Measuring Particle Size Distribution of Latex Particles in the

Chapter 17

Measuring Particle Size Distribution of Latex Particles in the Submicrometer Range Using Size-Exclusion Chromatography and Turbidity Spectra

Downloaded by MONASH UNIV on January 16, 2018 | http://pubs.acs.org Publication Date: February 12, 1987 | doi: 10.1021/bk-1987-0332.ch017

T. Kourti,A.Penlidis,J.F.MacGregor, andA.E.Hamielec Department of Chemical Engineering, McMaster Institute for Polymer Production Technology, McMaster University, Hamilton, Ontario L8S 4L7, Canada

Turbidity spectra and size exclusion chromatography (SEC) are two techniques which could be used for the on- and off-line monitoring of polymer particle size during the polymerization. An experimental evaluation of the two techniques is reported herein and it is shown that they satisfactorily follow the change of the particle size during the reaction. Information from SEC analysis is exploited to experimentally evaluate the turbidity spectra technique and investigate its potential to be used as an on-line measurement of particle size for latex reactor control.

P a r t i c l e n u m b e r and particle size d i s t r i b u t i o n (PSD) are key p a r a m e t e r s i n e m u l s i o n p o l y m e r i z a t i o n processes because they not only affect p o l y m e r i z a t i o n rate and p o l y m e r properties d u r i n g the reaction, but they also d e t e r m i n e a p p l i c a t i o n properties of the final latex such as s t a b i l i t y , viscosity, film forming, and others E f f o r t s to m a n i p u l a t e these two i m p o r t a n t p a r a m e t e r s d u r i n g p o l y m e r i z a t i o n should precede any attempt to c o n t r o l latex reactor performance and therefore there is a need for on-line m e a s u r e m e n t o f particle n u m b e r and size d i s t r i b u t i o n . V a r i o u s techniques have been developed for the d e t e r m i n a t i o n of PSD's of c o l l o i d a l dispersions but these are often t i m e c o n s u m i n g and u n s u i t a b l e for on-line applications. L i g h t s c a t t e r i n g techniques are fast, simple, reproducible a n d thus seem to be p r o m i s i n g for this purposed-2); c h r o m a t o g r a p h i c techniques can be used c o m p l e m e n t a r y for off-line measurements. T h e measurement techniques employed were t u r b i d i t y spectra and size e x c l u s i o n chromatography. T h e scope of this study is to investigate the a b i l i t y of these two techniques to monitor latex particle growth d u r i n g e m u l s i o n p o l y m e r i z a t i o n of v i n y l acetate and to evaluate the potential of t u r b i d i t y spectra to be used for on-line p a r t i c l e size measurements. TURBIDITY SPECTRA Theoretical Background The e x p e r i m e n t a l s i m p l i c i t y of t u r b i d i t y spectra i s the m a i n reason w h y the technique has received so m u c h attention i n the past years (1-5). T u r b i d i t y gives a measure of the a t t e n u a t i o n of a b e a m of l i g h t t r a v e r s i n g a d i s p e r s i o n of non-absorbing spheres:

0097-6156/87/0332-0242$06.00/0 © 1987 American Chemical Society

Provder; Particle Size Distribution ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

17.

KOURTI ET AL.

Size-Exclusion Chromatography and Turbidity Spectra 243

Î

I

where I a n d I represent intensity of the i n c i d e n t a n d the e m e r g i n g (from the s c a t t e r i n g solution) beam, respectively, a n d Î is the l e n g t h of the optical path. For a monodisperse suspension w i t h Ν non-absorbing spherical particles per cm3, i n absence of m u l t i p l e scattering, the t u r b i d i t y , τ, is g i v e n by: 0

nD

2

n

/ D \ — , — Vλ η /

(2)

p

; = Ν

Κ 4

Κ (D/X , n p / n ) , the extinction coefficient, is i n the general case a complicated function of the p a r t i c l e d i a m e t e r D, the w a v e l e n g t h i n the m e d i u m \ , a n d the refractive indices n and n of the particles a n d the m e d i u m , respectively. Κ c a n be calculated f r o m the g e n e r a l M i e theory (3). For a polydisperse suspension: m

m

m

p


m

n

π D

/ D \ (3) — ,— f(D)dD 0 4 \ λ η / m m where f(D) is the suspension's n o r m a l i z e d p a r t i c l e size d i s t r i b u t i o n . The concentration c of p o l y m e r i c solids i n the latex (gr/cm3 latex) is subsequently g i v e n by: P

