On-Line Particle Size Determination during Latex Production Using

7 On-Line Particle Size Determination during Latex Production Using Downloaded by CORNELL UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch007

Dynamic Light Scattering Theodora Kourti , John F. MacGregor , Archie E . Hamielec , David F. Nicoli , and Virgil B. Elings 1

2

1

1

2

McMaster Institute for Polymer Production Technology, Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7 Particle Sizing Systems, 6780 Cortona Drive, Santa Barbara,CA93117 1

2

This chapter describes a system for automatic sample acquisition and dilution designed to interface with a particle-sizing instrument based on dynamic light scattering. Results are shown of the successful use of this technology to monitor on-line particle growth during the emulsion polymerization of vinyl acetate in a pilot-plant reactor. Automatic sampling every 10-15 min is achievable; therefore this system is a powerful new tool for on-line monitoring and control of latex production.

PARTICLE

SIZE

D I S T R I B U T I O N IS A C R I T I C A L

PARAMETER

in

emulsion

polymerization because it influences the physical properties (and therefore the end use) of the latex product. The control of particle size is therefore of great importance in the production of latices. Even though the chemical recipe remains the same from run to run, the presence of impurities can significantly affect particle nucleation, and therefore particle size, during polymerization. When the latex is produced in continuous or semi-batch reactors, the particle size can be controlled during production by manipulating input variables such as emulsifier concentration and monomer feed rate. This task requires accurate and reliable on-line determination of particle size. Furthermore, the time required for particle size measurement must 0065-2393/90/0227-0105$06.00/0 © 1990 American Chemical Society

Craver and Provder; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1990.

106

POLYMER CHARACTERIZATION

Downloaded by CORNELL UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch007

be short e n o u g h to allow sufficient t i m e for the appropriate c o n t r o l actions to b e calculated a n d i m p l e m e n t e d . Various techniques have b e e n d e v e l o p e d for the d e t e r m i n a t i o n of the particle size d i s t r i b u t i o n i n c o l l o i d a l dispersions, b u t most of t h e m are t i m e c o n s u m i n g o r u n w i e l d y for o n - l i n e applications. L i g h t - s c a t t e r i n g t e c h n i q u e s are fast, s i m p l e , sufficiently accurate a n d r e p r o d u c i b l e , a n d s e e m p r o m i s i n g for o n - l i n e particle size measurements. T h e t e c h n i q u e o f d y n a m i c l i g h t scattering ( D L S ) has b e e n e v o l v e d i n recent years i n t o a p o w e r f u l research a n d q u a l i t y c o n t r o l t o o l , able to effect i v e l y characterize s i m p l e s u b m i c r o m e t e r particle size d i s t r i b u t i o n s . T h u s far, h o w e v e r , this technology has b e e n confined almost e x c l u s i v e l y to offl i n e q u a l i t y c o n t r o l e n v i r o n m e n t s . It has yet to be integrated successfully into p o l y m e r p r o d u c t i o n facilities to p r o v i d e an automatic o n - l i n e s i z i n g capability suitable for r e a l - t i m e process m o n i t o r i n g a n d c o n t r o l . T h e p r i n c i p a l factor b e h i n d this obvious s h o r t c o m i n g is the r e q u i r e m e n t of significant operator i n t e r v e n t i o n associated w i t h sample a c q u i s i t i o n , p r e p a r a t i o n , a n d i n t r o d u c t i o n i n t o the l i g h t - s c a t t e r i n g i n s t r u m e n t . T h e most critical r e q u i r e m e n t is the d i s p e r s i o n of the concentrated latex sample ( 3 0 - 5 0 % solids) i n a suitable d i l u e n t a n d d i l u t i o n o f the r e s u l t i n g suspension to a final c o n c e n tration o p t i m a l for the l i g h t - s c a t t e r i n g m e a s u r e m e n t . W i t h these needs i n m i n d , w e have d e v e l o p e d a p r o p r i e t a r y system for automatic sample a c q u i s i t i o n a n d d i l u t i o n (patents issued a n d p e n d i n g ) , d e s i g n e d to interface w i t h a D L S - b a s e d p a r t i c l e - s i z i n g i n s t r u m e n t . I n the w o r k p r e s e n t e d h e r e , this system was u s e d i n c o n j u n c t i o n w i t h a m o d i f i e d N i c o m p 370 s u b m i c r o m e t e r particle sizer. Results are s h o w n from the successful application of d y n a m i c l i g h t scattering to m o n i t o r o n - l i n e the particle g r o w t h d u r i n g the e m u l s i o n p o l y m e r i z a t i o n o f v i n y l acetate i n a p i l o t - p l a n t reactor.

Theoretical Background of Dynamic Light Scattering D y n a m i c l i g h t scattering (also c a l l e d quasi-elastic l i g h t scattering a n d p h o t o n correlation spectroscopy) is c o n c e r n e d w i t h the t i m e b e h a v i o r of the scattered i n t e n s i t y o b t a i n e d from a suspension o f particles. T h i s approach contrasts w i t h t r a d i t i o n a l l i g h t - s c a t t e r i n g techniques that measure the average scatt e r e d i n t e n s i t y . S u b m i c r o m e t e r - s i z e d particles i n suspension e x h i b i t significant r a n d o m m o t i o n because of collisions w i t h the molecules of the s u r r o u n d i n g l i q u i d m e d i u m ( B r o w n i a n motion). A s a result, w h e n a c o l l o i d a l d i s p e r s i o n is i l l u m i n a t e d b y a l i g h t source, the phases of each of the scattered waves (arriving at a detector at a fixed angle) fluctuate r a n d o m l y i n t i m e because of the fluctuations i n the positions of the particles that scatter the waves. Because these waves m u t u a l l y interfere, the net i n t e n s i t y of the scattered l i g h t fluctuates r a n d o m l y i n t i m e a r o u n d a m e a n value. T h e D L S t e c h n i q u e makes use of the fact that the t i m e d e p e n d e n c e of the i n t e n s i t y fluctuations (calculated f r o m the autocorrelation function of the scattered intensity) can be r e l a t e d to the translational diffusion coefficient of the p a r -


7.

