures, significant thermal gradients can develop inside the vat between the 

thermostatting cylinder and the peripheral region of the vat. Such thermal gradients were 

repressed by applying a flexible heating mantle to the external cylindrical surface of the vat 

housing, and controlling the mantle temperature at a few degrees Celsius below the experimental 

temperature. The mantle was specially constructed for this apparatus, and the control provided by 

HPS Division, MKS Instrument, Inc. (MKS Instrument, Inc, 5330 Sterling Drive, Boulder, CO 

80301). 

Light scattering cells were fabricated from precision ground and polished glass tubing to uniform 

wall thickness (Wilmad Glass Co.), with both inside and outside cylindrical surfaces polished. 

The tubing is of 33 mm outside diameter and has a refractive index nD = 1.50.

5.5 Instrument Calibration Protocol at 130 oC

1,2,4-trichlorobenzene (TCB) (Aldrich Chemical high purity, Milwaukee, WI) was employed as 

the working light scattering calibration standard at 130 oC. The calibration of TCB as the 

working standard is traced to the Rayleigh ratio (RV) of benzene at ambient temperature (23 oC) 

in vertically polarized incident light of 632.8 nm wavelength, determined by Kaye & McDaniel 

[27]. 

First, a Durasil optical glass rod was calibrated by comparing its scattering intensity at a 90o

angle with that of a benzene cell at the same angle, with the glass rod and benzene cell both at

21 oC. Then the vat temperature was increased to 130 oC in which environment three TCB cells 

were calibrated by comparison of their scattering intensities with that of the glass rod. The 

effective RV of the glass rod is assumed to be invariant with temperature in this range. However, 

relating the scattering intensity measurements at the two temperatures requires conservation of 

the optical alignment with change in temperature. The only significant disturbance in the optical 

alignment results from the change in refractive index of the vat fluid with change in temperature. 

This problem was solved by conducting the measurements at 21 oC with the vat filled with 

anisole which has nD = 1.5160 at 20 oC, and conducting the measurements at 130 oC with the vat 

filled with Dow Corning 705 silicone oil which has nD = 1.516 at that temperature. 

 

The scattering intensities at 90o angle (I90) of the benzene standard cell and the glass rod standard 

were measured alternately at 21 oC. A total of 40 such pairs of measurements were conducted 

over an interval of two days. The resulting population of experimentally determined scattering 

intensity ratios yielded an average [I90(GLASS)/I90(BENZENE)] with a relative standard 

uncertainty of 1.16 %.

A series of TCB standard cells was prepared by filtering high purity TCB into each cell through a 
18

double layer of Millipore cellulose acetate-nitrate membrane with 0.2 ì m pore size. Filtration of 

TCB into the cells was conducted at ambient temperature. It was found that a TCB sample could 

be maintained at the experimental temperature (130 oC) and slightly higher for at least two days 

without detectable change. A new TCB standard cell was prepared for use with each set of 

solutions during the characterization of this polymer by light scattering. The I90 of the glass rod 

standard was compared with the I90 of each of three TCB cells at 130 oC. The I90 values of the 

glass rod and the TCB cell were measured alternately. A total of 14 pairs of such I90

measurements were conducted with the glass rod and each of the TCB cells, resulting in three 

average values for the ratio [I90(TCB)/I90(GLASS)] in very close agreement. The three 

determinations resulted in a single average value for the ratio with a relative standard uncertainty 

of 0.20 %.

As small error was introduced because we measured the ratio of scattering from benzene to the 

glass cell, S, at 21 OC not at 23 O C where the Rv was measured by Kaye and McDaniel [27]. Ehl, 

Loucheux, Reiss, and Beniot [28] have measured this temperature variation. Our measurements 

of S give us S21, the S at 21 OC. We need S23 , the ratio measured with benzene and the glass rod 

at 23 OC. From Ehl, Loucheux , Reiss and Beniot [28] we estimate

S23 = 0.9946 S21

As noted earlier, Kaye and McDaniel [27] determined the value RV =12.63x10-6 for benzene 

under these optical conditions, with a standard uncertainty of 0.21x10-6. The product of ratios, 

[I90(GLASS)/I90(BENZENE)] and [I90(TCB)/I90(GLASS)] gave a value of S21. This was applied 

to the RV for benzene by Kaye and McDaniel to estimated working value of RV=35.6 x10-6 for 

the TCB at 130oC in vertically polarized incident light of 632.8 nm wavelength. The standard 

uncertainty for this value of S21 is computed as the root sum of squares of the standard 

uncertainties of the two ratios.

This method of calibration was tested by using TCB as the working standard in light scattering 

experiments to determine the molecular mass (Mw) of the polyethylene standard, SRM 1483. 

The resulting Mw from these experiments conducted with TCB as the calibrating standard were 

statistically indistinguishable from the certificate value of the Mw for SRM 1483 [2]. 

 

5.6 Solution Preparation

SRM 2887 samples from the SRMP vials were weighed on an OHAUS GA200D analytical 

electrobalance (Ohaus Corp., Florham Park, NJ), with 0.0001 g resolution, and transferred to 

sample bottles. All polymer samples weighed 30 mg or greater in order to repress relative 

uncertainty in the sample mass. The 1-chloronaphthalene was sparged for 2 h with dry N2 gas. 

