experimental evidence for slow theory of mutual diffusion coefficients in phase separating polymer...

British Polymer Journaf 21 (1989) 247-257

Experimental Evidence for Slow Theory of Mutual Diffusion Coefficients in Phase Separating Polymer Blends

J. S. Higgins, H. A. Fruitwala & P. E. Tomlins

Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 2BY, UK

(Received 2 February 1988; revised version received 25 April 1988; accepted 3 May 1988)

Abstract: Small Angle Neutron Scattering (SANS) is used to study the kinetics of spinodal decomposition of a blend of polymethyl methacrylate (PMMA) with solution chlorinated polyethylene. The early stages of phase separation are quantified using Cahn-Hilliard theory. Temperature and molecular weight dependences of interdiffusion are studied and it is shown that data can be better interpreted in terms of a wave vector dependent diffusional mobility M(q).

Key Words: polymer blends, spinodal decomposition, neutron scattering, polymethyl methcrylate, solution chlorinated polyethylene, wave vector dependent mobility.

INTRODUCTION

Recently there have been a number of studies of the experimental predictions of Cahn-Hilliard theory as applied to phase separation in binary polymeric systems.'- The effect of molecular parameters on the structure and properties of a polymer blend is dual, governing both the equilibrium and the kinetic aspects of phase separation. In a previous publi- cation we reported preliminary results of a study of the kinetics of spinodal decomposition in a high molecular weight system.6 In this paper we present a detailed study of the kinetics of phase separation of a similar system, a blend of solution chlorinated polyethylene (SCPE) with polymethyl methacrylate (PMMA). Chai et aL7 have studied the thermodynamic aspects of this blend and modelled the cloud point curve using the Flory equation of The negative heats of mixing measured from an anal- ogous mixture of chlorinated octadecane and oligomeric PMMA for the system are believed to result from a weak hydrogen bond formed between the hydrogen atom in SCPE and the carbonyl group of PMMA. A miscibility window has been found for blends with SCPE of 65% chlorine content and

higher. The system studied previously was shown by both small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS) to phase separate on a much smaller scale than could be observed by light scattering. In this study, only SANS is used to investigate the initial correlation length of phase separation and its quench depth dependence as well as the concentration dependence of the phase separation process.

THEORY

In any closed system at constant pressure the condition for equilibrium is that the Gibb's free energy of mixing, G, be a minimum where G = AHm - TAS,,,? and AHm and ASm are enthalpy and entropy of mixing respectively.

A more complete statement of the thermodynamic criteria for miscibility is that

Here Qi is the volume fraction of component i, T is temperature and P pressure. This inequality should

241 British Polymer Journal 0007- 1641/89/$03.50 0 1989 Society of Chemical Industry. Printed in Great Britain

248 J. S. Higgins, H , A . Fruitwala, P. E. Tomlins

be satisfied over the range of temperature and concentration of interest.

Partially miscible polymer blends which are initially homogeneous form two phases when heated above the cloud point curve. The appearance of new phases from a homogeneous mixture has been envisaged as occurring by two distinct mechanisms:" (a) nucleation and growth of droplets; (b) spinodal decomposition of a continuous phase. These two mechanisms have been described else- where." It is sufficient to say in the context of this paper that when a concentration fluctuation occurs in a nucleation and growth regime, there is a free energy barrier to the phase separation whereas any fluctuation in a spinodal regime leads to sponta- neous phase separation. The theoretical treatment of this latter situation was considered in detail by Cahn and Hilliard.' The Cahn-Hilliard (C-H) theory is based on linearization of a diffusion equation which was originally developed for low molecular weight systems. Later, de Gennes13 and Pincus14 among others presented the theory for spinodal decomposition in polymer blends, based on C-H theory. Cooki5 and Binder16 extended the C-H development to include the effects of thermal noise. There have been a number of applications of C-H linearized theory to describe the early stages of spinodal decomposition.'