Κ

i = Ν

3

nD

Np

(4)

f(D)dD 6

ίο

where ρ i s the p a r t i c l e density i n gr/cm^. C o m b i n a t i o n of equations (3) a n d (4) gives a ratio, the specific independent of N, as:

turbidity

2

D K( — , - ^ W ï d D Vλ η / m m

v

" C

2p

(5)

0 0

Γ

3

D f(D)dD Jo It is evident f r o m the above equation that for a k n o w n size d i s t r i b u t i o n a l form, (τ/c) is a f u n c t i o n of the refractive index and d e n s i t y of the particles, the w a v e l e n g t h of the i n c i d e n t l i g h t a n d the p a r a m e t e r s d e s c r i b i n g the p a r t i c l e size d i s t r i b u t i o n . Therefore, i n p r i n c i p l e , the p a r a m e t e r s of the particle size d i s t r i b u t i o n c a n be e s t i m a t e d f r o m specific t u r b i d i t y m e a s u r e m e n t s a t different wavelengths. T h i s is not true, however, i n the R a y l e i g h r e g i m e (i.e. s m a l l particles, ( D / \ ) less t h a n 0.1). In this case, the e x t i n c t i o n coefficient is p r o p o r t i o n a l to ( D / \ ) a n d m

4

m

Jo

*

f

(

D

)

d

D

= L —

D

3

_ = L D

(6,

3

f(D)dD

'0 4

l

4

2

2

2

where D is a " t u r b i d i t y " average particle d i a m e t e r a n d L = 4 n p~ Am" ( m - 1/m -I- 2) ; m = (np/n ). It is clear from equation (6) that use of different wavelengths w i l l not t

m


244

PARTICLE SIZE DISTRIBUTION

provide a d d i t i o n a l information; hence, only a " t u r b i d i t y " average d i a m e t e r can d e t e r m i n e d i n the R a y l e i g h regime.

be


Experimental P o l y i v i n y l acetate) ( P V A c ) latexes produced by batch and continuous e m u l s i o n p o l y m e r i z a t i o n were used i n t h i s study. Details for the apparatus a n d the p o l y m e r i z a t i o n procedure can be found i n P e n l i d i s et a l . (6,12,13). S a m p l e s t a k e n d u r i n g the reaction were subsequently a n a l y z e d to follow conversion- and p a r t i c l e growth-time histories. The batch e x p e r i m e n t a l runs were designed to y i e l d s i m i l a r conversion-time histories but different particle sizes. C o n v e r s i o n was measured both off-line, by g r a v i m e t r i c analysis, and on-line u s i n g an on-line densitometer (a U-tube D P R - Y W E model w i t h a Y-mode oscillator w i t h a PTE-98 e x c i t a t i o n cell a n d a DPR-2000 electronic board by A n t o n P a a r , A u s t r i a ) . A n u m b e r of runs were repeated to check for r e p r o d u c i b i l i t y of the results. F o u r batch runs are described i n T a b l e I below and t h e i r c o n v e r s i o n histories are plotted i n F i g u r e 1.