Dynamic Light Scattering during Latex Production

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107

t i d e s , w h i c h i n t u r n is related to the particle size t h r o u g h the S t o k e s - E i n s t e i n equation. D e t a i l s o n t h e theory b e h i n d D L S a n d t h e e x p e r i m e n t a l setup; examples from applications o f the t e c h n i q u e ; a n d discussions o f its a d v a n tages, p r o b l e m s , a n d difficulties can b e f o u n d i n a n u m b e r o f sources ( 1 ^ ) . T h e autocorrelation function G (t') o f t h e scattered l i g h t i n t e n s i t y is (2)

given by: G®(t')

=

t')>

(1)

w h e r e I(t) is t h e i n t e n s i t y at t i m e t, a n d f is a t i m e delay. T h e < > s y m b o l Downloaded by CORNELL UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch007

indicates a r u n n i n g s u m o f products taken at different t i m e s , t. F o r t' —» °°, G (oo) (2)

w h i c h is t h e square o f the average scattered i n t e n s i t y ,

, 2

equal to t h e base l i n e o f the autocorrelation function. T h e n o r m a l i z e d firsto r d e r autocorrelation f u n c t i o n , g (t'), can b e calculated f r o m t h e m e a s u r e d w

function: G«(0

= B ( l + 0|g (O| ) (1)

2

(2)

w h e r e B is the base l i n e a n d p (0 < (3 < 1) is an i n s t r u m e n t - r e l a t e d constant. F o r systems o f u n i f o r m particle size, g (t ) is a s i m p l e exponentially a)

f

d e c a y i n g f u n c t i o n o f t'\ g«)(n = e x p ( - H ' )

(3)

T h e decay constant T is related to t h e translational diffusion coefficient D

T

by: r

=

(4)

2

DK T

w h e r e K is t h e scattering w a v e vector, w h i c h d e p e n d s o n t h e w a v e l e n g t h (in vacuum) o f the l i g h t source (X ), t h e solvent refractive i n d e x (n), a n d t h e angle o f d e t e c t i o n , 8: 0

/0\ K = 4irn sin I - I X

0

.V (5)

F o r r a n d o m diffusion of n o n i n t e r a c t i n g particles, the single-particle diffusion coefficient (D ) is o b t a i n e d from equations 3-5; t h e h y d r o d y n a m i c radius R T

is o b t a i n e d from D v i a t h e S t o k e s - E i n s t e i n equation: T


108


w h e r e k is t h e B o l t z m a n n constant, T is t h e t e m p e r a t u r e (kelvins), a n d T| is the shear viscosity o f the l i q u i d m e d i u m . T h u s t h e particle size o f a m o n odisperse (single-sized) suspension can b e easily o b t a i n e d from the m e a s u r e d autocorrelation function v i a equations 1-6. F o r suspensions w i t h b r o a d u n i m o d a l o r w i t h m u l t i m o d a l d i s t r i b u t i o n s , the i n v e r s i o n o f t h e autocorrelation data to obtain t h e particle size d i s t r i b u t i o n is not a n easy task a n d remains a n area o f active research (4-14). F o r a polydisperse suspension, g (f') is a w e i g h t e d s u m of exponentially d e c a y i n g functions, each of w h i c h corresponds to a different particle d i a m e t e r D w i t h decay constant Y . (1)

{

{


00

0

F(T) is t h e n o r m a l i z e d d i s t r i b u t i o n o f the decay constants o f the scatterers i n t h e suspension. T h e p r o b l e m o f o b t a i n i n g t h e particle size d i s t r i b u t i o n from the r a w data, g ( f ) , i n effect reduces to solving equation 7 for F(T). A n u m b e r o f algorithms for i n v e r t i n g this equation (an i l l - c o n d i t i o n e d p r o b lem) have b e e n p r e s e n t e d (4-13). T h e approach used w i t h significant success i n t h e N i c o m p 370 a n d elsewhere is based o n a L a p l a c e transform i n v e r s i o n of g (t') u s i n g a n o n l i n e a r least-squares p r o c e d u r e (with a non-negative constraint). A r e v i e w of most of the available algorithms for the d e t e r m i n a t i o n o f F(r) a n d a n evaluation o f t h e i r performance for suspensions o f u n i m o d a l a n d b i m o d a l d i s t r i b u t i o n s c a n b e f o u n d i n ref. 15. (1)

{l)

F o r t u n a t e l y , s i m p l e particle size distributions (smooth, u n i m o d a l p o p ulations) for w h i c h F(T) is approximately G a u s s i a n i n shape are c o m m o n . F o r these cases ( i n c l u d i n g m a n y synthetic p o l y m e r distributions), t h e m u c h s i m p l e r m e t h o d o f cumulants analysis (16) usually provides a good fit to t h e autocorrelation function data, y i e l d i n g m o m e n t s o f the d i s t r i b u t i o n F(T). I n this approach, In g (f') (which for a m o n o d i s p e r s e sample is a straight line) is fitted to a l o w - o r d e r p o l y n o m i a l (quadratic o r cubic). F o r a t h i r d - o r d e r c u m u l a n t s fit: (1)

(8)

w h e r e T is t h e m e a n value o f t h e decay d i s t r i b u t i o n , a n d |x is t h e m t h m

c e n t r a l m o m e n t o f F ( F ) , d e f i n e d as: 00

(9) 0


7.


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109

T h e m e a n diffusivity of the suspension is calculated from T w i t h equation 4. T h e standard d e v i a t i o n of the d i s t r i b u t i o n of diffusion coefficients can be calculated from u, . A n average d i a m e t e r c o r r e s p o n d i n g to the m e a n diffusion 2

coefficient can be calculated f r o m e q u a t i o n 6, a n d an i n d i c a t i o n of the spread of the particle size d i s t r i b u t i o n is g i v e n b y |x . T h e advantage of the c u m u l a n t s 2

analysis is that it is c o m p u t a t i o n a l l y fast a n d settles r a p i d l y w i t h i m p r o v i n g statistical accuracy i n the autocorrelation function. T h i s m e t h o d gives v e r y accurate results for decay d i s t r i b u t i o n s w i t h n e g l i g i b l e h i g h - o r d e r c e n t r a l moments (15), as, for example, smooth, nearly s y m m e t r i c , single-peak d i s tributions.