In their basic theory Cahn and Hilliard derived an expression to describe the change in concentration as a function of time t during a spinodal process:

a@ - = M( $)P@ - 2Mkv4B + non-linear terms d t

(1) where G is the free energy of mixing, @ is the concentration, M is the diffusional mobility, and k is termed the energy gradient coefficient parameter. If non-linear terms are dropped, eqn (1) has the following solution:

(2) Here Q0 is the average composition before phase separation, q is the wave vector of the sinusoidal concentration fluctuations, t is the time variable, 7 is the position variable, A and B are the Fourier coefficients of a component with a wavenumber q, and R(q) is the rate at which the amplitude of q increases and is given by

From eqn (3) it can be seen that the fluctuations with a wave vector q smaller than qc (critical wave vector) yield a positive growth rate and that all

fluctuations with a larger wave vector than qc will decay with time. Also the rate R(q) has a fairly sharp maximum at

(4) The implication of this maximum is that one particular concentration fluctuation wavelength becomes dominant within the system.

In a scattering experiment, this situation is seen as a well-defined peak at neutron wave vector q = qm where

471 . q = - sin 812 /I

I I being the wavelength of the radiation in the medium and 6 the scattering angle.

The growth rate R(q) can be measured experimentally by the time dependence of the elastic scattered intensity of neutrons. The intensity of radiation scattered by concentration fluctuations varies as the square of their amplitude.I6 Thus from the linearized theory, in the early stages of spinodal decomposition this intensity will grow exponentially according to

S(q, t ) exp (2R(q)t) (6)

where S(q, t ) is the intensity of the scattered neutrons at time t.

The analogy between eqn (1) and a conventional Fick's second law for interdiffusion a@/at = DV2@ will yield a Cahn-Hilliard diffusion coefficient D where

D = - M(82G/d@2) (7)

and D is the diffusion coefficient. D can be calculated from the observed growth rate

R(q) via eqn (3). It should be noted that in the spinodal decomposition regime, a2G/aQ2 is negative and hence R(q) would be positive for values of q I q, and so any fluctuation with a wavenumber q I q, can grow. The linear theory predicts the maximum growth rate R(q,), and from eqn (3)

a2G R(q , )=D -( -- a@.) '8'

From eqns (4) and (8), it is clear that q, is controlled by the thermodynamic term a2Gjd@* whereas R(qm) is controlled both by the thermodynamics and by the intermolecular diffusion coefficient, M . The energy gradient coefficient k arises from the free energy due to the concentration gradient. It can be determined from eqn (3) if the thermodynamic term a2G/a02 or A4 are known independently.

If the theory of spinodal decomposition for polymer blends is reformulated in terms of the random phase approximation (RPA),l6*' then the

BRITISH POLYMER JOURNAL VOL. 21, NO. 3.1989

Slow theory of mutual diffusion coeficients in phase separating polymer blends 249

energy gradient coefficient k can also be obtained independently from the dimensions of the component polymer using the formula

where R, is the radius of gyration of polymer i, M i is the monomer mass of polymer i, M,, is the molecular weight of polymer i, and mi is the volume fraction of polymer i.

Following normal scattering theory we used the z-average radii of gyration to calculate k.

It should be noted that the RPA only applies to homogeneous systems and that therefore this development can only be applied to the very early stages of phase separation. This, however, is true of the whole C-H development itself and several other parameters (notably B and k) are assumed to be concentration independent.

There have been a number of more recent publications extending and refining the basic C-H theory.' 5 v ' 6,1 * We will introduce these as we discuss the shortcomings of C-H theory in interpreting the results presented.

