NATIONAL BUREAU OF STANDARDS REPORT

1 0 422

Progress Report

on DETERMINATION OF THE DEGREE OF POLYMERIZATION

OF A POLYMERIC AROMATIC AMINE FROM NMR DATA

USING A “LEAST-SQUARES” APPROACH

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS REPORT

ms PROJECT ^3$ REPORT

311.05-11-3110561 May 28, 1971 10 422

Progress Report

on DETERMINATION OF THE DEGREE OF POLYMERIZATION

OF A POLYMERIC AROMATIC AMINE FROM NMR DATA

USING A “LEAST-SQUARES” APPROACH

H. Argentar

Research Associate

American Dental Association

Research Unit

National Bureau of Standards

Washington, D. C. 20234

This investigation was supported in part by Research Grant

DE02494-04 to the American Dental Association from the

National Institute of Dental Research and is part of the

dental research program conducted by the National Bureau of Standards in cooperation with the American Dental Association;

the Dental Research Division of the United States Army Medical

Research and Development Command; the Dental Sciences Division

of the School of Aerospace Medicine, USAF; the National

Institute of Dental Research and the Veterans Administration.

NATIONAL BUREAU OF ST

for use within the Government, and review. For this reason, thf whole or in part, is not author Bureau of Standards, Washingtc

the Report has been specifically

IMPORTANT NOTICE

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

ss accounting documents intended

subjected to additional evaluation

listing of this Report, either in

e Office of the Director, National

>y the Government agency for which

opies for its own use.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
y r

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DETERMINATION OF THE DEGREE OF POLYMERIZATION

OF A POLYMERIC AMINE FROM NMR DATA USING A

"LEAST-SQUARES" APPROACH

A polymeric amine, the reaction product of 3,5-xylidine and

the diglycidyl ether of bisphenol A, which had been synthesized

and reported elsewhere, was analyzed by nuclear magnetic

resonance spectroscopy (NMR) . A statistical method was derived to estimate the degree of polymerization based on

linear multiple regression analysis of the intensity of the

NMR absorption peaks.
2

DETERMINATION OF THE DEGREE OF POLYMERIZATION

OF A POLYMERIC AMINE FROM NMR DATA USING A

" LEAST-SQUARE S" APPROACH

In a previously submitted paper 1 a method of using

nuclear magnetic resonance (NMR) data for the determination

of n. for the polymeric amine (the reaction product of

3,5-xylidine and the diglycidyl ether of bisphenol A) shown

was presented. In that paper, n equalled 1/ (R-l) where R,

the molar ratio of bisphenol A segment to 3,5-xylidine segment,

was determined by linear regression of the mean intensities

of the various peaks on the mean intensity of the benzylic

peak (adjusted to reflect the number of protons in each of

the two segments responsible for each peak) assuming no experimental error in the latter and zero intercept.

PBX
3

An alternative and more general procedure for determining _n is as follows:

Since the intensity of a given NMR peak is assumed

to be proportional to the number of protons of a

given configuration causing the peak" we may set up

the following system of simultaneous linear equations:

/wjl ^ = /w-.k(6n +6) = 6/wx nk + 6/wik

ch 3 * — — — —

/w2 I . = /w2 k(lln +8) = ll/w? nk + 8/w2 k aromatic — — ‘

v

/^w3 1 = /w3 k(10n + 10) = 10/ w3 nk + 10/w3 k aliphatic

/w4 Ice

3 = 6/w4 nk

where w is a statistical weighting factor inversely

proportional to the variance of the intensity of

the peak, I is the mean intensity of the peak caused

by the protons described by the subscript, CH3 * refers

to the methyl groups of the bisphenol segment, CH 3

refers to the benzylic methyl groups (on the xylidine

ring) , k is the proportionality constant relating the

intensity of a given peak to the number of protons causing
4

the peak, and n is the quantity of repeating units in

the polymer molecule. (In order to make use of a

computer program* for solving unweighted multiple

linear regression equations, w was chosen in such a

way that Zw_^ = number of simultaneous equations.)

The experimentally determined values for the intensities (in arbitrary units) of the mean (and standard

deviation for a single observation) are I , 7.3 (1.5); CH 3 *

I _ , 12.5 (3.4); I _ , 13.4 (2.7); and I , aromatxc alipnatrc CH3 6.0 (0.40). The weighted standard deviation for a single

observation is 0.76. Each value is the result of three

determinations

Using standard techniques, 0

we find that nk equals

1.00 and k equals 0.26. Solving for _n, n equals 3.8. The

standard error of estimate is 0.205. An F test performed

on the ratio of three times the weighted mean square residuals

from regression to the weighted variance of the individual

observations shows that the error due to regression is consistent with the estimated error of the individual observations

* A computer program entitled LMREG (copyrighted by Honeywell,

Inc, 1970) written in BASIC
- 5

at the 95% confidence level, where the factor three puts the

mean square residuals in terms of individual intensity values.

The degree of polymerization is defined as the average

number of monomer uni ts per polymer molecule. 4 Since the

number of amine segments per polymer molecule equals n and the

number of bisphenol A segments equals n + 1, the degree of

polymerization is 2n + 1 or 8.6 according to the above definition .

Previously, it was implicitly assumed that nk equals

1.00 by correlating all the intensity values with I

CH3 which was set equal to 6. L If, in the above equations with

all weights set equal to 1.0, nk is set equal to 1.00 then k

equals 0.269 and n equals i/k or 3.7 as before.
6

Reference s

(1) R. L. Bowen and H. Argentar. J. dent. Res., submitted

for publication.

(2) L. M. Jackman and S. Sternhall. "Applications of

Nuclear Magnetic Resonance Spectroscopy in Organic

Chemistry, 2nd ed, " Pergamon Press, Elmsford, N. Y.

1969, p. 13.

(3) M. G. Natrella. "Experimental Statistics," NBS Handbook

91, Washington, D. C. 1963, pp 4-21 and list of errata.

(4) P. J. Fiory. "Polymer Chemistry , "Cornell University

Press, Ithaca, N. Y. 1953, pp 29-37.
7
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