C o m m e r c i a l l y available D L S instruments usually e m p l o y

two

ap-

proaches to convert the autocorrelation data to particle size: (1) the m e t h o d of c u m u l a n t s ; a n d (2) an a l g o r i t h m that attempts to i n v e r t e q u a t i o n 7, solve for F(T), a n d y i e l d an estimate of the full particle size d i s t r i b u t i o n . T h e N i c o m p 370 particle sizer computes distributions b y u s i n g b o t h of these approaches a n d selects one of the c o m p u t e d distributions o n the basis of goodness-of-fit c r i t e r i a (17, 18).

Suitability of DLS for On-Line Applications: Importance of Autodilution T h e D L S t e c h n i q u e for particle s i z i n g contains a n u m b e r of i n h e r e n t a d vantages over o t h e r methods (e.g., optical t u r b i d i t y ) that m a k e it i d e a l l y suited to automated, o n - l i n e applications. F i r s t , it is an absolute t e c h n i q u e . T h e scattering wave vector K (equation 5), w h i c h connects the t i m e scale of the intensity fluctuations w i t h the particle diffusivity D , d e p e n d s o n three parameters, a l l of w h i c h are constant (for a g i v e n choice of solvent). T h e conversion of the c o m p u t e d m e a n diffusivity into a particle of radius R (equation 6) d e p e n d s o n two a d d i t i o n a l parameters that e i t h e r are k n o w n or can be h e l d constant (temperature T and solvent viscosity r\). H e n c e , any w e l l - d e s i g n e d D L S i n s t r u m e n t s h o u l d y i e l d consistent, r e p r o d u c i b l e results o v e r e x t e n d e d periods of t i m e , r e q u i r i n g no calibration. S e c o n d , the m e a s u r e d particle diffusivity (and h e n c e the calculated radius) is essentially i n d e p e n d e n t of the concentration of the m e a s u r e d suspension, p r o v i d e d it is sufficiently d i l u t e that m u l t i p l e scattering a n d i n t e r p a r t i c l e interactions (i.e., electrostatic repulsions for charged colloids) have no appreciable effect o n the autocorrelation f u n c t i o n . F i n a l l y , the particle diffusivity d e p e n d s o n l y o n its size a n d is i n d e p e n d e n t of c o m p o s i t i o n (density, m o l e c u l a r w e i g h t , i n d e x of refraction, etc.). A l t h o u g h these p h y s i c a l properties w i l l c e r t a i n l y influence the average scattered i n t e n s i t y , they w i l l not affect the particle diffusivity. t

C l e a r l y , these three characteristics of the D L S t e c h n i q u e m a k e i t i d e a l l y suited to an o n - l i n e m e a s u r e m e n t , i n w h i c h sample a c q u i s i t i o n , d i s p e r s i o n , a n d d i l u t i o n m u s t b e p e r f o r m e d automatically. T h e c r u c i a l n e w i n g r e d i e n t


110


r e q u i r e d for successful o n - l i n e particle size analysis u s i n g D L S i n s t r u m e n tation is a c o m p u t e r - c o n t r o l l e d m e c h a n i s m capable of automatically a c q u i r i n g a q u a n t i t y of concentrated suspension from a process stream o r reaction vessel a n d d i l u t i n g it to a final concentration that is o p t i m a l for the D L S i n s t r u m e n t . T h a t i s , the concentration m u s t b e sufficiently l o w to a v o i d m u l t i p l e scattering a n d i n t e r p a r t i c l e interactions b u t large e n o u g h to y i e l d


an acceptable signal-to-noise ratio i n the autocorrelation f u n c t i o n after a relatively short t i m e of data a c q u i s i t i o n (typically, just several minutes). T h e difficulty associated w i t h the use of c o n v e n t i o n a l d i l u t i o n schemes (i.e., those e m p l o y i n g fixed d i l u t i o n factors) is that the o p t i m a l d i l u t i o n factor varies greatly w i t h the properties of the starting concentrated suspension. T h e average scattered i n t e n s i t y from a suspension is a strong function of the particle size a n d the particle size d i s t r i b u t i o n . F o r example, i n the R a y l e i g h r e g i m e (diameters less than 100 n m u s i n g a H e N e l i g h t source), the s i n g l e particle scattered i n t e n s i t y is a function of the 6 t h p o w e r of the particle d i a m e t e r . T h e scattered i n t e n s i t y is also a strong function of the ratio o f the refractive i n d e x of the particles to that of the m e d i u m , a n d a l i n e a r f u n c t i o n of the p a r t i c l e c o n c e n t r a t i o n i n the suspension. I n practice, the strong d e p e n d e n c e of the scattered i n t e n s i t y o n these characteristics of the p a r t i c l e suspension r e q u i r e s that any automatic d i l u t i o n system possess a v e r y w i d e d y n a m i c range. T h a t is, it m u s t b e capable of a c h i e v i n g d i l u t i o n factors r a n g i n g from less than 1 0 0 : 1 to greater than 1 0 0 , 0 0 0 : 1 . Because the particle concentration a n d size d i s t r i b u t i o n are, at worst, c o m p l e t e l y u n k n o w n , t h e r e is no a p r i o r i k n o w l e d g e of the correct d i l u t i o n factor appropriate for the D L S m e a s u r e m e n t . A fixed d i l u t i o n m a y not b e acceptable e v e n for a k n o w n r e c i p e (routine analysis), because the d i l u t i o n factor changes d u r i n g the reaction as the p a r t i c l e size changes. M o t i v a t e d b y these tradeoffs a n d r e q u i r e m e n t s , N i c o l i a n d E l i n g s r e c e n t l y d e v e l o p e d a p r o p r i e t a r y m e t h o d (and associated apparatus), k n o w n as A u t o d i l u t i o n (19), w h i c h can automatically d i l u t e any starting concentrated particle suspension for d e l i v e r y to a f l o w - t h r o u g h scattering c e l l . A s i m p l i f i e d block d i a g r a m of a D L S i n s t r u m e n t w i t h A u t o d i l u t i o n is s h o w n i n F i g u r e 1. A s m a l l , arbitrary q u a n t i t y of a concentrated particle suspension is i n t r o d u c e d b y a valve (either m a n u a l l y o r electrically operated) i n t o a m i x i n g c h a m b e r . F i l t e r e d d i l u e n t flows c o n t i n u o u s l y into the c h a m b e r w h e r e the starting sample is c o n t i n u o u s l y d i l u t e d . T h e d i l u t e d sample passes t h r o u g h the scatt e r i n g c e l l a n d i n t o the d r a i n . T h e m a i n system c o m p u t e r ( M o t o r o l a 68000) monitors the l i g h t - s c a t t e r i n g i n t e n s i t y p r o d u c e d b y the c o n t i n u o u s l y d i l u t e d suspension a n d stops the d i l u t i o n process a n d flow w h e n the appropriate, preset scattering l e v e l is r e a c h e d . A f t e r a short t i m e delay to reach t e m perature e q u i l i b r i u m , data a c q u i s i t i o n c o m m e n c e s . T o g e t h e r w i t h the apparatus of F i g u r e 1, o n - l i n e analysis also r e q u i r e s a remote s a m p l e r - p r e d i l u t e r d e v i c e attached to the process p i p e , h o l d i n g tank, o r reaction vessel. A f t e r a series of e x p e r i m e n t s , w e a r r i v e d at the