The sparged solvent was then measured into bottles containing the polymer samples, plus two 

empty bottles to contain solvent samples. The solvent mass was determined by mass difference 

on a Mettler PE 3600 electrobalance.(Mettler Toledo, Columbus,OH). Atmospheric buoyancy 
19

corrections and densities of solvent and polymer were applied to calculate absolute solution 

concentrations at the experimental temperature. Both balances were checked during the 

certification period often by a NIST calibrated 50 mg mass for the Ohaus balance and a NIST 

calibrated 50 g mass for the Mettler. The balances read with accuracy to the last reading value.

Solution concentrations in range described in Section 5.9 were made directly by weighing, 

without employing successive dilution techniques. Concentrations were calculated from densities 

and partial specific volumes determined earlier in this laboratory [11]. The bottles were capped 

with ground glass tops and placed in an oven at about 150 oC. They were heated and agitated 

occasionally for about 2 h before commencing filtration.

The syringe filter assembly used was a 25 mm diameter stainless steel Swinny type (Millipore 

Corp., Bedford, MA). The Swinny filter was attached to a glass syringe modified by adding a 

spherical joint at the top end, to provide connection to a dry nitrogen source used to apply an 

inert low-pressure gas to propel solution through the filter at a realistic rate. Each Swinny was 

assembled with a double layer of Pall-Gelman Sciences ZEFLUOR all-Teflon filtering 

membrane with 0.5 ì m pore size (Pall Corp., Port Washington, NY). These filtering assemblies 

were heated to 150 oC in the oven along with the solvent and solution bottles.

After the polymer samples had dissolved to form clear homogeneous solutions, the solvent and 

solution samples were filtered into their respective light scattering cells.

The hot filtration was conducted in a thermostatted apparatus that maintained both cell and 

filtering assembly in the range 140 oC to 150 oC. The filtering assembly was heated in a vertical 

glass cylinder wrapped with a nichrome coil heating element. The cell was mounted in an 

aluminum block heater below.

After the solution sample was poured into the filtering assembly, and the low nitrogen gas 

pressure was applied, the first (5 to10) cm3 filtrate was collected in a waste vial and discarded. 

The next approximately 20 cm3 filtrate was directed into the light scattering cell. The N2 gas 

pressure was adjusted to obtain a filtration flux of about 1 drop per few seconds to a few drops 

per second.

Subsequent light scattering measurements generally indicated a high success rate in obtaining 

solution and solvent samples free from dust contamination. At the conclusion of an experiment, 

the cell components and filtering assembly components were cleaned with refluxing hot xylene 

vapors. This cleaning process appeared successful in removing dust and polymer exhaustively. 

5.7 Measurement Protocol 

The temperature was controlled at 130.0 oC ± 0.2 oC in all light scattering measurements on 

polyethylene in 1-chloronaphthalene. In all experiments, the intensity measuring system was 

calibrated with the scattering intensity at 90o angle (I(90)) by a TCB standard cell described 
20

above; the scattering intensity from the solvent and each solution was measured at eight angles in 

the range from 45o to 135o. Scattering intensity measurements versus angle (I(è)) were conducted 

with the solvent cell immediately following the calibration against TCB, and twice more after 

I(è) measurements had been conducted on all the solution cells.

All cells containing the TCB secondary standard and samples of solvent or solution were stored 

in an oven at (140 to150) oC. Each cell was transferred from the oven to the vat in preparation 

for scattering intensity measurements, and allowed to remain undisturbed in the vat for at least

10 min to equilibrate at the experimental temperature before initiating the measurements.

At the conclusion of each experiment, the TCB secondary standard cell was withdrawn from the 

oven and stored at ambient temperature. In two cases replicate light scattering experiments were 

conducted with a set of solution and solvent samples on the day following the initial experiment, 

after the polyethylene had been in hot solution environment for longer than 24 h. The TCB 

secondary standard cell was returned to the oven a few hours before initiating the replicate 

experiment in order to heat it up to the range of experimental temperature. These replicate 

experiments gave results, which appeared to indicate thermal stability of this polymer in its high 

temperature solution state over an interval of at least 24 h. 

5.8 Analysis of Light Scattering Data 

Light scattering data from polymer solutions of concentration c and scattering angle Θ may be 

analyzed by fitting the scattering signal I(Θ,c) to [29]

I(Θ,c)=I(Θ,0)+c IG/ {(sin Θ)∑Cijc

i

sin2j(Θ/2)}. (17)

 ij

 

In eq. (17), IG is the scattering signal from the TCB working standard at Θ = 90°.

We must first decide how many terms on the right-hand side of eq. (17) need to be included to 

provide an adequate fit to the experimental data. The dependence of c/Ic, where Ic = sinΘ[I(Θ,c)-

I(Θ,0)]/IG, upon c and upon sin2(Θ/2) reflects solute-solvent interactions and solute size, 

respectively. Accordingly, preliminary scattering data for SRM 2887 were first analyzed as c/Ic

versus sin2(Θ/2) and c and c2 , to see whether a linear expansion (i.e., retaining only C00, C01, 

and C10) would provide an adequate fit. The analysis revealed that the linear approximation was 

adequate at concentrations below 5 g/L for SRM 2887 (see Section 5.10.13 for a more complete 

discussion). 