T a b l e I. C l a s s i f i c a t i o n of B a t c h R u n s Run#

Emulsifier Level

Expected P a r t i c l e D i a m e t e r

B7 B10-B11 (replications) B8

low medium

large medium

high

small

A B a u s c h and L o m b Spectronic-20 spectrophotometer (and occasionally, a H e w l e t t - P a c k a r d 8450 A) was employed for the t u r b i d i t y measurements (cell l e n g t h 1.165 cm, b a n d w i d t h of 20 nm, w a v e l e n g t h f r o m 380 to 580 nm). F o r the t u r b i d i t y measurements, the samples were d i l u t e d w i t h water s a t u r a t e d w i t h emulsifier. The same degree of d i l u t i o n was used for a l l the samples of the b a t c h runs. A large n u m b e r of m e a s u r e m e n t s were repeated to check for reproducibility. D i s c u s s i o n of T u r b i d i t y R e s u l t s Specific t u r b i d i t y histories for r u n s B7, BIO and B l l are shown i n F i g u r e 2. It is obvious that the results are consistent; the r e p r o d u c i b i l i t y obtained i n r u n s B I O a n d B l l is c l e a r l y shown, w h i l e it i s evident t h a t the latex particles formed i n r u n B 7 are larger, as expected. Specific t u r b i d i t y histories are also plotted vs. d i m e n s i o n l e s s time for a continuous e m u l s i o n p o l y m e r i z a t i o n run; the samples were w i t h d r a w n f r o m the second reactor of a continuous t r a i n where the first reactor is a s m a l l seeding reactor. P a r t A of F i g u r e 3 shows the p a r t i c l e size behaviour d u r i n g start up; a l l monomer, water, i n i t i a t o r and soap feedrates were kept constant u n t i l the process reached a steady state. In part B, the soap concentration i n the seed reactor was increased; a decrease i n the particle size was expected and it is c l e a r l y shown from the specific t u r b i d i t y measurements. H o p e f u l l y , it has become evident that specific t u r b i d i t y gives consistent and reproducible q u a l i t a t i v e results. Two approaches have been used to translate the specific t u r b i d i t y measurements f r o m the p r e v i o u s l y mentioned e x p e r i m e n t s into latex p a r t i c l e size:



17.

KOURTI ET AL.


15

30

45

REACTION

RUN B7

Ο

RUN Β Θ

Δ

RUN BIO

•

RUN B l l

Ο

60

TIME

80

75

(min.)

F i g u r e 1. Conversion h i s t o r i e s o f the batch v i n y l acetate emulsion polymerizations (similar recipes; only the e m u l s i f i e r concentration i s different).

REACTION TIME

F i g u r e 2. S p e c i f i c t u r b i d i t y b e h a v i o r B10-B11 a r e r e p l i c a t i o n s .

(min)

f o r three batch

runs;


runs


246

(a)

(b)

A n a p p r o x i m a t e (apparent) diameter, D , was determined. T h i s D corresponds to a monodisperse latex that would have g i v e n the same specific t u r b i d i t y readings as the ones o b t a i n e d a n d it is u s u a l l y close to some average of the P S D (4,7,18). U n d e r the f r e q u e n t l y v a l i d i n practice a s s u m p t i o n that the latex P S D is w e l l represented by the l o g a r i t h m i c n o r m a l d i s t r i b u t i o n a l 8 ) ap

l

f(D) =

— — o D (2n)

ap

2

exp(-(€nD-€n

2

D) /2o ),

(7)

1/2


the p a r a m e t e r s D a n d o of the d i s t r i b u t i o n were d e t e r m i n e d by a non-linear least squares p a r a m e t e r e s t i m a t i o n technique based on Marquandt's compromise procedure. The n u m b e r a n d weight average d i a m e t e r s of the latex P S D were t h e n c a l c u l a t e d from D

N

=

D

2

exp(o /2) (8)

D

=

D

2

exp(3.5o )

w F i g u r e 4 shows contours of constant sum of squares i n the space of the p a r a m e t e r s D a n d o, for a set of specific t u r b i d i t y measurements, f r o m a batch run. The 9 5 % a p p r o x i m a t e j o i n t confidence r e g i o n e s t i m a t e d as:

S(o, D ) 0.95

= S(o, D ) . ( l + — min\ n —p

F

n f t

_(p,n-p))

005

(9)