EXPERIMENTAL

Materials

Solution chlorinated polyethylene was prepared in the laboratory by passing chlorine through a solution of linear polyethylene in chlorobenzene at 140°C for several hours.19 The product was frac- tionated using propan-2-01. The chlorine content of the SCPE was found by elemental analysis to be 66% w/w. Deuterated polymethyl methacrylate (d- PMMA) samples of varying molecular weights were obtained by exposing aliquots of a d-PMMA (kindly supplied by Dr H. Snyder, DuPont, USA) to y- radiation for controlled periods of time.2" This procedure produces samples with a polydispersity (Mw/Mn) of approximately 2.0 and does not induce crosslinks into the specimens. The molecular characteristics of the d-PMMAs and SCPEs used in this study are listed in Table 1.

Blend preparation

Thin films of blends were made by evaporating solutions containing known weights of PMMA and SCPE dissolved in dry butan-2-one to dryness. The films were then placed under vacuum at 80°C for 1 week to ensure the removal of all traces of solvent. Typical film thicknesses were 0-1-0-2 mm.

Kinetic experiments

Kinetic experiments were performed on the small angle neutron scattering (SANS) spectrometer D, 2 1 at the Institut Laue-Langevin (Grenoble, France). A sample-detector distance of 11.95 m was used with neutrons of wavelength 8.01 A. Correc- tions were made for the detector response using the incoherent scattering from water. No further corrections were considered necessary.

The experimental procedure was to clamp a film in the form of a 12mm diameter disc into a recess set in a thin brass finger using a narrow ring. This arrangement allowed us to use a lOmm diameter neutron beam. The brass finger was then inserted into a preheated brass block located in the neutron beam and set at a temperature above the cloud point (the cloud points were estimated on a similar system in our laboratory. The time taken to reach the working temperature was found to be 5-7 s. In some tests with a sensor at the centre of the sample area it was observed that the time to reach equilibrium temperature was longer than 7s, thus affecting the reliability of the very early stages. Examination of Fig. 4 (p. 251) shows that even a 20s delay would have little effect on the value of R(q). The time of insertion into the block was taken as time zero and spectra were recorded over 16 s intervals for periods of up to 20min, when the experiment was ter- minated. The time interval between the end of one spectrum and the beginning of the next was approximately 3 s. This period was accounted for in determining the time scale of the experiment. As the rate of phase separation is comparatively slow, the inevitable data smearing that occurred in each 16 s recording is of no significance. However, the high temperature jump involved in the experiment may be significant and will be discussed later.

TABLE 1. Molecular characteristics of polymers used in this study

Sample M W M W l 4 r, ("C) <q> :"/A

SCPEBB 1.04 x 10" 1.67 69 142 d-PM MA-2 1.12 x 105 1.75 104 87 d-PMMA-1 8.21 x 105 2.62 106 290

BRITISH POLYMER JOURNAL VOL. 21, NO. 3,1989

250

"5 7 1.2- 51 E

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TJ 0.6-

J. S. Higgins, H. A . Fruitwala, P. E. Tomlins

do=O'80, T= l50 .5 "C 0 o 0 0 - 0 " J - e z = . , " . n o = o n 0 0

RESULTS AND DISCUSSION

A number of different values of qm can be obtained from the experimental data. For clarity in the discussion we identify each with a separate symbol. Figure 1 shows typical data for time evolution of scattered intensity as a function of wavenumber q, for the blends containing 50% SCPE and PMMA. In this data for which we succeeded in accessing early stages of the spinodal decomposition, it can be seen that the intensity rises sharply and develops a maximum at y,(s). During the early stages q,(s) is not time dependent and the maximum remains at constant q. According to Cahn-Hilliard this would be true for the early stages as chains diffuse very slowly and so the kinetic process is diffusion controlled. In our previous study6 on this system, we were unable to obtain the initial correlation length as it was outside the range of light scattering and the neutron data did not access the early stages. However, in this study we have adjusted temperature conditions in order to obtain the initial correlation length as a function of temperature and also as a function of molecular weight of the d- PMMA. The results are listed in Table 2, and a typical plot of correlation length against time is shown in Fig. 2. In general the initial correlation length do = (dm)t+o where d, = 271/q,(~)~' at the

X .