Thus, we used for the final analysis

I(Θ,c) = I(Θ,0) + c IG/{sin Θ (C00 + C01 sin2(Θ/2) +C10c + C20c

2 )} (18)

The coefficients in eq. (18) are related to the Mw, molecular mean-square radius of gyration, RG

2

, 
21

the second viral coefficients, A2, and the third virial coefficients, A3, by [29,30]:

Mw = (K''C00)

-1

(19)

RG

2

 = 3[λ0/(4πn)]2C01/C00 (20)

A2 = K''C10 /2 (21)

A3 = K''C20 /3 (22)

K'' = 4π

2

nB

2

(dn/dc)2/(λ0

4NARvB

 S23) (23)

where:

λ0 is the wavelength in vacuum of the scattered light, 632.8 nm in this work, n and nB are the 

indices of refraction of the solvent at 130 oC and benzene at 23 oC taken as 1.5772 and 1.4941, 

respectively calculated as described in Section 5.3, dn/dc is the specific refractive index 

increment of the solution, measured as described in 5.6.7, NA is Avogadro's number, taken as 

6.022 x 1023 /mol, Rv

B

 is the Rayleigh ratio for the total scattering of vertically polarized light 

from benzene at 23 oC, used as the calibration standard. S23 is the ratio of the scattering of the 

benzene at 23 oC to the TCB working standard at 130 oC. The method of obtaining S23 is 

described in Section 5.5. 

Preliminary fitting was done in the Zimm form, that is, plots of c/Ic versus sin2(Θ/2) and c, or if 

we wish to include third virial terms as c/Ic versus sin2(Θ/2) and c and c2 . In the Zimm form we 

found less than 1% relative change in the fitting parameters, particularly the molecular masses, 

between the fits including or excluding the c2 term. We then fit to the nonlinear form in eq 18. 

This allows us to include the correct weighting of the data and also the zero concentration terms. 

Again we found only small changes in all fitting parameters between the fit to the Zimm form 

and the fit to the form of eq.18 even when we included c2 terms in the form of eq. 18.

5.9 Results for SRM 2887 

Five sets of light scattering solutions were made from SRM 2887 using 1-chloronaphthalene as 

solvent. Each set consisted of four to five independently prepared solutions of the approximate 

concentrations in the range of (0.3 to 2) g/L. The polymer for each solution within each set was 

taken from the SRM sample vials or the division supply lots. Intensities were measured at eight 

scattering angles in the range from 45o to 135o. The intensities of scattered light in each set were 

fitted by least squares as explained above, and the results were used to calculate Mw, A2, A3, and 

Rg using eqns (19)-(23). The values of Mw, A2, A3, and Rg obtained from the five sets were then 

averaged. Light scattering gave a Mw of about 196.4 x10+3 g/mole with a sample standard 

deviation of 6.6 x10+3 g/mole and a deviation of the mean of 3.0 x10+3 g/mole, a value of A2 of 

0.00076 mol mL/g2 with a standard deviation of the mean of 0.00009 mol mL /g2, a value of A3
22

of 0.020 mol mL/g2 with a deviation of the mean of 0.010 mol mL /g2and a value of Rg of 31.8 

nm with a standard deviation of the mean of 4.1 nm.

Han, Wagner and Verdier [29] in their earlier study on SRM 1482, SRM 1483 and SRM 1484 

estimated Rg = 8.2 nm for SRM 1483 which has an Mw = 32.1x10+3 g/mole and Rg = 21.7 nm for 

SRM 1484 with Mw =119.6 x10+3 g/mole. For SRM 1483, they consider the possibilities of large 

systematic uncertainties in Rg. We have the same problems with the Rg we estimate. This is due 

to problem of alignment we find with our I sin(È). Considering all these problems, our value of 

31.8 nm is in close agreement to their values if we do an extrapolation of their data as a function 

of molecular mass.

The standard deviation of the mean for the average Mw of SRM 2887 is 3.3 x10+3 g/mol. In 

compliance with the NIST policy [16] on reporting uncertainties in measurement, the component 

uncertainty due to variance among the five Mw determinations is computed as the standard 

deviation of the mean. Table 3 reports twice this value as the expanded uncertainty.

5.10 Estimation of Uncertainties Due to Systematic Effects in the Light Scattering

We list the likeliest sources of systematic uncertainty in the determination of Mw by light 

scattering measurements described in the preceding sections, and attempt to estimate upper limits 

for their magnitudes. For this purpose, we employ a scheme similar to that used in ref. [29] for 

the estimation of systematic uncertainties in SRM's 1482, 1483 and 1484 and ref [31] on the 

recertification of SRM 706a. These uncertainties are listed in Table 2 for SRM 2887.

5.10.1. Indices of Refraction 

Following Ref. [29], we estimate that 0.1% is a proper upper limit for systematic relative 

standard uncertainties in Mw arising from uncertainties in the literature values of benzene index 

of refraction, the calibrating liquid. 

5.10.2 Calibration of the Differential Refractometer 

5.10.2.1 Literature Values of dn/dc for Aqueous NaCl 

Calibration of the differential refractometer required interpolation of the data of Ref. [17,18,19] 

to the 632.8 nm wavelength used in the light-scattering measurements. We estimate the relative 

uncertainty in the interpolated values of Än as 0.6 %, due primarily to uncertainties in the 

interpolation process. The calibration factor determined for our differential refractometer had a 

relative standard deviation (rsd) of 0.097 %. Applying a coverage factor of 2 to this rsd yields a 

Type A expanded uncertainty of 0.19 % for this measurand [16]. Combining this uncertainty 

with an allowance for possible linear uncertainties in the refractometer, we estimate that a proper 
23

upper limit for relative uncertainty in dn/dc is 1%. Considered as a 95 percent confidence 

interval estimate, this quoted uncertainty provides a expanded uncertainty in dn/dc of 1 % which 

would contribute a 2 % or 4.0 x10+3 g/mol expanded uncertainty in Mw determination.

