**1. Introduction**

312 Materials Science and Technology

Jung, T. Y.; Kim, D. H. & Lim, H. B. (2006).Molecular Emission of CF4 Gas in Low-pressure

(March 2006), pp. 373-376, ISSN 0253-2964

Inductively Coupled Plasmas. *Bulletin of Korean Chemical Society,* Vol.27, No.3,

Gel permeation chromatography (*GPC*) method is a widely used and accepted method for measuring the *MW* and *MWD* for polymers. However, the method has its limitations. The key of this method is to find the suitable solvents to dissolve the polymer well. But cellulose can not be dissolved in most of the organic solvents because of the inter- and introhydrogen bonding of the cellulose chains. Lithium chloride/N, N-dimethlylacetamide (LiCl/DMAc) can dissolve cellulose, but the dissolution process is very complicated, which includes pre-activation, solvent exchange, swelling and dissolution. Furthermore, more attention must be paid to each step, and cellulose has to be dissolved for 5-10 days according to the type of cellulose pulp [1-4]. Therefore, it is necessary to develop a simple and fast method which can get the *MW* and *MWD* of cellulose.

Wu [5] got the *MWD* from storage modulus *G'* and stress relaxation modulus *G*(*t*) using approximations derived from the Doi-Edwards description of chain dynamics. Wu's method accurately predicted the *MWD* of polymers with narrow distribution. However, often, it led to a distorted shape of the *MWD* for the sample with bimodal distributions. Therefore, Tuminello [6-8] developed a theory based on a diluted assumption in 1986. His method rigorously applies only to linear polymers. Especially, it works better for linear polymers with PI < 3.5. According to his theory, the relative differential *MWD* of polymer can be determined well from dynamic modulus master curve.

Gu [9] applied the diluted assumption theory to the concentrated cellulose in Nmethlymorpholine-N-oxide monohydrate (NMMO·H2O) solution. He got relative differential *MWD* curves of three kinds of cellulose pulps from the dynamic data of cellulose/NMMO·H2O solution in 2000. But the results were not compared with the results reported by *GPC*. In 2004, the relative differential *MWD* curves of four kinds of cellulose pulps were calculated on the basis of that method and the calculated results were compared with the non-calibrated *GPC* results by Zhang [10]. In their rheology experiments, the cellulose concentration in NMMO·H2O solution was fixed (9%, wt), and the polydispersity index (*PDI*) of cellulose was not calculated.

In the present work, the effect of cellulose concentration in NMMO·H2O solution on prediction of the *MW* and *MWD* of cellulose using the rheology-based method was

Rheological Method for Determining Molecular Weight and Molecular Weight Distribution 315

 1/*ω* ∝ *η<sup>0</sup>* ∝ *M* 3.4 (4) where *ω* is the frequency of dynamic rheology data, *η0* is the zero-shear viscosity of dynamic

The above equations were employed in the calculation of the relative differential *MWD*

The relative differential *MWD* curve is a Wesslan function which is the logarithm of the normal distribution function and is especially applied to measure the *MWD* of polymers.

where *Y* is the relative content percent of *MW*, *M* is the molecular weight, *σ* is the standard

There is a correlation between the peak value of the ordinate (*Yextre*) and the *σ* with respect to

2*σ*

 *PDI* = exp(*σ*2 ) (8)

**Dissolution of cellulose in LiCl/DMAc***.* A 10mg sample of each of the three pulps was placed in a 10mL centrifuge tube, respectively. Then 5mL of distilled water was added to each tube. The mixtures were stirred for 5min and left overnight to pre-activate the cellulose. The samples were centrifuged at 4000rpm for 15min. The supernatant fluid was decanted and 5mL of DMAc was added, respectively. After stirring for 15min, the centrifugation and the decantation steps were repeated. The whole solvent exchange procedure was repeated five times. Finally, 1.25mL of 8% LiCl/DMAc (wt/vol) was added, stirred for 60s, and left for approximately one week to dissolve completely, with occasional gentle stirring. The dissolved cellulose solutions were diluted to 20ml with DMAc to give a

d( ( )) d(log(1 / )) *C M*

exp <sup>2</sup> 2 <sup>1</sup> ( ) <sup>2</sup> *M MP*

*σ*

d( ( )) d(log ) *C M*

*M* (3)

*ω* (5)

(6)

(7)

 *MWD* =

 *MWD* =

The Wessllan function is given by [15, 16]:

*<sup>Y</sup>* = <sup>1</sup>

rheology data, therefore, log (1/*ω*) is proportional to log *M*, then

*σ* 2

deviation, and *Mp* is the peak *MW* on the *MWD* curve.

 *Yextre* = <sup>1</sup>

Then the PDI value is calculated by *Eq*.(7) [15, 16]:

the logarithm normal distribution, as given by *Eq*.(6) [15, 16]:

where *M* is the molecular weight. It is well know for the relations

curve of the cellulose pulps.

**2.1.2 GPC measurements** 

investigated. Furthermore, the calculation of the *PDI* of cellulose was developed. In addition, it also realized the conversion of the reciprocal of the frequency to the actual *MW* scale, obtaining *MWD* scale curve of cellulose [11,12].