O x

X X

X

Y

n

Fig. 1. Evolution of scattered intensity as a function of wavevector q for the sample of 50% SCPE. The sets are at 16 s

intervals. The first 26 s after the temperature jump.

1.2 t

maximum (Table 2) decreases slightly as temperature increases inside the spinodal curve. This is in agreement with the prediction that the initial wavelength of the composition fluctuation will tend to infinity as the spinodal is approached, although as discussed below the actual observed decrease is much less than predicted by C-H theory (eqn 3). It is also evident from Fig. 2 that dm remains constant as a function of time for about 400s. During this period, the scattered intensity increases exponentially as shown in Fig. 3. The exponential increase can be clearly seen from the linear behaviour of the logarithmic plot in Fig. 4. Recently Okada and Han' observed double exponentials in the intensity-time plots for the polystyrene-polyvinyl methyl ether (PS-PVME) system indicating the importance of thermal noise and higher order terms in eqn (1). However in our case we observed only one exponential for each q value, probably due to the fact that the intensity increase is large enough to neglect these terms. The intensity increase with time

$10

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Fig. 3. Intensity as a function of time. The exponential growth suggests the early stages of spinodal decomposition.


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252 J. S . Higgins, H. A . Fruitwala, P . E. Tomlins

I I I 1 I

2.0 I t

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Fig. 4. Logarithmic intensity as a function of time. The slope gives Cahn-Hilliard growth rate 2R(q).

starts to deviate from that expected from the linear theory in the late stages which will not be considered here.

From Fig. 4, the slope of the straight line yields the relaxation rate R(q) for that particular q. Similar plots give values for R(q) at different wavenumber q. Figure 5 shows R(q) versus q for the 50% blend with a clear maximum at q,(R). In Fig. 5 the effect of temperature on q,(R) is clearly seen. For deeper quenches, as d2G/d02 becomes more negative, q, moves to higher q values. q,(R) should be approximately 27c/do as Table 2 shows.

In order to obtain the Cahn-Hilliard diffusion coefficient D, from eqn (3), R(q)/q2 is plotted against q2 in Fig. 6. We have found that even at temperatures close to the spinodal temperature, the plot is curved at low q values but data at high q values are linear. It

2.6 I

has been suggested that omission of the non-linear term in the Cahn-Hilliard theory might be the cause. Alternatively Binder et ~ 1 . ~ ~ have recently shown numerically that the initial curvature may be due to the slow relaxing variables of polymer mixtures undergoing phase separation near a glass transition. These slow relaxing variables are structural variables associated with the T, values of the components, clusters of impurities relaxing after the quench and the strain field associated with the lattice constant misfit of constituents. However, as shown in Table 2 all our experiments were carried out at least 30°C above T, for PMMA, the stiffer component in the blend. For these reasons we do not attribute curvature in Fig. 5 to the proximity of T, at least until other possibilities have been ruled out.

It has been pointed o ~ t ' ~ 3 ' ~ that the effect of thermal fluctuations is to modify eqn (6) to

S(q, 1) = S,(q) + cm, 0) - S,(q)l exp 2R(q)t (10) where S,(q) is the so-called virtual structure factor, that is, the scattering that would be observed if a homogeneous blend existed at this temperature and concentration. Sx(q) is in fact negative over values of q < q, as observed by Okada and Han' very close to the spinodal. These authors obtained Sx(q) by a fit of eqn (10) to their observed data for S(q,t). Their results indicated that S,(q) is only important very close to the spinodal. Moreover, when S,(q) is important a plot of In S(q, t ) versus t is no longer linear. The linearity of the plots of which an example is shown in Fig. 4 together with the fact that our quench depths are all of the order of 2°C or more argues against the contribution from Sx(q) being important enough to cause the curvature in Fig. 5.