5.10.3 Measured Value of dn/dc of SRM 2887 

The differential refractive index dn/dc of SRM 2887 in 1-chloronaphalene at a temperature of 

130 oC was determined as described in Section 5.2.4. The mean value obtained for dn/dc was

-0.1798 mL/g, with a standard deviation of 0.0029 mL/g. The uncertainty in the mean is then 

0.0013 mL/g. We take the expanded uncertainty of this measurement as 0.0026 mL/g or a 

relative uncertainty of 1.4 %.

There appears to be a small concentration drift in the data. This is mainly due to the highest 

concentration point. To check the effect of this drift, we refit the data dropping the highest 

concentration and found a dn/dc of -0.1791 mL/g, a number well within our expected expanded 

uncertainty. Furthermore, an ANOVA of the data did not indicate the that the highest 

concentration dn/dc to fall out of the error expected from the rest of the data. We therefore 

accept that we can average the data.

As the dn/dc appears as the second power in the Mw calculation, the uncertainty in the calculated 

Mw that results from the uncertainty in the dn/dc is estimated as twice the estimated relative 

expanded uncertainty in the dn/dc, or 2.8 %. This gives an expanded uncertainty in the Mw of 5.6 

x 10+3 g/mole. 

Contributions to the uncertainty of the value of the density of the solvent to dn/dc are discussed 

in Section 5.10.8.

5.10.4 Wavelength of Radiation

For the He-Ne laser employed in this work, uncertainties in the wavelength of the radiation are 

completely negligible compared with uncertainties from other sources.

5.10.5 Calibration Constant for Light Scattering

The protocol for the calibration is described earlier. For each step, we estimate an uncertainty.

5.10.5.1 Rayleigh Ratio of Benzene at Room Temperature

For benzene at 632.8 nm, Ref. [25] gives: RV,V+H = 12.63x10-6 cm-1. We abbreviate RV,V+H by 

R. The authors of Ref. [25] apparently believed that their R-values have a relative standard 

uncertainty of < 2 % (all from systematic uncertainty). They quote a relative standard deviation 
24

for their R-value for benzene of 0.21/12.63, or 1.7 %. This yields a relative expanded uncertainty 

of 3.9 %, or 7.8 x10+3 g/mol. 

5.10.5.2 Estimating Ratio of Benzene Scattering to Glass Rod Scattering at Room Temperature

We have run 20 repeats of the measurements of the ratio of the scattering of the benzene 

calibrant to the scattering of the glass rod as described in Section 5.5. We take the uncertainty in 

the repeatability of this experiment as the overall uncertainty of the measurement. The relative 

standard deviation of this measurement is given as 1.2 %. The relative standard deviation of the 

mean is 0.27 %. We take 0.6 %, or 1.2 x10+3 g/mol, as the expanded uncertainty from the ratio 

of the benzene scattering to the glass rod scattering.

A small correction is introduced arising from the fact we calibrated our rod against benzene at

21 oC, rather than benzene at 23 oC. We estimated that correction was 0.9946 from literature 

value on the temperature variation of the scattering from benzene [28]. We estimate from that 

work as a generous estimate of the relative expanded uncertainty from this calculation to be

0.2 %, or less than 0.4 x10+3 g/mol. 

From both above corrections we take an expanded uncertainty from all these contributions to be 

1.3x10+3 g/mol.

5.10.5.3 Temperature Dependence of Scattering of Glass Rod from 21 oC to 130 oC

Han, Wagner and Verdier [29] discussed this issue in Section 4.1.3 of their paper on Mw

determinations of SRM 1482, SRM 1483, and SRM 1484. Since the uncertainty is in the 

calibration it appears as a percentage of the final result. In that paper, they concluded the 

maximum relative expanded uncertainty of assuming the scattering of the rod is unchanged from 

23 oC to 130 oC is 0.4 % of the Mw. Here, we accept their estimate as the expanded uncertainty. 

This leads to an expanded uncertainty of Mw for this polymer of 0.8x10+3 g/mol.

5.10.5.4 Estimating ratio of Glass Rod Scattering to TCB Scattering at 130 oC

We have 42 repeat measurements of the ratio of the scattering of the glass rod to the scattering 

from the TCB working standard, described in Section 5.5. We take the uncertainty in the 

repeatability of this experiment as the overall uncertainty in this measurement. Fourteen 

measurements of the ratio of the glass rod scattering to that of TCB, the working standard, were 

made for each of three different scattering cells containing TCB. The relative standard deviation 

of the mean is 0.2 %. We take 2 times this uncertainty as the expanded uncertainty from the

ratio of the benzene scattering to the glass rod scattering. This yields 0.4 % as the relative 

expanded uncertainty, or 0.8x10+3 g/mol.
25

5.10.6. Uncertainties in the Polarization of Light

There are two uncertainties associated with the laser light. First, the "vertically polarized" laser 

beam actually contains "horizontally polarized" components for two reasons: the polarizer inside 

the laser head lets through a small fraction ε of the "wrong" polarization and the principal axis of 

polarization of the light from the laser may not be exactly perpendicular to the optic plane 

defined by the incident and scattered beams. Both uncertainties will cause light, assumed to be 

vertically polarized, to contain a small admixture of horizontally polarized light. The effect upon 

scattering signals from SRM 2887 will be slight, but the effect upon the benzene calibration 

signals is to change the effective Rayleigh ratio that should have been used toward the RH,V+H

value. The resulting uncertainty in Mw is ε/(1-ε) for the first effect and tan2α, where α is the 

angular mis-setting, for the second. We take ε = 1/500 and α = 5

o

. Then the relative expanded 

uncertainty from ε is less than 0.2 % with at least a 95 % level of confidence considering the 

liberal boundaries assigned to the constituent uncertainties. The uncertainty from α is less than 

0.8 % with at least a 95 % level of confidence considering the liberal boundaries assigned to the 

constituent uncertainties. Following NIST guidelines we take the root-sum-of-squares from 

these contributions to yield the standard uncertainty of 0.85 % and the relative expanded 

uncertainty from this contribution of 1.7 %, or 3.4 x10+3 g/mol.

