25
Small-Angle Neutron Scattering
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Recent Applications to Multicomponent Polymer Systems L . H . Sperling, J. N . Yoo, S. I. Yang, and A. Klein Materials Research Center, Center for Polymer Science and Engineering, Materials Science and Engineering Department, Department of Chemical Engineering, Lehigh University, Bethlehem, PA 18015
Small-angle neutron scattering, of determining
SANS, is a new instrumental method
polymer chain radii of gyration,
in phase-separated materials,
domain dimensions
and diffusion constants. Instruments
currently in service include those at Grenoble, Jülich, Oak Ridge, National Institute of Standards
and Technology, and Los Alamos.
The basic theory is reviewed, and examples of results are
illustrated.
JL HREE MAJOR SCATTERING METHODS exist for t h e d e t e r m i n a t i o n o f the m o r p h o l o g y i n m u l t i c o m p o n e n t p o l y m e r materials: l i g h t - s c a t t e r i n g , s m a l l angle X - r a y scattering ( S A X S ) , a n d small-angle n e u t r o n scattering ( S A N S ) (1-9). E a c h is m o r e useful t h r o u g h particular ranges o f d o m a i n sizes, contrast r e q u i r e m e n t s , a n d information d e s i r e d . S e v e r a l t e r m s c o m m o n t o l i g h t scatt e r i n g a n d n e u t r o n scattering are s u m m a r i z e d i n T a b l e I (1). T o achieve contrast, for e x a m p l e , a good light-scattering e x p e r i m e n t r e q u i r e s a reasonable difference i n refractive i n d e x b e t w e e n the t w o p o l y m e r s , b u t a reasonable difference i n e l e c t r o n d e n s i t y is r e q u i r e d for S A X S e x p e r i m e n t s . F o r S A N S e x p e r i m e n t s , good contrast can b e o b t a i n e d b y d e u t e r a t i n g one o f the phases o r a d d i n g d e u t e r a t e d p o l y m e r to o n e o f the phases. T h e general p r o b l e m o f the size a n d shape of d o m a i n i n m u l t i c o m p o n e n t p o l y m e r materials stands at the v e r y heart o f the field. T h e m o r p h o l o g y is i n f l u e n c e d b y t h e synthetic m e t h o d a n d b y processing. O n c e f o r m e d , i t 0065-2393/90/0227-0455$06.00/0 © 1990 American Chemical Society
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
POLYMER
456
CHARACTERIZATION
Table I. Scattering Term Equivalents Light Scattering
Neutron Scattering
R, Rayleigh ratio n, refractive index X, wavelength ( - 5 0 0 0 A) (dn/de) , determines scattering intensity
cE/dft, cross section 2fe,/V, scattering length density X, wavelength (~5 A) (a - a )\ determines scattering intensity
2
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SOURCE:
H
Reproduced with permission from reference
D
1.
Copyright
1984.
determines the usefulness of the final product. At one time, almost the only instrumental techniques available for the examination of morphology were electron microscopy and dynamic mechanical spectroscopy. Although enormous amounts of new fundamental information were obtained, many more types of samples could not easily be examined by these routes. Multicomponent polymer materials, such as interpenetrating polymer networks, (IPNs), latex dispersions, and block copolymers, can be characterized via small-angle neutron scattering. For phase-segregated systems, the experiments reveal the correlation length, specific surface areas, and domain diameters. For example, domains of the order of several hundred angstroms were found for I P N systems, roughly in agreement with transmission electron microscopic (TEM) studies. For block copolymers, the domains are larger via SANS. The value of the difference is that SANS can be used in some cases where T E M cannot be conveniently used, and in other cases SANS provides entirely new information. For example, the kinetics of phase separation can also be analyzed, because phase separation via spinodal decomposition is far different from that of nucleation and growth. Depending on the ratio of end-to-end distance to particle diameter, latices may undergo a type of core-shell segregation. Recent experiments show that maximum segregation occurs when the chains are about half as big as the latex particle. Each of these areas will be briefly reviewed in this chapter. Unlike ordinary light and X-rays, neutrons are actually particles of matter. The relationship between the particle mass characteristics, velocity through space, and corresponding wave-like behavior have been known since the works of Louis deBroglie in 1924 (10). The wavelength of thermal neutrons is about 1 A . The longer the wavelength, and the smaller the angle, the larger the objects that can be studied. Quantitatively, this relationship is expressed in terms of the wave vector K
K = ^ sin 6 X
(1)
where the quantity X represents the wavelength of the neutron radiation, and 26 is the angle of scatter.
