Particle Size Distribution II - American Chemical Society

Chapter 6

Fiber Optic Dynamic Light Scattering from Concentrated Dispersions Potential for On-Line Particle Size

Measurement

Downloaded by PENNSYLVANIA STATE UNIV on August 3, 2012 | http://pubs.acs.org Publication Date: September 24, 1991 | doi: 10.1021/bk-1991-0472.ch006

John C. Thomas Brookhaven Instruments Corporation, 750 Blue Point Road, Holtsville, NY 11742

The method offiberoptic dynamic light scattering is outlined and its application to particle size measurement in concentrated dispersions is described. We present results of particle size measurements during emulsion polymerization and crystallization reactions. These results indicate that thefiberoptic dynamic light scattering technique has potential for use in on-line particle sizing applications.

Particle size plays a fundamental role in most industrial applications of polymeric and colloidal materials. To satisfy the demand for particle size information, a large range of techniques is available (lr2). These all have their relative advantages and disadvantages, which, ultimately determine their suitability for a particular application. For example, during the last ten or so years, dynamic light scattering (DLS) has enjoyed wide usage, particularly in the sub-micrometre size range. The popularity of the DLS technique arises because it is rapid, absolute and, with modern instrumentation, simple to use (2,4). The principal disadvantage of the technique is its inherent low resolution. One characteristic that most particle sizing techniques have in common is that they may only be applied to dilute systems, i.e., typically much less than 0.1% solids. This precludes their use in on-line or at-line applications where the solids concentration is more often in the range ~20%-70%. It also has the undesirable consequence that particle size is invariably measured under physical conditions which are vastly different from those under which the material is produced and ultimately used. In the case of polymeric materials, many sensors

N O T E : This chapter is Part 4 i n a series. 0097-6156/91/0472-0098$06.00/0 © 1991 American Chemical Society

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


6. T H O M A S

Fiber Optic Dynamic Light Scattering

99

are available for monitoring parameters such as temperature, pressure, flow, density, viscosity, composition etc. directly in the reactor (5). However, sensors for monitoring particle size under these conditions are essentially non-existent. A fast, non-invasive technique such as light scattering is a prime candidate for development as an on-line sizing technique. Indeed, DLS has been used to follow particle size during emulsion polymerization using a sophisticated dilution scheme (6). The primary disadvantages of this approach would appear to be the long time delay between measurements (10-12 minutes) and the plumbing required to achieve the dilution. With the aid of fiber optics it is possible to perform DLS measurements directly on concentrated dispersions (7-10). Here an optical fiber carrying the incident light has its tip placed in the sample and either the same or a different fiber collects the backscattered light from the sample. These measurements are complicated by the possibility of multiple scattering, particle interactions and a changing heterodyne/homodyne ratio in the detected signal (9). Nevertheless, it is possible to determine useful information in many situations. In the following we outline the method of fiber optic dynamic light scattering (FODLS) and present some typical results of these measurements on concentrated dispersions. Basic Theory O f DLS The fundamental quantity measured in a DLS experiment is the photocount autocorrelation function (ACF) of the scattered light 8 (r) m

-

2

n(x) is the photon count measured at time delay x. The dynamics of the scattering system are manifested in the electric field ACF, £ (x). The relationship between g (x) and g (x) depends on the method of detection being used. DLS measurements may be performed in the homodyne or heterodyne mode. Homodyning occurs when only scattered light falls on the photodetector. In heterodyning a strong, unscattered local oscillator signal is superimposed on the scattered light at the photodetector. In general, when a local oscillator signal is present, there will be a mixture of homodyne and heterodyne components in the measured g (x ) a n d (1)

(1)

(2)

(2)

V(x)

g

= 1 +

b\2 g^) nLO

+

V(x)\ ] 2

(2)

2

Here b is an instrumental constant of order 1, n is the (constant) local oscillator count rate, is the average scattered light count rate, and LO

s


100

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

=

n

w

+

(3)

is the total photon count rate. For a dilute suspension of monodisperse, non-interacting spheres (4)

= exp(-TT)


and the decay constant is T =

K*D

(5)

where D is the particle diffusion coefficient and ww _ 4tt/i,sro(8/2)

(6)

is the magnitude of the scattering vector. Here n is the refractive index of the suspending liquid, 9 is the scattering angle and k is the laser wavelength. For spheres, D is related to the particle radius, r, by the Stokes-Einstein relationship 0

k T D = -=*L

(?)