5.10.7 Ratio of Working Standard Scattering to Sample Scattering

Since photon-counting techniques were employed, there should be no systematic uncertainties 

from this source. Random uncertainties are reflected in the overall random uncertainty of the 

Mw.

5.10.8 Solvent Density

For the density of 1-chloronaphalene at 130 °C, we used the value 1.098 g/mL as given in 

references [11,26]. Following Han, Wagner and Verdier [29], we estimate that this value has a 

relative expanded uncertainty <0.1 %. The resulting relative expanded uncertainty on Mw is just 

0.2 %, or 0.4x10+3 g/mol.

5.10.9. Solute and Solvent Masses

For the measurements actually used in the final determination of Mw for SRM 2887, the 

concentrations employed were nominal (.5 to 2.0) g/L. Solvent masses were chosen so that the 

solute masses were always about 0.05 g. Using the uncertainty limit of 0.05 mg we usually 

assign to the balance used to weigh the PE samples, we have relative uncertainties of 0.1 % in the 

solute masses. The balance used for solute measurements was regularly checked with a 50 mg 

mass standard calibrated by the NIST Mass Division and was found to vary by less than 0.01 mg 

from the standard. The uncertainty in Mw is then the relative uncertainty in solute masses, or 
26

about 0.1 % with at least a 95 % level of confidence. This 95 % confidence interval estimate 

provides a relative expanded uncertainty of 0.2 %, or 0.4x10+3 g/mol. 

Solvent masses of at least 30 g were used in solution preparation. The solvent balance was 

checked against a 100 g mass standard and found to be off by less than 0.01 g. The solvent 

masses were measured to 0.01 g. Thus, there are negligible uncertainties in solvent masses.

5.10.10 Reflection Correction 

The refractive index of 1-chloronaphalene at 130 °C is given as nD = 1.5772 by an estimate 

described in Section 5.3. The refractive index of the sample cell is given by the vendor as n D = 

1.500. Although the wavelength of the reported refractive index of 1-chloronaphalene and of the 

cell are different from that used in our experiments, these values should be adequate to estimate 

what will turn out to be an extremely small uncertainty. Han, Wagner and Verdier [29] assumed 

that the refractive index difference between the sample cell and 1-chloronaphalene was about 0.1, 

an extreme overestimation for our case. With that assumption, they found for a scattering system 

like ours, a reflection correction of 0.1 yields a reflectance factor f = 2 x 10-3. Comparison 

calculations of Mw for SRM 1484 with and without this correction show the resulting relative 

standard uncertainty to be less than 0.01%. The equivalent calculation for SRM 2887 would 

yield a standard uncertainty of less than 0.01%. We take the uncertainty in the molecular mass 

from this contribution to be zero.

5.10.11 Instrumental Misalignment 

The effects of instrument misalignment are difficult to estimate. For the geometry of the current 

high temperature light scattering instrument, it is expected that any deviation from constancy of

I sin(Θ) is indicative of instrument misalignment. We look at this effect in two different ways.

First, I sin(Θ) values calculated from solvent scattering indicated alignment problems. Whereas 

these values divided by the intensity at 90° should be independent of Θ they showed a fractional 

variation of 0.6 % to 1.0 %. If we assume that the data scales with this uncertainty, we would 

estimate a relative expanded uncertainty of 0.6 % to 1.0 % in Mw. 

Second, from our experience with the alignment, we would also estimate the maximum 

misalignment to be 0.2°. We have examined two sets of data by purposefully recomputing the 

Mw putting in a misalignment of 0.2°. They consistently both show for a systematic angle 

variation of +0.2° the Mw varies by a fraction of about 1.0 % and for an angle of -0.2 ° the Mw

varies by -1.0 %. 

Since both estimates of uncertainty yield a maximum expanded uncertainty of about 1 % from 

misalignment, we estimate a total relative expanded uncertainty arising from instrument 

misalignment of 1.0 %, or 2.0 x10+3 g/mol for SRM 2887.
27

5.10.12 Anisotropy of Solute

Following Han, Wagner, and Verdier [29], we find that equations for Mw and K'' in Section 5.8 

are derived on the assumption that the light scattering from the polyethylene is not depolarized. 

When the solute is optically anisotropy, Mw should be replaced with Mw(1+ε) where the 

correction term is given by:

ε = (1/45)(1/Mw) (<γ

2

>/Mw)[4πnsNa/(dn/dc)2

 where < γ

2

 > is given approximately by 267 x10-50 cm6 per CH2 group [32,33]. Thus < γ

2 >/M 

is 1.91 x 10-49 mL2 /g. We estimate ε for SRM 2887 as 0.0003. We take this to be a relative 

expanded uncertainly of 0.03 % on Mw. We consider this correction and uncertainty on this 

measurement negligible.