/

corresponds to a s u m of squares e q u a l to 0.25. S(o, D ) i is the s u m of squares c o r r e s p o n d i n g to the s o l u t i o n o b t a i n e d by the search routine, ρ is the n u m b e r of p a r a m e t e r s t h a t were e s t i m a t e d (p = 2), η is the n u m b e r of specific t u r b i d i t y m e a s u r e m e n t s (n = 6), FQ.05(VI, V 2 ) gives the upper 5 % ofj i n F - d i s t r i b u t i o n w i t h v i , V 2 degrees of freedom. A h i g h n e g a t i v e c o r r e l a t i o n between D a n d o i s evident. It i s c l e a r t h a t a whole l i n e of a l m o s t " e q u a l l y good" p a i r s of e s t i m a t e s exists. The d i s t r i b u t i o n s w h i c h correspond to some of these " a l t e r n a t i v e " solutions (denoted by χ i n F i g u r e 4) are plotted i n F i g u r e 5. A l t h o u g h these r e s u l t s are not r e p r e s e n t a t i v e of b a t c h reactor operation, where one w o u l d expect a l m o s t monodispersed latexes, a n d r e g a r d l e s s of the fact that the d i s t r i b u t i o n i s c h a n g i n g as one moves a l o n g the confidence region, i t was observed, however, t h a t the e s t i m a t e d weight average d i a m e t e r of these d i s t r i b u t i o n s was not affected by t h i s shift. F u r t h e r m o r e , its n u m e r i c a l v a l u e r e m a i n e d close to that of U c a l c u l a t e d i n (a) under the monodisperse assumption, as s h o w n i n F i g u r e 5 and T a b l e II. S i m i l a r r e s u l t s were also observed (7) for p o l y v i n y l acetate) latexes w i t h l a r g e r particles; a l l the " a l t e r n a t i v e " (D, o) solutions i n the elongated confidence r e g i o n correspond to d i s t r i b u t i o n s w i t h a constant weight average d i a m e t e r w h i c h is n u m e r i c a l l y very close to the a p p a r e n t d i a m e t e r of the suspension, o b t a i n e d under the monodisperse assumption. The o b t a i n e d weight average d i a m e t e r s can r e a s o n a b l y w e l l follow the progress of the r e a c t i o n as can be seen f r o m F i g u r e 6, where e x p e r i m e n t a l l y e s t i m a t e d weight average d i a m e t e r s are plotted w i t h those t h e o r e t i c a l l y predicted by a m a t h e m a t i c a l model for the b a t c h e m u l s i o n p o l y m e r i z a t i o n of v i n y l acetate.® F r o m the above discussion it has hopefully become clear that at the lower subm i c r o n range, for p o l y ( v i n y l acetate) latexes, specific t u r b i d i t y m e a s u r e m e n t s can provide a w e i g h t average p a r t i c l e d i a m e t e r w h i c h is r e a s o n a b l y close to the apparent d i a m e t e r r e s u l t i n g under the monodisperse assumption. These r e s u l t s were f u r t h e r v e r i f i e d w i t h s i m u l a t i o n studies; it was s h o w n j 7 ) t h a t the m a x i m u m e r r o r introduced by a s s i g n i n g the U v a l u e to D was - 4 % for D v a l u e s up to 4000 Â and polydispersities up to 1.5. Hence, w h e n low p o l y d i s p e r s i t y i s expected, one m i g h t have fast, on-line p a r t i c l e size m

n

ap

ap

w

a p


17.

Size-Exclusion Chromatography and Turbidity Spectra

KOURTI ET AL.

247

I .6 IO wavelength

Ο

X

1.2

4 4 0 nm

k_ σ» £ ο

0.8

> Ι

part Β

TU

ω ce

part A

0.4

ο ϋ.

ο

LU

0

SP


Ο

2

4

6

DIMENSIONLESS

10

8

TIME(t/0 ) 2

F i g u r e 3. Specific t u r b i d i t y m e a s u r e m e n t s for the continuous r u n (Θ2 = residence t i m e i n the second reactor of the continuous train).

Τ"

I

τ

1

I

1

Ο 4.2 X " Ό

ζ 4.0 Ο

< >

3.8

ο \

-

UJ Ω Q 3.6 -

< Û

?