DILUENT (WATER)

AUTOCORRELATOR

DIGITAL

T (68000)

SYSTEM COMPUTER/ CONTROLLER

PC/XT SMART CONTROLLER

SAMPLE / PREDI LUTER

DRAIN

Figure 1. Simplified diagram of the DLS instrument with Autodilution.

PREDI LUTED SAMPLE INPUT

PRE AMP/ DISCRIM.

SCATTERING CELL

PUMP


112

POLYMER

CHARACTERIZATION


configuration shown schematically in Figure 2. This simple apparatus consists of three one-way valves plus a check valve connected to a small central mixing chamber. The purpose of this accessory device is to capture an arbitrary small volume of fresh, concentrated-particle suspension (latex in our case) and predilute it to some arbitrary, but much lower, concentration suitable for delivery to the main Autodiluter in the D L S instrument (Figure 1). For this preliminary study we used a Nicomp model 370 submicrometer particle sizer with added Autodilution capability.

Figure 2. Configuration of the sampler-prediluter device used with the Autodilution-DLS instrument for on-line particle size measurements in a batch latex reactor. The sampler-prediluter consisted of three pneumatically driven ball valves plus a check valve (1 psi) connected to a small manifold-mixing chamber (all parts are stainless steel). The valves were powered by compressed air (80 psi) and actuated remotely by electrically controlled solenoid valves. Filtered water (0.4-|xm large-area Gelman filter) at 3-5 psi of pressure was the only other input requirement for the system, used for both predilution and final Autodilution of the captured latex emulsion sample. Air-driven valves were chosen because they are explosion proof and therefore meet the safety needs of a typical latex production facility. The valve assembly served to connect the three principal components of the system: (1) the pressurized pilot-scale batch reactor, (2) the D L S instrument, and (3) a source of filtered diluent.


7.

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113

T h e system was c o n t r o l l e d b y a P C X T c o m p u t e r , operating u n d e r M S DOS,

w i t h flexible software s e r v i n g two m a i n functions: (1) c o n t r o l of the

external b a l l valves (via the electrical solenoid actuators) for the operations of sample a c q u i s i t i o n , p r e d i l u t i o n , i n t r o d u c t i o n into the A u t o d i l u t i o n system of the D L S i n s t r u m e n t , a n d

flushing;

a n d (2) an i n p u t - o u t p u t d e v i c e for

serial c o m m u n i c a t i o n w i t h the D L S i n s t r u m e n t ( i n c l u d i n g data storage). In fully automatic m o d e the s a m p l i n g cycle c o m m e n c e s b y c a p t u r i n g a small q u a n t i t y of concentrated sample from the latex reactor. F o l l o w i n g a short p r e d i l u t i o n t i m e , the partially d i l u t e d sample is t h e n passed to the A u t o d i l u t e r , w h e r e the d i l u t i o n factor is a l l o w e d to increase

continuously


u n t i l the scattering i n t e n s i t y falls to a l e v e l appropriate for the digital a u tocorrelator a n d consistent w i t h the considerations just discussed. A f t e r a p r e d e t e r m i n e d delay to achieve t e m p e r a t u r e e q u i l i b r a t i o n i n the scattering c e l l , the d i l u t e d sample is analyzed b y the D L S i n s t r u m e n t . A t a p r e d e t e r m i n e d t i m e the particle size d i s t r i b u t i o n results are p r i n t e d , the r a w data are stored o n a diskette, a n d the system is flushed w i t h fresh d i l u e n t . T h e c o m p u t e r c o n t r o l l e r t h e n awaits the p r e p r o g r a m m e d start o f the next m e a surement cycle. C y c l e times of 15 m i n or less, w h e r e 7-8 m i n is allocated to data acquisition a n d analysis, are practical.