5.10.13 Cutoff of Virial Expansion for SRM 2887

 

We follow the method of Han, Verdier and Wagner to judge if our analysis of the data for SRM 

2887 is affected by the cutoff of the virial series at the third virial term. First, we notice the third 

virial has a very large error suggesting the effect of this contribution is small. The error between 

sets is large and an inspection of our fitting data suggests the error of fit within a set is large too. 

If we look at the contribution from each term in the series for the average of the sets we find the 

ratio of terms C00 : C10 c: C20 c

2

 at the maximum concentration used for the fitting , 2g /L , is 

1:0.6: 0.05 which seems to be a rapidly converging series. To check this, we examined the effect 

of the fourth virial on the calculated quantities. Following Han, Verdier and Wagner, we 

estimate C30 ≤ C10C20/C00 . The equality gives the maximum contribution from C30. The effect 

of the maximum size of the C30 contribution was estimated by subtracting the value of C30c

3

 from 

every data point. The Mw was recomputed from these modified data. The change in molecular 

mass from the data without the contribution was used to estimate the maximum relative standard 

uncertainty resulting from this contribution. For the five data sets the effect ranged from 0.15 % 

to 0.25 %. We estimate the relative expanded uncertainty from this contribution to be 0.5 %, or 

1.0 x 103 g/mol.

5.10.14 Scattering Changing during the Measurement: Degradation and other Sources 

By their nature light scattering experiments are of short duration. A number of solutions can be 

prepared and examined by light scattering in a single day. To avoid instability problems solutions 

used in the certification of Mw were prepared and measured on the same day. To test stability we 

conducted a second set of measurements on the same solutions a few days later. Of the two runs 

of SRM 2887 where stability was investigated, Mw was seen to increase by a fraction of 2.2 %, or 

1.9 x10+3 g/mol, and 4.4 %, or 3.8x10+3 g/mol, when the solutions were stored at 130 °C as long 

as 2 d after preparation. We estimate that the light scattering data used in certification of SRM 
28

2887 were acquired within 12 h after the solutions were first heated. We take the factional 

contribution to the uncertainty due to changes during the first 12 h of heating to be at most 2 %, 

or 4.0x10+3 g/mol. We take this to be our expanded uncertainty from this part of the 

measurement. 

5.10.15 Summary

The combined expanded uncertainties, Uc, of SRM 2887 are computed as root-sum-of-squares of 

the component expanded uncertainties, ui', following the formal NIST policy for evaluating and 

expressing uncertainty in measurements [16]. In Table 3, we find that the combined expanded 

uncertainty, Uc, of SRM 2887 is 13.7x10+3 g/mol. 

6.0 Conclusions

The Mw of SRM 2887 by light scattering was determined to be 196.4 x10+3 g/mol with a sample 

standard deviation of 6.6 x10+3 g/mol. A combined expanded uncertainty for this light scattering 

Mw determination including all type A and type B uncertainties was 13.7x10+3 g/mol. The 

intrinsic viscosity of SRM 2887 by solution viscosity in 1,2,4-trichlorobenzene was determined 

to be 276.9 mL/g with a sample standard deviation of 2.5 mL/g. The standard deviation on the 

mean value was 0.4 mL/g. A combined expanded uncertainty for this intrinsic viscosity 

determination including all type A and type B uncertainties was 3.1 mL/g. The bottle-to-bottle 

variation of the SRM was check by size exclusion chromatography and found to be negligible. 

Acknowledgements

The authors would like to thank Charles Han for the use of his high temperature light scattering 

instrument and his help and discussions concerning this project. Sachin Bhatt assisted with the 

limiting viscosity measurements.
29

Table 1

Contributions to Expanded Uncertainty in Measured Intrinsic Viscosity of SRM 2887

 

Source of Uncertainty Uncertainty ( mL/g)

Shear rate dependence 0.0

Solvent density, ρ(0) 0.6

Polymer specific volume, vve 0.04

Buoyancy corrections 0.0

Solute masses 0.5

Solvent masses 0.0

Timer 0.1

Kinetic Energy correction factor 0.8

Measurement temperature 0.8

Sample uncertainty in fit of data 2.5

Combined Expanded Uncertainties 3.1

 
30

Table 2

Contributions to Combined Expanded Uncertainty

 Of the Mw of SRM 2887

Source of Uncertainty Contribution

(10+3 g/mol)

Expanded Uncertainty from standard deviation of the mean 6.6

Solvent index of refraction 0.2

Calibration of differential refractometer 4.0

Differential refractive index 5.6

Wavelength of light <0.1

Rayleigh ratio of scattering standard, benzene 7.8

Ratio Scattering Benzene to glass rod 1.3

Temperature Dependence Glass Rod 0.8

Ratio Scattering glass rod to TCB scattering standard 0.8

Polarization of light 3.4

Ratio of standard scattering to sample scattering <0.1

Solvent density 0.4

Solute and solvent masses 0.4

Light reflection <0.1

Instrumental misalignment 2.0

Anisotropy of polymer in solution <0.1

Truncation of virial expansion 1.0

Scattering change during the scattering measurement 4.0

Combined expanded uncertainty *, Uc 13.7

* by root-sum-of-squares [16]
31

References

[1] "Standard Practice for Dilute Solution Viscosity of Polymers" D2857-93, Annual Book of 

ASTM Standards, Vol 08.02 1995, ASTM, Philadelphia, PA.

[2] Peter H. Verdier and Herman L. Wagner, "The Characterization of Linear Polyethylene 

SRM's 1482, 1483, and 1484. I. Introduction" NBS Special Publication 260-61, P.H. Verdier 

and H.L. Wagner ed. December 1978 or National Bureau of Standards, Journal of Research, Vol. 