3.4

* X

PROGRAM EQUALLY 1

SOLUTION GOOD 1

16

5

PAIRS 1

1

1

1

405.0 425.0 445.0 465.0 485.0 505.0 M E A N OF L O G - N O R M A L DISTRIBUTION F i g u r e 4. Contours^of constant s u m of squares ( S S = 1 6 , 5, 2) a n d possible, "equally good", a l t e r n a t i v e (D,o) solutions.

American Chemical Society Library 1155 16th St., N.W.

Provder; Particle Size Distribution Washington, 20036 ACS Symposium Series; American ChemicalD.C. Society: Washington, DC, 1987.


248


3.01

1

1

1

r

F i g u r e 5. P a r t i c l e size d i s t r i b u t i o n s corresponding to some a l t e r n a t i v e ( m a r k e d as x) of F i g u r e 4.

solutions

CONVERSION F i g u r e 6. P a r t i c l e g r o w t h histories for the batch runs; model predictions (continuous lines) and e x p e r i m e n t a l data. Reproduced w i t h p e r m i s s i o n f r o m Ref. 6. C o p y r i g h t 1985, M a r c e l D e k k e r Inc.


17.

KOURTI ET AL.


measurements by d i s p e n s i n g w i t h p a r a m e t e r e s t i m a t i o n a n d a p p r o x i m a t i n g the weight average d i a m e t e r w i t h D . In this case, concentration m e a s u r e m e n t (from on-line densitometer) a n d a t u r b i d i t y m e a s u r e m e n t at one w a v e l e n g t h would provide sufficient data for the weight average d i a m e t e r c a l c u l a t i o n . ap

T a b l e II. A v e r a g e D i a m e t e r s f r o m Specific T u r b i d i t y M e t h o d


( R u n B7, wavelengths: 400, 440, 480, 500, 560 nm) Sample #

Conversion %

5 6 7 8 10

49 66 84 97 100

"Dap s h o u l d be c l o s e r t o t h e t r u e

D from(b),Â w

D from(a),Â

715 805 870 890 930

ap

785 900 985 1020 1045

Dw than Dw from ( b )

SIZE E X C L U S I O N C H R O M A T O G R A P H Y Theoretical Background P a r t i c l e chromatography u s i n g packed beds has attracted considerable a t t e n t i o n of those interested i n m e a s u r i n g p a r t i c l e size d i s t r i b u t i o n of s p h e r i c a l p a r t i c l e s i n the s u b m i c r o n range (8,9,11,14,16). T h e r e exist two c o m p l e m e n t a r y approaches to the use of t h i s technique, according to the p a c k i n g m a t e r i a l employed: a. H y d r o d y n a m i c C h r o m a t o g r a p h y ( H D C ) u t i l i z e s non-porous p a c k i n g a n d r e l i e s m a i n l y o n the velocity profile i n the c a p i l l a r i e s formed by the p a c k i n g . L a r g e particles a r e excluded f r o m regions near the c a p i l l a r y w a l l , where the a x i a l velocities are s m a l l a n d hence, on the average, experience a h i g h e r velocity a n d therefore a s m a l l e r r e t e n t i o n volume. b. Size E x c l u s i o n C h r o m a t o g r a p h y ( S E C ) u t i l i z e s porous p a c k i n g m a t e r i a l ; steric e x c l u s i o n of particles i n suspension from the pores i s a n a d d i t i o n a l force for size separation. Suspended particles, s m a l l e r t h a n the d i a m e t e r i n the pore, c a n diffuse into porous, g i v i n g a n efficient m e c h a n i s m of r e t a r d a t i o n a n d size separation. D e t a i l s c o n c e r n i n g the h y d r o d y n a m i c ( H D C ) a n d size e x c l u s i o n chromatography ( S E C ) as a p p l i e d to separate particle suspensions a c c o r d i n g to t h e i r size a n d a n extensive l i t e r a t u r e review can be found i n P e n l i d i s et al. (9) a n d they w i l l not be repeated here. A detection system is connected to the outlet of the packed column for m o n i t o r i n g the p a r t i c l e concentration. T h e passage of a n injected sample t h r o u g h the c o l u m n a n d detector provides a n output trace o n the recorder, the chromatogram. A c h r o m a t o g r a m can never f u l l y represent the d i s t r i b u t i o n of colloid sizes i n the injected sample; i n s t r u m e n t a l s p r e a d i n g or a x i a l d i s p e r s i o n causes e l u t i o n of a single species to occur over a range of retention volumes. T h e contents of the detector c e l l are not monodispersed, but r a t h e r have a d i s t r i b u t i o n that is l i k e l y to be u n i m o d a l , a n d it is often quite broad (14). Interpretation of a c h r o m a t o g r a m must therefore account for the a x i a l d i s p e r s i o n a n d involves a n e v a l u a t i o n of i n s t r u m e n t a l s p r e a d i n g a n d correction of the detector response to o b t a i n the true picture of the injected sample. The detector response at retention v o l u m e v, F(v), can be expressed as (15)