Off-Line Evaluation of the DLS Measurements: Potential for On-Line Applications A s s h o u l d be e v i d e n t from the p r e c e d i n g discussion, use of o u r D L S - b a s e d system w i t h A u t o d i l u t i o n for o n - l i n e latex particle size d e t e r m i n a t i o n s h o u l d y i e l d results w i t h accuracy a n d r e p r o d u c i b i l i t y comparable to those o b t a i n e d i n a " n o r m a l " off-line laboratory setting. T h a t is, once a fresh latex sample has b e e n c a p t u r e d a n d p r e d i l u t e d b y the s a m p l e r - p r e d i l u t e r d e v i c e of F i g u r e 2, its treatment b y the A u t o d i l u t i o n - D L S i n s t r u m e n t is i d e n t i c a l to that o c c u r r i n g o n a laboratory b e n c h , w h e r e concentrated samples are i n t r o d u c e d m a n u a l l y into the system. H e n c e , it is useful to r e v i e w o u r extensive experience i n off-line analysis of a w i d e variety of latex samples u s i n g the N i c o m p 3 7 0 - A u t o d i l u t i o n system. T h i s r e v i e w w i l l serve to establish the potential of D L S i n general, a n d o u r system i n p a r t i c u l a r , for o n - l i n e latex particle size measurements. A b r i e f presentation of this study is g i v e n h e r e , a n d further details can be f o u n d i n ref. 17. T h e m e t h o d was evaluated for (1) ability to p r o v i d e a reliable estimate of the particle size d i s t r i b u t i o n i n a short t i m e , (2) consistency a n d a b i l i t y to follow particle g r o w t h d u r i n g the reaction, a n d (3) r e p r o d u c i b i l i t y . A total of 650 samples w e r e analyzed. T h e s e i n c l u d e d a variety of latices [polystyrene, poly(styrene-butadiene), poly(methyl methacrylate), p o l y ( b u t a d i e n e - a c r y l o n i t r i l e ) , a n d polyvinyl acetate)] w i t h a variety of p a r ticle size d i s t r i b u t i o n s (bimodal, b r o a d u n i m o d a l , a n d monodisperse) a n d c o v e r e d a w i d e range of particle diameters (34 to 560 nm). S o m e of these


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latices w e r e p r e p a r e d w i t h soap-free p o l y m e r i z a t i o n s a n d others w i t h e m u l sifier present. M o s t of t h e m w e r e at conversions b e l o w 9 0 % (and some at conversions as l o w as 10%). T h e presence of e m u l s i f l e r a n d u n r e a c t e d m o n o m e r i n the p a r t i c l e suspension can p o t e n t i a l l y a d d u n d e s i r e d " n o i s e " c o m ponents to the D L S autocorrelation data a n d thus make d e c o n v o l u t i o n m o r e difficult. T h e s e n o n i d e a l samples w e r e chosen because they approximate the


type of samples that w o u l d have to b e a n a l y z e d b y an o n - l i n e s i z i n g i n s t r u m e n t o n a r o u t i n e basis. A N i c o m p 3 7 0 - A u t o d i l u t i o n s u b m i c r o m e t e r particle sizer (Particle S i z i n g Systems, Santa B a r b a r a , C A ) was used for the off-line p a r t i c l e size d e t e r m i n a t i o n . T h i s i n s t r u m e n t uses two different methods to c o n v e r t the autocorrelation function data to particle size d i s t r i b u t i o n : G a u s s i a n analysis a n d N i c o m p d i s t r i b u t i o n analysis. T h e G a u s s i a n analysis uses a second-order c u m u l a n t s fit to the data, a s s u m i n g a G a u s s i a n d i s t r i b u t i o n of decay constants, w i t h h i g h e r o r d e r (^3) c e n t r a l m o m e n t s of the d i s t r i b u t i o n e q u a l to zero. A c h i - s q u a r e d ( x ) fitting e r r o r parameter is u s e d to test w h e t h e r this ass u m p t i o n is reasonable (18). T h e analysis is a two-parameter fit, y i e l d i n g a m e a n diffusivity a n d coefficient o f variation (measure of the variance) of the d i s t r i b u t i o n of the diffusion coefficients. T h e m e a n diffusivity is c o n v e r t e d to an i n t e n s i t y - w e i g h t e d m e a n d i a m e t e r ( D ) . T h e d i s t r i b u t i o n of diffusion coefficients is c o n v e r t e d to a particle size d i s t r i b u t i o n o n an i n t e n s i t y , v o l u m e , o r n u m b e r basis, a n d the c o r r e s p o n d i n g average diameters are c a l culated. 2

c u m

T h e N i c o m p d i s t r i b u t i o n analysis e m p l o y s a n a l g o r i t h m based o n a v a r i ation of P r o v e n c h e r s t e c h n i q u e (7-9). T h i s approach makes no a s s u m p t i o n o f the shape o f the d i s t r i b u t i o n ; it is a n o n l i n e a r least-squares p a r a m e t e r estimation a n d r e q u i r e s longer times to settle because of its greater sensitivity to noise i n the autocorrelation f u n c t i o n . A variety of p o l y d i s p e r s e latices w i t h k n o w n particle size d i s t r i b u t i o n s w e r e a n a l y z e d w i t h b o t h o f the techniques discussed. F o r u n i m o d a l d i s t r i butions (broad a n d narrow), the G a u s s i a n analysis gave a good estimate of the location of the m a i n b o d y of the true d i s t r i b u t i o n o n a w e i g h t (volume) basis, a n d a good estimate of the weight-average d i a m e t e r (the estimated value was always w i t h i n 8% of the true one). It s h o u l d be k e p t i n m i n d that the G a u s s i a n a s s u m p t i o n relates to the shape of the d i s t r i b u t i o n of the decay constants (diffusion coefficients) o n an i n t e n s i t y basis; d e p e n d i n g o n the particle size range c o v e r e d b y the d i s t r i b u t i o n , the c o r r e s p o n d i n g p a r t i c l e size d i s t r i b u t i o n o n a w e i g h t or n u m b e r basis m a y b e s k e w e d . T h e m e a n diffusion coefficient e s t i m a t e d from the c u m u l a n t s analysis was correct e v e n for d i s t r i b u t i o n s w h e r e the G a u s s i a n assumption does not h o l d (for e x a m p l e , b i m o d a l distributions). T h e weight-average d i a m e t e r estimated from the N i c o m p d i s t r i b u t i o n analysis was sometimes v e r y different f r o m the t r u e one ( 1 0 - 1 5 % error). F u r t h e r m o r e , w h e n the estimated d i s t r i b u t i o n was o v e r l a i d w i t h the t r u e