83, No. 2, March - April, 1978, pg. 169-171.

[3] C. M. Guttman, J. R. Maurey and W. R. Blair, "Certification of the Relative Molecular Mass 

and the Limiting Viscosity of SRM 2886, a Polyethylene of Narrow Molecular Mass Distribution", 

NISTIR 6487, 2001. 

[4] M. G. Natrella, "Experimental Statistics", National Bureau of Standards Handbook 91, U.S. 

Department of Commerce, 1963.

[5] Charles M. Guttman and John R. Maurey, "Recertification of Standard Reference Material 

1475a, A Linear Polyethylene Resin", NISTIR 5199, 1993.

[6] L. Huber, "Application of the Diode-Array Detector in HPLC", Hewlett Packard, France, 

08/89, pg. 89-100.

.

[7] Barry J. Bauer, Brian Dickens and William Blair, "Chromatographic Examination of Intaglio 

Inks, Resins and Varnishes", NISTIR 4949, 1991 

[8] Charles M. Guttman, William R. Blair, John R. Maurey, "Recertification of SRM 1482a, a 

Polyethylene", NISTIR 6054, 1997.

[9] "PC-OMNITAB: An Interactive System for Statistical and Numerical Data Analysis, 

available from National Technical Information Service, Technology Administration, U.S. 

Department of Commerce, Springfield, VA 22161.

[10] See for example Howard W. Alexander "Elements of Mathematical Statistics", John Wiley 

& Sons, 1961, pg. 165-170 or K. A. Brownlee "Statistical Theory and Methodology in Science 

and Engineering," John Wiley & Sons, Inc., 1960, pg. 56.

[11] Richard G. Christensen, "The Characterization of Linear Polyethylene SRM 1475 V. 

Solution Viscosity Measurements" NBS Special Publication 260-42, H.L. Wagner and P.H. 

Verdier, Editors. September 1972 or National Bureau of Standards, Journal of Research, Vol. 

76A, No. 2, March - April 1972, pg. 147-148.
32

[12] Herman L. Wagner and Peter H. Verdier, "The Characterization of Linear Polyethylene 

SRM's 1482, 1483, and 1484. IV. Limiting viscosity number Numbers by Capillary Viscometry" 

NBS Special Publication 260-61, P.H. Verdier and H.L. Wagner ed. December 1978 or National 

Bureau of Standards, Journal of Research, Vol. 83, No. 2, March - April, 1978, pg. 195-201.

[13] "Operating Instructions for the Viscosity Measuring System AVS 400", Schott Gerate, 

Yonkers NY and Hofheim, Germany 

[14] See for example F.W. Billmeyer, Jr, "Textbook of Polymer Science, 2nd edition", Wiley 

Interscience, NY (1971) pg 84.

[15] H. C. Booij, H. M. Schoffeleers and M. M. C. Haex, Macromolecules, 24, 3334-3339 

(1991).

[16] B. N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of 

NIST Measurement Results." NIST Technical Note 1297, January 1993.

[17] A. Kruis, Z. Physik. Chem. B 34, 13-50 (1936).

[18] R. J. Anderson, Appl. Opt. 8, 1508-1509 (l969).

[19] LDC Analytical, "Instruction Manual for KMX-16 Laser Differential Refractometer" 

Section 5.3, "Calculation of Calibration Constant," Riviera Beach, FL, USA.

[20] H. L.Wagner and C.A.J.Hoeve, J. Poly. Science, Part A-2, 9, 1763-76 (1971). Although this 

is at a different wavelength we do not expect the overall variation to be wavelength dependent.

[21] J. Horska, J. Stejskal, and P. Kratochvil, "Refractive Increments of Polyolefins", J. Appl. 

Polym. Sci.,Vol 28, p3873(1983) 

[22] J. Horska, J. Stejskal, and P. Kratochvil, "Refractive Increments of Polyolefins", J. Appl. 

Polym. Sci.,Vol 24, p1845(1979) 

[23] J. A. Riddick and W. B. Bunger, "Organic Solvents, Phys. Properties and Methods of 

Purification," Wiley-Interscience, New York, 1970, Table 58, pg 145 or Table 30, pg 107. Also 

see B. L. Johnson and J. Smith, "Refractive Indices and Densities of Some Common Polymer 

Solvents," Ch. 2 in "Light Scattering from Polymer Solutions," Ed M. B. Huglin, Academic 

Press, London and NY (1972).

[24] "Instruction Manual for Laser Light Scattering Goniometers", Brookhaven Instrument 

Company, Ronkonkoma, New York, May 1984, catalog number BI-IM version 1.4
33

[25] G. B. Arrowsmith, G. H. Jeffrey, and A. I. Vogel, J. Chem. Soc., pg 2072 (1965)

[26] H. L. Wagner, "The Characterization of Linear Polyethylene SRM 1475. VI. Differential 

Refractive Index of Polyethylene Solutions" NBS Special Publication 260-42, H.L. Wagner and 

P.H. Verdier, Editors. September 1972 or National Bureau of Standards, Journal of Research, 

Vol. 76A, No. 2, March - April, 1972, pg. 151-155

[27] W. Kaye and J. B. McDaniel, Appl. Opt., 13, l934-1937 (l974).

[28] J. Ehl, C. Loucheux, C. Reiss, and H. Benoit, Makromol. Chem., 75, 35 (1964).