250


(

QO ( 1 0 )

W(y)G(v,y)dy

0

where W(y) is the true c h r o m a t o g r a m , that would have been obtained i n the absence of a x i a l dispersion, a n d G(v, y) is the n o r m a l i z e d detector response for a t r u l y monodisperse system w i t h mean retention v o l u m e y; G(v,y) i s c a l l e d the i n s t r u m e n t a l s p r e a d i n g function The solution of the above equation i n order to o b t a i n W(y) r e q u i r e s a n appropriate form of the s p r e a d i n g f u n c t i o n a n d the n u m e r i c a l v a l u e s of its parameters. F u r t h e r m o r e , to convert W(y) into a size d i s t r i b u t i o n requires a r e l a t i o n s h i p between the m e a n retention volume y and the p a r t i c l e d i a m e t e r D (i.e., a c a l i b r a t i o n curve).


S p r e a d i n g Function. A g e n e r a l s t a t i s t i c a l shape function, w h i c h accounts for skewed chromatograms, i n i t i a l l y proposed by P r o v d e r and Rosen (16), has been used: A3 G(v,y) = G ( v , y ) 1 + — H3(x) + 3!

A4 — H4(x) 4!

Q

vhere ( v - Λy rν \ 2

/ G

v

n< .y> =

— = = V2no

e x 2

P ^ -— 1 ~ ' 2σ Λ

)

2

(11)

(v-y) χ = 0 H3(x) = χ3-3χ2 H4 (χ) = χ - 6x + 3 4

2

(Hermite polynomials)

and

Α

3

= -έ

A

4

=

- - 3 .

P2, P3 a n d μ4 are the second, t h i r d a n d fourth moments of the d i s t r i b u t i o n . measure of skewness and A4 a measure of kurtosis.

A3 i s a

E s t i m a t i o n of the S p r e a d i n g Function. W h e n the injected sample is monodispersed, peak b r o a d e n i n g occurs solely due to a x i a l dispersion; i f y is the m e a n r e t e n t i o n volume of the c h r o m a t o g r a m , then the detector response is g i v e n by: F(v) = WG(v, y)

(12)

where W i s the a r e a under the chromatogram. T h e parameters (μ2, P3, P4) of the d i s t r i b u t i o n c a n therefore be e s t i m a t e d f r o m the heights of c h r o m a t o g r a m s of s t a n d a r d monodispersed latexes. C a l i b r a t i o n Curve. T h e c h r o m a t o g r a m s of s t a n d a r d monodisperse samples m a y be used to construct a c a l i b r a t i o n c u r v e r e l a t i n g the p a r t i c l e d i a m e t e r D w i t h its m e a n r e t e n t i o n volume, y, by: In D = a + by + c y

2


(13)

17.

KOURTI ET AL.