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
25.
SPERLING ET AL.
SANS in Multicomponent
457
Systems
Table II. Selected S A N S Instrumentation S-D (m)
Location
Grenoble, France Julich, Federal Republic of Germany Oak Ridge, T N NIST, Gaithersburg, M D NIST (under construction) Los Alamos, N M
Max. k
40 20
15
19 3.5 20 4
4.75 18
a
18 16.5
(A)
Min. K
(A' ) 1
0.0008 0.001 0.002 0.005 0.002 0.004
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"— indicates not available.
The maximum particle size (or morphology) that can be characterized depends on the minimum value of K obtainable by a given instrument. In general, the maximum particle size that can be studied is the inverse of the minimum value of K. Several internationally important instruments are described in Table II. The sample-to-detector distance, S - D , controls the minimum angle obtainable. The maximum sizes now characterizable are about 1 0 0 0 A with appropriate allowance for resolution ( 3 ) . At the time of this writing, the facility at Oak Ridge National Laboratories is restarting after being closed for inspection and repairs. The facility at the National Institute of Standards and Technology (NIST) is closed for 3 - 6 months to install beam guides, and major new facilities are being built. A schematic of the low-Q (low-angle) diffractometer at Los Alamos is illustrated in Figure 1 (4). One way to obtain smaller values of K is to design instruments that use colder and colder neutrons in order to increase their wavelength. The practical limit seems to be the temperature of liquid helium. The wavelength distribution obtained at NIST as a function of temperature is shown in Figure 2
(11-13).
The alternative is to design equipment with smaller and smaller attainable angles. This condition requires longer and longer distances between the sample and the detector. Eventually, such techniques become selfdefeating because of the inverse square relationship between distance and beam intensity. Another way to reach low K is via the double-crystal diffractometer ( D C D ) technique. The only available instrument in the United States is at Oak Ridge, where data have been taken down to K — 2 x 1 0 " A". The current state-of-the-art D C D has been built by Schwann and coworkers at Julich ( 1 2 , 13). The evolution of SANS instrumentation is given in Table III. 4
1
Some instrumentation now available includes 1. The Los Alamos Neutron Scattering Center, Los Alamos N a tional Laboratory • low-Q diflractometer (Q = K) • surface profile analysis reflectometer
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
Downloaded by UNIV LAVAL on October 2, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch025
458
POLYMER
CHARACTERIZATION
Dial-in Figure 1. Schematic diagram of the low-Q diffractometer (LQD). A wellcollimated pulse of neutrons with a broad wavelength range strikes the sample. Those neutrons scattered at forward angles between 0.3° and 3.5° are detected. The angular position in the detector and the elapsed time since the neutron pulse (time of flight) for each event are tallied in memory in the FASTBUS for subsequent examination and analysis by computer. (Reproduced with permission from reference 4.) 2. NIST reactor, National Institute of Standards and Technology, small-angle scattering facility 3. Argonne National Laboratory intense pulsed neutron source (IPNS) 4. Brookhaven National Laboratory Oak Ridge, Los Alamos, and NIST are available to the public, and proposals are required. This review will focus on small-angle neutron scattering.
Theory One of the more important approaches to the application of SANS is derived from the correlation function, y(r), of Peter Debye (14). The scattering intensity, 7, is related to the correlation function as follows: I =
AC
f
Jo
7(r)
r
2
™-j^>
K
r
dr
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
(2)
|0 ' 0 9
459
SANS in Multicomponent Systems
SPERLING E T AL.
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25.
1
2.0"
' 6.0 8.0 X(A) 1
4.0
1
1
10.0
12.0
Figure 2. Neutron wavelength dependence on the temperature of the moderator. (Reproduced from reference 11.)
Table III. Evolution of S A N S Instrumentation Method
Location
Long flight path
Long wavelength
(a) ILL, Grenoble (b) Oak Ridge (c) Julich NIST
Comments Inverse square distance law means long experiment times Neutrons cooled via liquid He or H "White" neutrons, liquid H , pulsed source 2
Time-of-flight (TOF) a
Los Alamos
"Pulsed neutrons separated via wavelength via TOF, equivalent of FTIR to IR.