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one, the larger particles w e r e correctly e s t i m a t e d , b u t the s m a l l ones w e r e not i n c l u d e d . D e t a i l e d discussions a n d explanations for this b e h a v i o r can be f o u n d i n ref. 17. T h e N i c o m p d i s t r i b u t i o n analysis can detect some b i m o d a l distributions (two populations of particles w i t h significantly different d i a m eters) i n a short t i m e , a n d this feature is useful w h e n a n a l y z i n g samples f r o m processes w h e r e secondary nucleation m a y take place. T h e results from the G a u s s i a n analysis s h o w e d better r e p r o d u c i b i l i t y , a n d , as expected, settled faster t h a n those f r o m the N i c o m p analysis. It was c o n c l u d e d that w h e n e v e r the Gaussian a s s u m p t i o n holds (indicated b y a s m a l l x value), the G a u s s i a n analysis can be u s e d to obtain a r e l i a b l e estimate of the weight-average d i a m e t e r i n a short t i m e . Downloaded by CORNELL UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch007

2

F i n a l l y , it was s h o w n (17) that for r o u t i n e analysis, D (calculated from the m e a n diffusion coefficient), together w i t h the coefficient of variation estimated f r o m the G a u s s i a n analysis, can be used successfully to m o n i t o r particle g r o w t h d u r i n g latex p r o d u c t i o n (both for monodisperse a n d p o l y disperse latex). I n processes w h e r e secondary n u c l e a t i o n is l i k e l y to occur, the display f o r m of the N i c o m p analysis can b e used, i n p a r a l l e l w i t h the Gaussian analysis, to detect the presence of a second generation of particles. c u m

T h e N i c o m p 370 i n s t r u m e n t collects scattered i n t e n s i t y data c o n t i n u ously, a n d a particle size d i s t r i b u t i o n is estimated a n d d i s p l a y e d a p p r o x i m a t e l y e v e r y 45 s. T o d e t e r m i n e h o w fast the results from the G a u s s i a n analysis settle, the intensity-average d i a m e t e r ( D ) o b t a i n e d from this a n a l ysis was r e c o r d e d as a function of t i m e ; this study was d o n e for 217 samples, w i t h a variety of distributions a n d values of D r a n g i n g f r o m 38 to 560 n m . T h e analysis t i m e for each sample v a r i e d from 1 to 4 h . T h e estimate of the Gaussian analysis was c o n s i d e r e d to have settled w h e n the fluctuations i n the value of D h a d a standard d e v i a t i o n less t h a n or e q u a l to 0 . 5 % of t h e i r m e a n value. T h i s m e a n value is r e f e r r e d to as settled D . c u m

c u m

c u m

c u m

Table I s u m m a r i z e s the settling history of these 217 samples; the samples are classified i n c o l u m n s a c c o r d i n g to the t i m e that the value of D was first r e c o r d e d . E a c h c o l u m n shows the percentage of samples (total n u m b e r of samples is s h o w n at the top) for w h i c h the value of D recorded within the t i m e range specified was w i t h i n c e r t a i n d e v i a t i o n of its final settled v a l u e . c u m

c u m

Table I. Deviation of the Value of Dcum Recorded at Various Times with Respect to Its Settling Value for 217 Samples Maximum Deviation from End Value

min, 78 samples

0.5-2

2 - 5 min, 50 samples

5-10 min, 47 samples

10-30 min, 42 samples

1.0

46

72

85

90

2.0

85

96

98

97 100

3.0

92

96

98

4.0

95

96

98 100

5.0

97

98

6.0

100

98

NOTE:

All values are given in percents.


116

POLYMER

CHARACTERIZATION

F o r e x a m p l e , i n the first c o l u m n , for a total of 78 samples, a value of D was first r e c o r d e d at a t i m e b e t w e e n 0.5 a n d 2 m i n ; for 8 5 % of those samples the d i a m e t e r value r e c o r d e d w i t h i n that t i m e slot d e v i a t e d b y less t h a n 2 % from the final settled value for that sample. O n l y the d e v i a t i o n of the first r e c o r d e d value is l i s t e d . C l e a r l y , D settles v e r y r a p i d l y ; after o n l y 5 m i n of data a c q u i s i t i o n , 9 6 % of the samples m e a s u r e d y i e l d e d estimates of D that w e r e w i t h i n 2 % of the final settled values. A f t e r 10 or 15 m i n , no significant d e v i a t i o n of the m e a s u r e d value o c c u r r e d w i t h a d d i t i o n a l r u n time. c u m

c u m

c u m

S e c o n d , 80 dispersions w e r e tested for r e p r o d u c i b i l i t y . F r o m each one of the o r i g i n a l dispersions, two, t h r e e , or m o r e d i l u t e d samples w e r e p r e p a r e d a n d r u n t h r o u g h the D L S i n s t r u m e n t . T h e settled value of D was r e c o r d e d for each of the replicas. T a b l e II gives the m a x i m u m difference observed b e t w e e n replicas of the same d i s p e r s i o n expressed as a p e r c e n t of t h e i r m e a n value (the standard d e v i a t i o n for a set of replicas i n each case is less than the m a x i m u m difference). I n 9 1 % of the cases, the m a x i m u m difference was 5%, a n d i n 7 2 % of the cases the m a x i m u m difference was less t h a n 2 % . T h e m a x i m u m difference o b s e r v e d b e t w e e n replicas of the same d i s p e r s i o n reflects the expected m a x i m u m e x p e r i m e n t a l e r r o r d u e to p r e p a r a t i o n , d i l u t i o n , a n d the presence of d i r t particles i n the suspension. T h e standard d e v i a t i o n for a l l the cases, expressed as p e r c e n t of the m e a n d i a m e t e r , was 1.08%. Tables I a n d II show that for a total data a c q u i s i t i o n t i m e of 5 m i n , the e r r o r i n the estimated value of D w i t h respect to the final settled value is smaller than the r e p r o d u c i b i l i t y error.


c u m

c u m

Table II. Maximum Difference between Replicas of D with Respect to Their Mean Value Maximum Percent Deviation

Cumulative Number of Dispersions

Cumulative Percent

0.5

22

28

1.0

38

47

2.0

58

72

3.0

68

85

4.0

70

87

5.0

73

91

80

100

7.5

dispersions were duplicated; 27 were triplicated; and 13 had 4, 5, 6, or 7 repeats. NOTE:

40

T h e latex samples u s e d to study the b e h a v i o r of D included both monodisperse a n d p o l y d i s p e r s e suspensions. T h e results j u s t p r e s e n t e d r e flect the capability of the c u m u l a n t s analysis to p r o v i d e a r e p r o d u c i b l e estimate of a c e r t a i n p r o p e r t y of the suspension, n a m e l y D , i n a v e r y short time. D is the best estimate of particle size for monodisperse suspensions. F o r p o l y d i s p e r s e suspensions, D corresponds to an average of the particle c u m

c u m

c u m

c u m


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size d i s t r i b u t i o n . T h i s average d i a m e t e r d e p e n d s o n the size range c o v e r e d b y the d i s t r i b u t i o n a n d the refractive i n d e x of t h e particles; for R a y l e i g h scatterers, D

c u m

corresponds to the D

6 5

average (17), d e n n e d as the ratio o f

the sixth to the fifth m o m e n t of the particle size d i s t r i b u t i o n . A s discussed e a r l i e r , a m o r e m e a n i n g f u l average (the weight-average diameter) can b e easily o b t a i n e d w h e n the G a u s s i a n a s s u m p t i o n holds. T h e b e h a v i o r o f the weight-average d i a m e t e r estimated b y t h e G a u s s i a n analysis for b r o a d d i s t r i b u t i o n s was also s t u d i e d (17). F o r 9 0 % o f t h e suspensions s t u d i e d , the m a x i m u m d e v i a t i o n o b s e r v e d b e t w e e n replicas was 5 % of t h e i r mean value. T h e weight-average d i a m e t e r also settles r e l a t i v e l y fast; w i t h a


total o f 5 m i n o f data a c q u i s i t i o n , t h e weight-average d i a m e t e r is w i t h i n 2 to 4 % o f its m e a n settled v a l u e , a d e v i a t i o n smaller than the r e p r o d u c i b i l i t y error. T h e a b i l i t y o f the D L S m e t h o d to follow latex particle g r o w t h d u r i n g a reaction is s h o w n i n F i g u r e 3. P a r t i c l e diameters o b t a i n e d f r o m the G a u s s i a n analysis ( D

c u m

) are p l o t t e d as a function o f the reaction t i m e for t w o soap-

free p o l y m e r i z a t i o n s of v i n y l acetate (runs H 2 1 a n d H 2 2 ) a n d two p o l y m erizations w i t h l o w soap concentrations (runs H 2 4 a n d H 2 3 ) . L a t e x samples w e r e w i t h d r a w n from t h e reactor e v e r y 5 m i n ; the off-line D L S system successfully d e t e c t e d t h e change i n particle d i a m e t e r that o c c u r r e d w i t h i n 2 h . T h e s e four runs have the same basic recipes a n d b e l o n g to a group w h e r e the effects o f soap a n d i m p u r i t i e s o n particle n u c l e a t i o n w e r e s t u d i e d i n a factorial design. T h e effects o n particle size can b e easily ascertained from the D L S results s h o w n i n F i g u r e 3. T h e effect of i m p u r i t i e s was s t u d i e d for t w o pairs o f r u n s : H 2 1 - H 2 2 a n d H 2 3 - H 2 4 . T h e o n l y difference b e t w e e n

600.0

•

f

500.0

v H 21, ? H 22 (HQ)

jj 400.0 T

300.01-

•

K

£ 200.0

o H 24, • H 23 (HQ)

til | 100.0

O

08

M

Q

6

0.0 0.0

30.0

60.0 90.0 TIME < w i n >

120.0

150.0

180.0

Figure 3. Particle growth histories for four emulsion polymerizations of vinyl acetate. Particle size was estimated with DLS.


118



the p o l y m e r i z a t i o n recipes o f runs H 2 1 a n d H 2 2 is that v e r y s m a l l amounts (~10 p p m ) o f water-soluble i m p u r i t i e s w e r e a d d e d i n H 2 2 ; these s m a l l amounts r e s u l t e d i n a significant decrease i n particle size. [ T h e results f r o m off-line D L S w e r e corroborated w i t h results from e l e c t r o n m i c r o s c o p y (17)]. T h e i m p u r i t i e s h a d t h e same effect i n t h e runs w i t h l o w soap c o n c e n tration; t h e reacting m i x t u r e o f r u n H 2 3 h a d i m p u r i t i e s i n i t , b u t r u n H 2 4 w i t h t h e same recipe was i m p u r i t y free. A g a i n , t h e presence o f i m p u r i t i e s caused a measurable decrease i n particle size, b u t considerably smaller t h a n i n t h e soap-free cases. [ T h e absolute decrease o f 8 - 1 0 n m is significantly smaller than t h e 100-250 n m o b s e r v e d i n t h e soap-free case. H o w e v e r , t h e relative decrease is significant (—10%) a n d indicates a 3 0 % increase i n t h e n u m b e r o f n u c l e a t e d particles i n H 2 3 c o m p a r e d to H 2 4 (17).] T h e effect o f soap was s t u d i e d for pairs H 2 1 - H 2 4 a n d H 2 2 - H 2 3 . Latexes p r o d u c e d b y soap-free p o l y m e r i z a t i o n s are e x p e c t e d to have m u c h larger particles than those p r o d u c e d w h e n soap is a d d e d to t h e reacting m i x t u r e . T h i s result can be clearly seen i n F i g u r e 3. R u n s H 2 1 a n d H 2 4 have the same p o l y m e r i z a t i o n r e c i p e , b u t H 2 1 is soap free. T h e particles p r o d u c e d i n this r u n are m u c h larger than those i n H 2 4 . S i m i l a r l y , t h e soap-free r u n H 2 2 results i n larger particles than r u n H 2 3 . I n these cases, t h e latex p r o d u c e d was nearly monodisperse, a n d t h e D d i a m e t e r was u s e d to follow particle g r o w t h . N u m e r o u s examples o f the use o f weight-average d i a m e t e r to follow particle g r o w t h i n processes w h e r e polydisperse latex was p r o d u c e d are s h o w n elsewhere (17); the results w e r e o b t a i n e d b y u s i n g t h e Gaussian analysis o f a N i c o m p 3 7 0 for latices p r o d u c e d i n a continuous s t i r r e d tank reactor o r i n a train o f reactors. c u m

T h e studies s u m m a r i z e d s h o w e d that d y n a m i c l i g h t scattering c a n p r o v i d e r e l i a b l e estimates o f particle size i n polydisperse a n d m o n o d i s p e r s e latex samples i n less t h a n 5 - 1 0 m i n at a n y l e v e l of conversion. T h e m e t h o d is consistent, r e p r o d u c i b l e , fast, needs no calibration, a n d therefore has a n excellent potential for o n - l i n e applications.