S o l u t i o n for A x i a l Dispersion. W i t h different degrees of success, numerous techniques have been proposed for s o l v i n g e q u a t i o n (10). T h e most p r o m i s i n g method seems to be that of Ishige et al. (10). It i s a n u m e r i c a l method that does not require s i g n i f i c a n t c o m p u t i n g time. The method uses the fact that any response F*(v) a l w a y s has a broader d i s t r i b u t i o n t h a n the i n p u t d i s t r i b u t i o n W(y). Hence, i f a d i s t r i b u t i o n Fi(v) is broader t h a n F*(v), the a s s u m e d Wi(y) must be sharpened to give a response closer to F*(v). U s i n g F*(v) as the i n i t i a l guess for W(y), subsequent i m p r o v e d estimates are c a l c u l a t e d by: W

i

(14)

i = (F*/Fi)Wi

+

where F j i s the c h r o m a t o g r a m c a l c u l a t e d u s i n g W[. T h e procedure is repeated u n t i l F satisfies a convergence c r i t e r i o n . W (y) is a l w a y s n o r m a l i z e d before use.

t


t

P a r t i c l e Size D e t e r m i n a t i o n . T h e corrected detector response at retention volume ν i s g i v e n as Y

ô

ί 1 5 )

W(v) « N ( v ) D ( v ) K ( v )

where Ν a n d Κ are the n u m b e r concentration a n d e x t i n c t i o n coefficient, respectively, of particles of d i a m e t e r D a t retention volume v; indices γ and δ are defined as follows: γ = 3,δ = 0 γ = 2,δ = 1.

mass detector: t u r b i d i t y detector:

T h e e x t i n c t i o n coefficient c a n be c a l c u l a t e d from the general M i e theory (8). The frequency d i s t r i b u t i o n of the p a r t i c l e size is related to the n u m b e r of particles e l u t i n g at v o l u m e ν as follows: N(v)dv

KD)dD =

N(v)dv

«D) =

(16)

N(v)

-

(I

o

N(v)dv)(dD/dv) /

F o r a n o n l i n e a r c a l i b r a t i o n curve In D = a + bv + c v

2

and dD/dv = D (b + 2cv) F r o m equations (15-17):


(17)


252

W(v)

«D) = -

(18)

/ Γ

W(v)dv \ « — (dD/dv)(D (v) Κ (ν)) J 0 D (v) Κ ( ν ) / v

Y

V

Y

δ

δ

Average Diameters. After the frequency distribution has been obtained, the following average diameters can be calculated: (19a)

DfTD)dD

number average:


4

D ftD)dD

weight average:

(19b)

D... = D fTD)dD

b

D ftD)dD

turbidity average:

—

(19c)

Γ

D fl(D)dD

\l/2

surface average:

2

D ftD)dD

(19d)

Experimental A dry packed column with porous material was used for the characterization according to size of the PVAc latex samples. The packing employed was CPG (Controlled Pore Glass), 2000 Â, 200-400 mesh size. Deionized water with 0.8 gr/lit Aerosol O.T. (dioctyl sodium sulphosuccinate), 0.8 gr/lit sodium nitrate and 0.4 gr/lit sodium azide served as the carrier fluid under a constant flowrate. The sample loop volume was 10 \xt. A Beckman UV detector operating at 254 nm was connected at the column outlet to monitor particle size. A particle size-mean retention volume calibration curve was constructed from commercially available polystyrene standards. For reasons of comparison, the samples previously characterized by turbidity spectra were also characterized by SEC. A number of injections were repeated to check for the reproducibility of the method. Discussion of SEC Results As a preliminary indication of the capability of SEC to qualitatively follow particle growth, the diameters corresponding to the peak retention volume were calculated directly from the calibration curve (without any correction for axial dispersion). "Peak" average particle diameters are plotted vs. conversion for the batch runs in Figure 7, where it is clearly shown that runs B10 and B l l are replications, with latex particles smaller than those produced from run B7, as expected. In the continuous run, shown in Figure 8,


17.

KOURTI ET AL.

Size-Exclusion Chromatography and Turbidity Spectra

Ι.4

253

ι—

ι RUN

g χ

L

B7

Δ

RUN BIO

·

RUN B l l

Ο

or LU


< 1.0 LU Ο < OC UJ

ο

ο° · · ·ί

80

100

«ο

Δ

ο

ο ·

·

Ο

0.8h

Measuring Particle Size Distribution of Latex Particles in the

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