X

\ - $ I

/ "

I I I I I I I I I I I 5 6 7 8 9 10 11 12 13 14 15 *

q x 105 (cmP

Fig. 5. Calin-Hilliard growth rate R(q) as a function of wave vector q at two different temperatures: 0, 150°C; x , 155.2"C. For 50150 blend of PMMA-1.


Slow theory of mutual digitsion coeficients in phase separating poIymer blends 253

I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 *

q2 x 10" (crnI-2

T

- Lz

I I I I I I 1 I I 8 10 I! 14 16 18 0 2 4 6

q2 x 1011 (cmT

(4 Fig. 6. Comparison of different approach to obtain apparent diffusion coefficient for PMMA-1 50/50. (a) Cahn-Hilliard; (b)

P i n c ~ s . ' ~ (c) Binder;16 (d) Cahn-Hilliard for PMMA-2 blend at 14743°C.


254 J. S. Higgins, H . A . Fruitwulu, P. E. Tomlins

A further reason for curvature of the R(q)/q2 plots has been suggested by Pincus14 and Binder.I6 In applying eqn (3) it has been assumed that the quantities M and k are independent of q. Equation (9) shows that in the random phase approximation this assumption is true for k. However, when distances are small compared with the radius of gyration, this assumption can no longer be made about M .

Pincus14 calculated the wave vector dependent Onsager coefficient, A(q), which should replace Mq2 in eqn (3). By considering the dynamical properties of one labelled chain in an entangled melt which undergoes rapid small amplitude local motions and slow large amplitude creep the following form for A(q) was obtained:

Wd2 A(q)=@(l -@)-[1 -exp(-q2R;)] (11)

q2R,2 where Wis the rate ofmotion of a subunit in the melt and d is the tube diameter in the reptation Equation (1 1) has been derived for the symmetric case where WA = W,, R,, = R,, and dA = d, for the blend.

Binder16 has a slightly different form for A(q), though the limiting behaviour at large and small q is the same. His form is given by

2cWd2 A(q)=@(l -@)-

q2 Rg’ 1

1 --[1 -exp(-q2Rg’)]

where c is a constant of order unity. From Binder’s discussion of these two expressions

it is not clear which has the stronger basis, though he does point out that the Pincus expression implies that the collective structure factor for qR, >> 1 never reduces to the single chain term as his own does.

Using eqns (11) or (12) to replace M in eqn (3) we obtain

R(q) Pincus 1 -exp(-q2Ri)

or

R(q) (1 - (q2 R;)- ’( 1 - exp ( - q2Ri))

Binder

= -@(l- @)-

In Fig. 6 we compare each of these two methods of plotting R(q) data with the Cahn-Hilliard R(q)/q2

plot. As can be seen the Pincus expression, eqn (13), gives excellent linearity but the Binder expression, while an improvement on the C-H plot, is still noticeably curved. This was found to be system- atically the case for all the R(q) data.

In both cases we had to use an average value for R; which we calculated as

R,2 = @A(Ri>ZA + @B(R,Z>a

where (Rg’),, is the z-average radius of gyration of component A. For PMMA the relationship between (R;), and M , was observed to be 0.26 by SANS.24 For SCPE no values are available in the literature, but values for polyethylene and for PVC are comparable if the increased weight due to chlorine content is taken into a c ~ o u n t . ~ ’ . ~ ~ The ratio is 0.44. These ratios allow us to calculate the values of ( R ; ) , listed in Table 1.

Since the Pincus form gives the best effect in improving linearity we consider only this form in the following discussion.

From Fig. 6 and eqn (13) the ordinate intercept is

(15) -@(l - a) Wd2 a2G

a a ) 2 Int =

R p’ and the slope S is given by

Wd2 s= -2@(1- @)- R92

As in simple C-H theory the ratio of slope to intercept gives a value for q, which identified as qmax. This value should be compared with q,(R) and do in Table 2.

q m = ( - ) ’ ” = i ( - Int - a 2 G l a w ) 112 (17) 2 slope

In conventional C-H the intercept gives the C-H diffusion coefficient, D (= - M d 2 G p 2 ) .