6nTjr

Here k is the Boltzmann constant, T the absolute temperature and r\ is the viscosity of the suspending liquid. This equation provides the basis for particle sizing with DLS. Note that the relative amplitude of the two time-dependent terms in Equation 2 is determined by the r a t i o / I L O / < / I > . When/iLo/ » 1, the first term dominates and heterodyning occurs. Conversely, when n / « 1, the second term dominates and homodyning occurs. Note also that, since the homodyne term is basically the square of the heterodyne term, it will decay twice as rapidly as the latter term. Thus, the fundamental practical difference between a homodyne and a heterodyne measurement is that the ACF decays twice as rapidly in the former case as it does in the latter case. The complexity of FODLS measurements on concentrated dispersions makes it difficult to model the ACF. Here we resort to simply determining a mean decay constant, using the method of cumulants (11-12) and calculate an apparent diffusion coefficient, Z) , and particle size using Equations 5 and 7 respectively. B

s

s

LO

s

app

Experimental Arrangement Figure 1 shows the optical setup used in this work. It is based on a three-port, single-mode fiber optic system containing a 1:1 beam splitting directional coupler. The output of the 5mW HeNe laser is coupled into the fiber on the two-port side, passes through the coupler, out the fiber on the one-port side and



6. T H O M A S

101

Fiber Optic Dynamic Light Scattering

into the sample being measured. Backscattered light from the sample returns up the same fiber to the coupler at which point half goes back towards the laser and is lost and half goes to the photomultiplier detector (PMT). The output of the photomultiplier goes through an amplifier-discriminator (A/D) and on to a Brookhaven Instruments BI-2030A T digital correlator. The correlator computes the ACF of the scattered light. The fiber optic system generates a large backscattered signal from reflections at the fiber end face and from scattering within the coupler. This constitutes a local oscillator signal which beats with the light scattered from the sample and gives rise to a heterodyne component in the detected signal. Results and Discussion To test the operation of the FODLS system, measurements of £> were made on an - 170nm diameter latex sphere sample as a function of volume fraction, over the range 5.8xl0" to 0.43, i.e., four orders of magnitude. A s reported earlier (9), we observed a pronounced variation of Z> with . These results are reproduced in Figure 2, which shows Z ) and the amplitude of the timedependent component of the ACF as a function of . D is normalized to D the value of the diffusion coefficient measured in dilute suspension in a normal DLS experiment. From these data we were able to draw a number of conclusions. A t the lowest concentration measured, the backscattered light was insignificant compared with the inherent local oscillator signal from the fiber. In this case the time dependence of # (T ) is dominated by the second (heterodyne) term in Equation 2 and our data analysis, which arbitrarily assumed a homodyne signal, would yield a value for D which is half the true value, D . This is what was observed. With increasing , increases because there is more scattered light, whereas n remains constant, so that the third (homodyne) term in Equation 2 contributes more and more to the time dependence of g (t) and the second (heterodyne) term contributes less and less. Eventually the homodyne term will dominate and the value obtained for D will approach D . This occurs at < | > > 10" . Beyond this point any changes in Z ) cannot be due to the changing heterodyne/homodyne mix and are ascribed to the dynamics of the concentrated suspension. Thus, the decrease in D which occurs for < | > > 10" is due to the behavior of the suspension. Note that, in the region 10" < < 10" , D is fairly constant and within 10-20% of D . This means that, over a range of two orders of magnitude in , a reliable value for D , and hence particle size, can be obtained. To assess the potential of the FODLS technique for monitoring particle size in a process situation, measurements were made over the course of a latex emulsion polymerization reaction and compared with the particle size measurements obtained from DLS on the diluted samples (10). The FODLS measurements were made with a commercial instrument, the Brookhaven Instruments BI-FOQELS, which has an optical setup similar to that of Figure 1. The DLS measurements were made with a Brookhaven Instruments BI-90 Particle Sizer. The reaction was a standard styrene-acrylonitrile polymerization app

5

app

app

o9

a p p

(2)

Q

a p p

&

LO

(2)

Q

a p p

3

app

1

a p p

3

a p p

Q

a p p


1


102

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

Figure 1. Experimental setup for FODLS experiments. (Reproduced with permission from Ref. 10. Copyright 1990 Optical Society of America.)

1.00 €>

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Particle Size Distribution II - American Chemical Society

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