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
2
460
POLYMER
CHARACTERIZATION
where A is proportional to the total volume of the sample divided by the square of the difference between the coherent neutron scattering length of the mers, C represents the mean square deviation of the fluctuations in scattering length density, and
7 (r) = exp
[T]
(3)
and a represents the correlation length. As shown in Figure 3, the quantity a can be interpreted in terms of the correlation length, the average distance
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across a domain,
/ -
-
1 / -
q>2-
JL
or in terms of the specific surface area, S
S
SP
(4)
= 4, 2i
(6)
where i and represent the volume fractions. 2
A maximum in the scattering due to spinodal decomposition can be interpreted in terms of "wavelength", A , a characteristic distance across a domain
A
=
2ir
(7)
I — A Figure 3. Schematic illustration of correlation lengths (%), specific surface areas (S ), and wavelength (A), as determined by SANS. sp
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
25.
SPERLING E T AL.
SANS in Multicomponent Systems
461
w h e r e K is the wave vector at w h i c h t h e angular m a x i m u m is o b s e r v e d . O t h e r m a t h e m a t i c a l formulations exist t o treat s p h e r i c a l domains, etc. O f course, for m o l e c u l a r solutions, r a d i i o f gyration o f r a n d o m coils c a n b e calculated. m
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Selected Results to Date Block Copolymers. B l o c k copolymers such as polybutadiene-fcZocfcp o l y s t y r e n e are k n o w n to phase separate. T h e t r i b l o c k c o p o l y m e r forms thermoplastic elastomers because o f phase separation, c e r t a i n l y not i n spite of it. P r e v i o u s l y , T E M o n samples stained w i t h o s m i u m tetroxide r e v e a l e d that the domains m a y b e s p h e r i c a l , c y l i n d r i c a l , o r l a m e l l a r shaped. I m p o r t a n t parameters to b e d e t e r m i n e d for s p h e r i c a l domains are diameters a n d t h e shape o f the p o l y m e r chains i n s i d e o f the domains. T h e most i m p o r t a n t S A N S studies o n b l o c k copolymers w e r e c a r r i e d out b y C o h e n a n d co-workers (15-17). D o m a i n diameters r a d i i w e r e c a l c u l a t e d f r o m t h e m a x i m a as a f u n c t i o n of angle. T h e angular peaks of s p h e r i c a l particles bear a r e l a t i o n s h i p to the r a i n b o w , w h e r e diffraction m a x i m a o c c u r from u n i f o r m w a t e r droplets. D o m a i n r a d i i are c o m p a r e d to T E M results i n T a b l e IV. T h e S A N S studies result i n significantly larger r a d i i than T E M . B y partially d e u t e r a t i n g t h e p o l y b u t a d i e n e phase, c h a i n d i m e n s i o n s c a n be d e t e r m i n e d . T h e highest m o l e c u l a r w e i g h t has relaxed c h a i n d i m e n s i o n s that e x c e e d the d i a m e t e r o f the domains. A s m i g h t b e expected, the chains are elastically c o m p r e s s e d . Latex Dispersions. S i m i l a r results w e r e o b t a i n e d b y L i n n e et al. (18) o n 6 X 1 0 g / m o l p o l y s t y r e n e i n latices of380-A d i a m e t e r . I n this case, the p o l y m e r chains are r e s t r i c t e d b y a w a t e r phase rather t h a n a n i m m i s c i b l e p o l y m e r phase. 6
A m a i n finding o f the investigations o n latex dispersions u s i n g S A N S was a significant segregation o f the first p o l y m e r i z e d m a t e r i a l from that p o l y m e r i z e d later (see F i g u r e 4) (19). Segregation goes t h r o u g h a m a x i m u m w h e n t h e c h a i n d i m e n s i o n s are about h a l f the latex d i a m e t e r . T h e cause o f the segregation is t h e o r i z e d to b e r e l a t e d t o the t h e r m o d y n a m i c difficulties Table IV. Mean Radii of Polybutadiene Spheres from Electron Microscopy and SANS Sample SB-1 SB