In this case, by comparing the limit of eqns (1 1) or (13) at low q with C-H behaviour we identify the modified diffusion coefficient as

In Table 2 we list values of qmax and D’. It is noticeable that the thermodynamic q, defined

by eqns (4) and (17) fall at considerably higher q values than the observed maxima q,(R) in Fig. 5. Examination of eqn (13) shows that for q2Ri << 1 this form returns to that in eqn (3) with M = @( 1 - (D)Wd2 while for q’Ri >> 1 the form tends to

R(q)= -@(l - @)-


Slow theory of mutual diffusion coeficients in phase separating polymer blends 255

150

- 140 I-

h

Y J (b)

Fig. 7. (a) Temperature dependence of apparent diffusion coefficient d for the different compositions of SCPE. 0, 25% SCPE; x , 50% SCPE; A 75% SCPE. Straight lines are extrapolated to zero diffusion coefficient to get spinodal

temperatures. (b) Spinodal curve.

which has the maximum at q = 0. Thus the Pincus form for R(q) moves the apparent maximum to lower q values as q’R; increases.

A small amount of data was obtained for a blend containing a much lower molecular weight PMMA (d-PMMA-2 in Table 1). For this sample (R:)‘ is very much lower in value so that the condition q’R; < 1 applies over most of the q range. Thus we would expect the original C-H theory to be a better approximation and indeed for this sample R(q)/q2 varied approximately linearly with q2 as Shawn in Fig. 6d. This is further support for our argument that for the other blends with PMMA-1 the wave vector dependence of M is responsible for the curvature.

If the temperature dependence of W is ignored then eqn (18) shows that D’ extrapolates to zero, at the spinodal. Figure 7 shows these extrapolations for the three compositions and the corresponding spinodal.

Equation (4) relates qm to the thermodynamic quantity d2G/a@’ via values of k. These were calculated from eqn (9) using the same z-average values for ( R : ) , as previously used for the calculation of eqn (13) or (14). In Table 2 we list values of a2G/d@’ calculated from qmax via eqn (4). Next to these we list the values of the quench depth AT (= T - Tsp) where Tsp is the spinodal temperature. It is interesting to note that a’G/d@’ shows a reasonable quench depth dependence whereas the observed q,(R) and do do not. This lack of quench depth dependence has been noted for other systems when the C-H theory is applied.27.28 At least in the present case it appears that the q-dependent Onsager coefficients A(q) are obscuring the thermodynamic behaviour when R(q) or S(q, t ) are considered.

The intensity of forward scattering from a one phase blend depends directly on d2G/[email protected]*’9 For the 50/50 composition of this blend we have some preliminary mea~urements’~ which, when extrapolated against T-’ through the spinodal to the temperature of the kinetics experiment ( 150°C), give a value of lop2 in reasonable agreement with the values given in Table 2. For other blends, a more detailed comparison has shown good agreement between behaviour inside the spinodal and values of d’G/d@’ extrapolated from the one phase r e g i ~ n . ~ ~ . ~ ’

From the plots in Fig. 6 and using eqn (1 S), values of Q(1- @)Wd2 can be obtained, using the same values of k. These are tabulated as M‘ in Table 2. In order to consider the concentration dependence of M‘ we have first to take into account the fact that the mobility of individual chains is strongly temperature dependent. The normal dependence of such terms as viscosity, etc., on temperature is exponential. Moreover the Rouse relaxation times 7 are related to q/T, where rl is vis~osity.~’ We have therefore identified W as proportional to t-l and compared values of In (M’IT) in Table 2. In order to shift these values to a common reference temperature the values of In (M’IT) are plotted against Tin Fig. 8. As can be seen all the values fall roughly on a single straight line. Thus at any given reference temperature there would be very little concentration dependence observable. This is consistent with the @( 1 - @) dependence of M’ suggested by eqns (13) and (14). (For the three samples considered Q(1 - @) is 0.187, 0.25, 0.185).