O n - l i n e Application of DLS: Results and Discussion O n e o f t h e p r i m a r y concerns w h e n d e a l i n g w i t h latex measurements is w h e t h e r t h e fluidics system o f the i n s t r u m e n t w i l l b e c o m e c l o g g e d after a certain t i m e . Before b e i n g c o n n e c t e d to a latex reactor, t h e s a m p l e r - p r e d i l u t e r apparatus was tested for r e p r o d u c i b i l i t y , stability, a n d a b i l i t y to d e l i v e r samples to t h e A u t o d i l u t i o n - D L S i n s t r u m e n t o v e r a p r o l o n g e d t i m e w i t h o u t p l u g g i n g . A quantity o f a polyvinyl acetate) latex was p l a c e d i n a h o l d i n g tank p r e s s u r i z e d w i t h air, a n d t h e tank was c o n n e c t e d to t h e automatic s a m p l i n g - p r e d i l u t e r apparatus. T h e s a m p l i n g system was t h e n r u n i n automatic m o d e to simulate a n actual o n - l i n e measurement. Samples w e r e automatically d r a w n from t h e tank every 15 m i n a n d a n a l y z e d w i t h t h e system. T h e t i m e for t h e o n - l i n e data acquisition was 5 m i n . T h e results o b t a i n e d o v e r 5 h o f continuous s a m p l i n g are s h o w n i n F i g u r e 4. T h e r e -


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p r o d u c i b i l i t y was excellent ( m a x i m u m deviation o b s e r v e d b e t w e e n t w o ext r e m e values, w i t h respect to the m e a n value, was 3%), a n d n o p l u g g i n g o c c u r r e d . T h e m e a n value o f the o n - l i n e estimates of the intensity-average d i a m e t e r was e q u a l to the value obtained off-line w i t h a data acquisition t i m e o f 40 m i n .

150.01 0.0

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Figure 4. A preliminary on-line test with continuous sampling for 5 h. Latex samples were acquired automatically from a holding tank and analyzed in a DLS instrument. T h e s a m p l e r - p r e d i l u t e r apparatus was t h e n c o n n e c t e d to a pilot-scale batch reactor [stainless steel j a c k e t e d , w i t h temperature control ( C h e m i n e e r , D a y t o n , O H ) ] to m o n i t o r particle g r o w t h d u r i n g t h e 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. I n these p r e l i m i n a r y r u n s , the initiator was a d d e d to the reactor together w i t h t h e other ingredients, a n d t h e n the t e m p e r a t u r e of the reacting m i x t u r e was brought to 60 ° C . T h e reaction t i m e (shown o n t h e abscissas o f F i g u r e s 5 a n d 6) is e q u a l to the total elapsed t i m e f o l l o w i n g t h e charge of the initiator i n the reactor. A l l t h e reactions w e r e c a r r i e d out u n d e r a nitrogen blanket (10 psi). H y d r o q u i n o n e was a d d e d to the d i l u e n t to i n h i b i t the reaction once the samples w e r e a c q u i r e d . F i g u r e 5 shows o u r first attempt to follow particle g r o w t h o n - l i n e d u r i n g latex p r o d u c t i o n . I n t e n s i t y - w e i g h t e d average diameters, o b t a i n e d from the Gaussian analysis, are p l o t t e d as a function of the reaction t i m e . Results are s h o w n from b o t h o n - l i n e a n d off-line measurements. T h e off-line m e a s u r e ments w e r e p e r f o r m e d o n latex samples w i t h d r a w n at the e n d of the reaction. T h e t i m e allocated for data acquisition was 7 m i n for the o n - l i n e m e a s u r e ments a n d m o r e than 30 m i n for the off-line measurements. A f t e r a reaction t i m e of 80 m i n the conversion h a d reached 100%. Therefore the last t w o Craver and Provder; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1990.

120

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40.0

80.0 120.0 TIME < w i n )

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Figure 5. On-line particle size determination during an emulsion polymerization (Run Al) in a pilot-plant reactor. The sampling cycle was initiated manually. on-line samples and the four off-line samples are essentially replicas of the same dispersion. There seem to be no significant differences between the on-line and the off-line estimates. A complete cycle involves sampling, predilution, Autodilution, temperature equilibration, measurement, printout of the results, storage of the raw data, and flushing-cleaning the cell and the sampling valves. In this first run, the sampling cycle was initiated manually; parameters such as length of the predilution time, flushing time, and total cycle time were reset after each cycle to determine the optimal duration for these functions and decide on other parameters such as diluent flow rate. Figure 6 shows results from a run where the complete cycle (sampling, predilution, Autodilution, measurement, flushing) was carried out automatically every 17 min for 4 h; 5 min of this cycle was devoted to collection of light-scattering data, and the remainder was dedicated to sample acquisition, Autodilution, temperature equilibration, and system flushing. For this run the reacting mixture was not degassed at the outset; consequently the presence of oxygen (an inhibitor in emulsion polymerization) resulted in a long induction period. On-line dynamic light scattering successfully followed particle growth during the reaction and detected the start and end of the reaction. More samples were analyzed at the end of the reaction both on-line and off-line to test the reproducibility and consistency of the results. The results obtained after the reaction had reached 100% conversion are replotted in Figure 7, where the fluctuations in the particle size measurement can be seen in more detail. The off-line results showed excellent agreement with the on-line estimates, with no statistical difference between


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On-Line Particle Size Determination during Latex Production Using

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