Particle Size Measurements with a Disc Centrifuge - American

Chapter 11

Particle Size Measurements Centrifuge

with a Disc

A Density-Gradient Method with Light-Scattering Corrections

Downloaded by CORNELL UNIV on August 2, 2012 | http://pubs.acs.org Publication Date: September 24, 1991 | doi: 10.1021/bk-1991-0472.ch011

Finn Knut Hansen Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo 3, Norway

An improved technique for particle analysis by disk centrifugation utilizing an externally produced density gradient and with corrections for the wavelength and angular distribution of the transmitted light has been developed. The sedimentation constant is calculated from the radial dependence of spin fluid viscosity and density. Light scattering corrections are calculated by means of calibration curves, representing the efficiency of light scattering as a function of size and relative refractive index of particles. Calibration curves for the white light in the photosedimentometer are obtained by integration across the wavelength distribution of the lamp, the sensitivity distribution of the photo diode and the angular distribution of the forward scattered light obtained from Mie theory. Coefficients of variation below 2% may be calculated using different spin fluid volumes to estimate the instrument variance. Sedimentation methods based on gravitational or centrifugal sedimentation are s t i l l superior i n many people's opinion i n dealing with wide and/or multimodal size d i s t r i b u t i o n s . Such p a r t i c l e size d i s tributions are often found i n products of the polymer industry (paint, binders, PVC pastes, glue binders e t c . ) where the presence or absence; of undersized/oversized p a r t i c l e s i s of c r u c i a l importance to the product q u a l i t y . Several papers dealing with chis technique have been published (1-10) i n which the theoretical basis f o r the method i s established, and also expressions for the size d i s t r i b u t i o n s are developed. These are based either on gravimetric ( i . e . sampling and weighing) or light: scattering ( i . e . t u r b i d i t y ) methods, where either a laser or an o r dinary lamp i s used as a l i g h t source. With monochromatic l i g h t ( l a sers) calculations of l i g h t scattering coefficients as a function of p a r t i c l e size and refractive index i s r e l a t i v e l y easy, using the Mie. theory. However, there are also several problems with a laser 0097-6156/91/0472-0169$06.00/0 © 1991 American Chemical Society

In Particle Size Distribution II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

170

P A R T I C L E S I Z E D I S T R I B U T I O N II

instrument, one of these i s s t a b i l i t y of the l i g h t i n t e n s i t y , another i s the fact that the t u r b i d i t y function o s c i l l a t e s very strongly with p a r t i c l e s i z e , e s p e c i a l l y when the r e f r a c t i v e index i s high. This means that p a r t i c l e size ( i . e . density and time) have to be very correct to avoid large errors i n the d i s t r i b u t i o n such as a r t i f a c t peaks due to t u r b i d i t y o s c i l l a t i o n . Therefore, most producers prefer using a white l i g h t source. This sort of "smoothes" out the maxima and minima, but introduces the problem of c a l c u l a t i n g correct c a l i b r a t i o n curves. This problem has been treated by Oppenheimer (fj») who introduced the average e x t i n c t i o n c o e f f i c i e n t Q * t by integrating over the range of wavelength s e n s i t i v i t y . He showed that i t i s necessary tc include t h i s factor to obtain correct size d i s t r i b u t i o n s , and more the larger the p a r t i c l e s i z e . A second problem with the detector system i n the disk centrifuge i s that some forward scattering w i l l be included i n the t u r b i d i t y signal due to a f i n i t e angle of acceptance i n the photo c e l l . This problem may become important with large part i c l e sizes or/and r e f r a c t i v e index. In t h i s paper, these problems are solved by numerical integration of the theoretical equations. When extremely narrow sized p a r t i c l e suspensions (such as Dynosphers), or very low density products ( -< 1 g/crn^) are to be analyzed by a disk centrifuge, we have not succeeded to obtain stable conditions using the ordinary s t a r t techniques such as the buffered l i n e or homogenous s t a r t . Turbulence w i l l most often occur i n the disk cavity during the run, thus i n v a l i d a t i n g the r e s u l t s . By using s. density gradient i n the disk however, stable conditions can been obtained (9,1Q). The added d i f f i c u l t y of c a l c u l a t i n g the p a r t i c l e s i z es i n a density gradient system i s also treated i n t h i s paper. The essential part of the wcrk reported here was done several years ago (1982) at Dyno Industrier A . S , Norway, and has been an important component i n the development of Dynospheres monosized p a r t i cles. In view of recent developments i n size analysis techniques, i t i s f e l t that the fundamental treatments presented s t i l l has considerable a c t u a l i t y .


e x

Experimental A Joyce Loebl Disk Centrifuge Mk II with the standard photo-sedimentometer with a white l i g h t source has been used. The density gradient was produced by means of a Beckman Density Gradient Former with two p a r a l l e l 30 ml glass syringes and a mixing chamber with a magnetic s t i r r e r . The two components most often used were 15% w/w glycerol/water mixture (heavy component) and water ( l i g h t component). When p a r t i c l e s with diameters below c a . 1 pm were to be analyzed, 0.15% sodium dodecyl sulfate (SDS) was added to both components to avoid coagulation i n the disk. The spin f l u i d volume was usually 30 ml. In order to measure emulsions of low density l i q u i d s a gradient cons i s t i n g of methanol and water was used. The latex was d i l u t e d with a solution of 0.15% SDS i n deionized water. Of t h i s suspension 0.5 ml was injected into the disk center. The p a r t i c l e concentration i n the injected sample was varied dependent on p a r t i c l e s i z e ; larger p a r t i c l e s required larger concentrations. The disk speed was also adjusted to the p a r t i c l e size i n order to give sedimentation times between 4 and 16 minutes. In t h i s man-


11.