[29] Charles C. Han, Herman L. Wagner, and Peter H. Verdier, "The Characterization of Linear 

Polyethylene SRM's 1482, 1483, and 1484 III Weight-Average Molecular Weights by Light 

Scattering." NBS Special Publication 260-61, P.H. Verdier and H.L. Wagner ed. December 1978 

or National Bureau of Standards, Journal of Research, Vol. 83, No. 2, March - April, 1978, pg. 

185-193.

[30] H. Yamakawa, "Modern Theory of Polymer Solutions," Harper & Row, N.Y., (1971).

[31] Charles M. Guttman, William R. Blair, John R. Maurey, "Recertification of SRM 706a, a 

Polystyrene", NISTIR 6091, 1998.

[32] "Instruction Manual for Laser Light Scattering Goniometers", Brookhaven Instrument 

Company, Ronkonkoma, New York, May 1984, catalog number BI-IM version 1.4

[33] H. Utiyama, "Calibration and Correction Factors," Ch. 4 in "Light Scattering from Polymer 

Solutions," Ed M. B. Huglin. pp 61-88, Academic Press, N.Y., (1972).
34

National Institute of Standards & Technology

Certificate of Analysis

Standard Reference Material® 2887

Polyethylene

(Mw, 196 400 g/mol)

This Standard Reference Material (SRM) is intended primarily for use in calibration and performance evaluation of

instruments used to determine the molar mass* and molar mass distribution by size exclusion chromatography. A unit of 

SRM 2887 consists of approximately 0.3 g of polyethylene powder. The certified values and uncertainties for massaverage molar mass and intrinsic viscosity are presented in Table 1.

Table 1. Certified Properties

Property Certified Value

Mass-Average Molar Mass* (Mw ) 196.4 x 103 g/mol ± 13.7 x 103 g/mol

Intrinsic Viscosity [η] in 

1,2,4-trichlorobenzene at 130 °C 276.9 mL/g ± 3.1 mL/g

* Previously expressed as molecular weight [1].

Certified Values and Uncertainties: The certified value for Mw was originally measured using static light scattering 

with 1-chloronaphthalene as the solvent at 130 °C [3]. The certified value for the intrinsic viscosity was determined in 

1,2,4-trichlorobenzene at 130 °C.

The certified measurement uncertainty is expressed as a combined expanded uncertainty with a coverage factor, k = 2, 

calculated in accordance with NIST procedure [2]. Type A and Type B contributions to the expanded uncertainty of the

measured mass-average molar mass include the uncertainties in the Rayleigh ratio of the scattering standard, optical 

alignment, and calibration of the differential refractometer.

Expiration of Certification: The certification of SRM 2887 is valid until 01 January 2008, within the measurement 

uncertainties specified, provided that the SRM is handled in accordance with the storage instructions given in this

certificate. This certification is nullified if the SRM is modified or contaminated.

Maintenance of SRM Certification: NIST will monitor this SRM over the period of its certification. If substantive 

technical changes occur that affect the certification before expiration of this certificate, NIST will notify the purchaser. 

Return of the attached registration card will facilitate notification.

The technical coordination leading to certification of this SRM was provided by B.M. Fanconi of the NIST Polymers 

Division. Technical measurement and data interpretation were provided by C.M. Guttman, W.R. Blair, J.R. Maurey, and

C.R. Schultheisz of the NIST Polymers Division.

The support aspects involved in the preparation, certification, and issuance of this SRM were coordinated through the 

NIST Standard Reference Materials Program by J.W.L. Thomas.

Eric J. Amis, Chief

Polymers Division

Gaithersburg, MD 20899 Nancy M. Trahey, Chief

Certificate Issue Date: 06 April 2001 Standard Reference Materials Program
35

Storage: The SRM should be stored in the original bottle with the lid tightly closed and under normal laboratory

conditions.

Homogeneity and Characterization: The homogeneity of SRM 2887 was tested by size exclusion chromatography 

analysis of solutions in 1,2,4-trichlorobenzene at 130 °C. The characterization of this polymer is described in Reference

3. SRM 2887 is the result of a clean-up, blending, and rebottling of the fractionation of SRM 1475. It was produced in 

the same fractionation as SRM 1482, SRM 1483 and SRM 1484 [4].

REFERENCES

[1] Taylor, B.N., “Guide for the Use of the International System of Units (SI),” NIST Special Publication 811, 1995 

Ed., (April 1995).

[2] Guide to the Expression of Uncertainty in Measurement, ISBN 92-67-10188-9, lst Ed. ISO, Geneva, Switzerland, 

(1993): see also Taylor, B.N. and Kuyatt, C.E., “Guidelines for Evaluating and Expressing the Uncertainty of

NIST Measurement Results,” NIST Technical Note 1297, U.S. Government Printing Office, Washington DC,

(1994); available at http://physics.nist.gov/Pubs/.

[3] Guttman, C.M., Maurey, J.R. , and Blair, W.R., “Certification of the Relative Molecular Mass and the Intrinsic 

Viscosity of SRM 2887, a Polyethylene of Narrow Molecular Mass Distribution,” NISTIR 6456.

[4] Verdier, P.H. and Wagner, H.L., “The Characterization of Linear Polyethylene SRM’s 1482, 1483, and 1484, I.

Introduction,” NBS Special Publication 260-61, (December 1978); or National Bureau of Standards, Journal of 

Research, 83, No. 2, pp. 169-171, (1978).

Users of this SRM should ensure that the certificate in their possession is current. This can be accomplished by

contacting the SRM Program at: telephone (301) 975-6776; fax (301) 926-4751; e-mail srminfo@nist.gov; or via the 

Internet http://www.nist.gov/srm.