As was pointed out, however, eqns (12) and (13) were derived on the assumption that the polymers in the blend are identical in their values of W, d and


256 J. S . Higgins, H . A . Fruitwala, P. E. Tomlins

-30 t

Fig. 8. ln(M’/T) as a function of temperature. Single straight line shows concentration independence of the mobility term. The data correspond to molecular weight d-PMMA = 8.2 x lo5 blend compositions: x , 25/15; 0 , SO/SO; A, 15/25 and molecular weight of d-PMMA = 1.1 x lo5 composition; H,

50150.

( R ; ) , . Moreover it is assumed that the Onsager coefficients are combined as

A-Yq) = AA1(d + &l(q) (20)

Binder16 has discussed the situation where the components are less symmetric in their properties. If we assume a partially symmetric case where ( Ri)z are close in value but the dynamic properties of the polymers differ, we replace the term M‘ (=@(1 - @ ) W d 2 ) in eqn (13) by

MI- = @ - I ( W&), + (1 - a)- l ( W&), ’ (21)

Now, even if ( Wd2)A is very different from ( Wd2)B there is a relatively small variation in M’ over intermediate concentrations, and moreover the motion of the slower component tends to dominate. For this reason theories based on combination of mobilities following the form of eqn (21) are called ‘slow theories’.33 The basic idea is that fluxes should cancel. There has been some discussion in recent literature about the correctness of eqn (21) for polymer blends. There are a number of proponents of a ‘fast t h e ~ r y ’ ~ ~ , ~ ’ in which the osmotic pressure gradients cancel, leading to a linear combination replacing eqn (21) by

(22) In this case it can be seen that the motion of the fastest moving species dominates.

Experimentally, interdiffusion measurements of two miscible polymers seems to favour the fast t h e ~ r i e s . ~ ~ . ~ ’ In the present case we anticipate rather large differences in mobility of the SCPE and PMMA based on the much lower glass transition

M = a)( W&), + (1 - @)( Wd2),

temperature of the former. If this is the case then the observed low effect of concentration favours the slow theories of combining component mobilities in the situation of spinodal decomposition.

The effect of molecular weight on the mobility is shown by the inclusion in Fig. 8 of data for the low molecular weight (PMMA-2) blend. Binder1 points out that for entangled chains if reptation is important one would predict M’ oc N - while the Rouse models M’ cc N - l, where N is the number of repeat units in the chain. From the limited data available in Fig. 8 and Table 2 we note that M , (and hence N ) is reduced by a factor of about 8 and M’ increases by a factor of 2, when compared with a common reference temperature. Thus these preliminary observations do not agree well with either theoretical prediction.

CONCLUSIONS

For a blend of SCPE with PMMA we have observed the early stages of spinodal composition using small angle neutron scattering. The behaviour is in agreement with the overall predictions of Cahn-Hilliard theory if we take account of a wave vector dependent mobility term. Following this treatment, values of the thermodynamic term 8’G/802 extracted from the data show a reasonable quench depth dependence even though the observed maxima at q,(R) do not. Very small concentration dependences in the blend mobility may be evidence that slow theories for the combination of the component mobilities apply to the spinodal decomposition process.

ACKNOWLEDGEMENTS

The authors would like to thank A. Rennie for his assistance during these experiments at ILL, Gren- oble. Their special thanks to R. G. Hill for making SCPE during his stay at Imperial College. H. Fruitwala would like to thank DuPont, USA, and ICI, Wilton, for financial assistance during the course of this work.

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experimental evidence for slow theory of mutual diffusion coefficients in phase separating polymer...

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