HANSEN

Density-Gradient Method

171


ner, polystyrene and polyacrylate p a r t i c l e s from 0.5 to 20 um could be measured. P a r t i c l e s above 20 /im could also be analyzed by this method, provided the spin f l u i d was thickened with hydroxyethyl c e l lulose (HEC) i n order to decrease the rate of sedimentation. A s i m i l a r gradient method was developed to analyze size d i s t r i butions of alkyd emulsions. Because these droplets have densities close to water, a gradient consisting of water (heavy component) and methanol ( l i g h t component) was applied. The samples were d i l u t e d i n 50% w/w methanol/water with a nonionic s t a b i l i z e r , such as T r i t o n X100. Data Logging and Presentation. The output from the Disk Centrifuge was fed into a 12-bit A/D-converter connected to a microcomputer where 480 voltage values were logged at equal time i n t e r v a l s ( v a r i able). To minimize signal noise, each data value was calculated as an average of a number (20-100) of measurements. In t h i s way, an accuracy better than 12 b i t s could be obtained and f a c i l i t a t e d detect i o n of small peaks i n the d i s t r i b u t i o n . At the end of the run, the data was saved automatically to s. disk f i l e together with key data for the run, such as time i n t e r v a l , run-ID, gradient type etc. Peaks were selected manually on-screen. The program sets the baseline as the straight l i n e between the f i r s t and l a s t peak l i m i t s . The time values between the l i m i t s were converted to diameters as described below. The gradient constants (Table I) were read from a disk f i l e together with density and refract i v e index. From the diameters and voltage values, r e l a t i v e p a r t i c l e numbers were calculated. From the D/N-data were also calculated stat i s t i c a l parameters for each peak separately and for the j o i n t d i s tribution. The d i s t r i b u t i o n curve together with the s t a t i s t i c a l parameters may be output i n a report, to be used i n product documentation. The computer program was o r i g i n a l l y written i n BASIC for a DEC PDP-11 computer, but has l a t e r been converted to PASCAL on a PC. Theory and c a l c u l a t i o n P a r t i c l e size d i s t r i b u t i o n s are calculated i n two steps. F i r s t the p a r t i c l e diameters are calculated from the sedimentation time (the xa x i s ) , then p a r t i c l e numbers can be calculated from the j o i n t turbidi t y signal from the photo c e l l (the y - a x i s ) by means of a s i z e - and r e f r a c t i v e index dependent c a l i b r a t i o n curve. Sedimentation i n a density gradient. The sedimentation rate i s represented by Stoke's law. Figure 1 shows the disk and the size parameters used i n t h i s work. Stokes equation i s e a s i l y integrated from rp to r | when the spin f l u i d density and v i s c o s i t y are independent of radius r , giving a simple logarithmic dependence between time t and r. When density and/or v i s c o s i t y are not constant, the p a r t i c l e d i ameter may s t i l l be represented by, D - 2a - K /

(n Jl )

Where a i s the p a r t i c l e radius and n the disk speed (frequency). "constant", K, or i t s square, K^, i s given by the i n t e g r a l (1Q),


(1) The

172

P A R T I C L E S I Z E D I S T R I B U T I O N II

(2)

Where p and p are the densities of the p a r t i c l e s and spin f l u i d , respectively and 17 i s the spin f l u i d v i s c o s i t y . The dependence of q and p on r may be found from the r a d i a l d i s t r i b u t i o n of volume (or weight) f r a c t i o n s . The gradient former produces a l i n e a r density gradient as function of volume, as long as the p a r t i a l molar volumes are constant (ideal mixing), but even i f t h i s i s not so, the weight fractions w i l l always be l i n e a r . Therefore, weight fractions of the components i n the disk cavity may be calculated from the disk geomet r y and from these density and v i s c o s i t y as separate functions. If the volume f r a c t i o n i s l i n e a r , the expression f o r the volume f r a c t i o n ^ i n the disk at a radius r ( i n c i r c u l a r coordinates) i s , p

w


w

-V

(*2"*o>

* - +0 +

> A

r

/

*

o>

r

2

3

The radius r i s an instrument constant, while the inner radius TQ i s dependent on the spin f l u i d volume V, 2

x

2

0

-

x

- V/(irl)

2

2

(4)

where 1 i s the inner thickness of the disk cavity (Figure 1). 4>Q and. 42 the volume fractions at the outer and inner spin f l u i d surface, respectively. These are dependent on the composition of the l i g h t and heavy l i q u i d i n the gradient former, on the spin f l u i d v o l ume and on the type of syringes used i n the gradient former. They may be described by the following equations (derived from a nomogram i n the gradient former's manual), a

r

e

*0 " * 0 + W W

Particle Size Measurements with a Disc Centrifuge - American

Recommend Documents