Swelling equilibrium and light spectroscopy in swollen polymeric networks at theta conditions

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Swelling equilibrium and light spectroscopy in swollen polymeric networks at theta conditions

S. Candau, J.P. Munch, G. Hild

To cite this version:

S. Candau, J.P. Munch, G. Hild. Swelling equilibrium and light spectroscopy in swollen polymeric networks at theta conditions. Journal de Physique, 1980, 41 (9), pp.1031-1038.

�10.1051/jphys:019800041090103100�. �jpa-00208917�

Swelling equilibrium ^and light spectroscopy in swollen polymeric

networks at theta conditions

S. Candau, ^{J. P. Munch}

Laboratoire d’Acoustique Moléculaire (*), Université Louis-Pasteur, 4, ^rue Blaise-Pascal, 67070 Strasbourg ^{Cedex, France}

and G. Hild

Centre de Recherches sur les Macromolécules, 6, ^rue Boussingault, Strasbourg, ^France

(Reçu ^{le 13 novembre} 1979, révisé le 29 février, accepté ^{le 8 mai} 1980)

Résumé. 2014 Les variations thermiques ^du temps de corrélation de la lumière diffusée quasi élastiquement ^{et du}

taux de gonflement ^à l’équilibre ^ont été mesurées pour des réticulats de polystyrène gonflés soit par du benzène soit par du cyclohexane.

Les résultats obtenus montrent qu’il ^se produit ^une séparation ^de phase ^{interne à une} température Tc inférieure à la

température ^{« 03B8 » et} qui dépend ^du degré de réticulation.

Un comportement critique des fluctuations de concentration est observé à Tc.

Abstract.

The temperature dependences of the correlation time of laser light ^{scattered and of} equilibrium swelling degree ^for polystyrene networks swollen in cyclohexane ^are reported.

The results provide evidence of an internal microphase separation ^{at a} temperature Tc below the « 03B8 » temperature which depends ^on the crosslink density.

The concentration fluctuations show critical behaviour at Tc.

Classification Phy.sics ^Abstracts

36.20

61.40

64.70

78.35

Introduction.

It has been recently established that the scaling ^theories developed ^for polymer ^solu-

tions [1-2] ^{are also} applicable ^to gels [3-5]. ^The analogy

between polymer solutions and swollen networks is based on the following assumption : ^{a network,}

swollen to equilibrium, ^{is similar to a} solution of free chains with the same number of statistical segments ^N

as the network-chains, ^{at the crossover concentra-} tion ({J*(N) ^{between the} dilute and semi-dilute

regimes [2]. ^{As a} consequence the network swollen in an excess of solvent adjusts ^{its volume fraction to}

the value o,, given by :

where RG ^{is the radius of} gyration of the free chain

containing ^N segments, ^{in the same solvent. The above}

relationship ^can be derived from the classical mean

field Flory theory [6] ^{if one assumes that the} change ^of swelling ^{is affine in} the dimensions of the chains of the network [2, 5]. ^{Such an} assumption ^is equivalent ^to

the following packing condition :

where R is the radius of gyration of the chains of the

gel ^{at a monomer} concentration C.

The validity ^{of the} previous approach ^{has been}

confirmed by the results of quasi-elastic ^{and elastic} light scattering experiments which demonstrate that networks swollen in a good ^solvent obey ^{the same} scaling ^{laws as} the semi-dilute polymer ^solutions [3, 7].

In the present paper ^we consider the influence of the quality ^of the diluent on the thermodynamic

and dynamic properties ^of gels. ^{Such a} problem ^raises

two fundamental questions :

-

Is it possible ^{to extend} Flory’s theory ^{to the}

networks swollen in a « theta » or poor solvent ?

-

How is the phase diagram ^{of a} gel compared ^to

that of a polymer ^{solution ?}

In this regard, ^{a recent} theory ^{of Tanaka} [8] ^based

on the extension of Flory’s formula for free _energy of gel predicted ^essential differences between phase separation ^of gels ^{and that of} binary fluid mixtures.

The shape ^{of the} phase diagram depends critically

on the crosslinks density. ^{As a matter of} fact, ^two polyacrylamide ^{networks of} different crosslinks den-

sity swollen in an acetone-water fluid mixture exhibited volume curves of significantly ^different shapes. ^Ano-

ther interesting ^feature, related with the phase ^dia-

gram of gels, ^{is the} ability ^{of a} gel ^to undergo ^a spinodal

(*) ^{E.R.A. au C.N.R.S.}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019800041090103100

1032

decomposition under sudden cooling [9-12]. ^The resulting concentration fluctuations exhibit a critical behaviour which ^can be probed by light scattering experiments [9].

This paper presents ^some measurements of the temperature dependence ^{of the} equilibrium ^volume

fraction for series of polystyrene ^{networks of various} crosslinking degrees, ^{swollen in a} good ^solvent (ben- zene) ^{and in a} « theta » solvent (cyclohexane). ^The experimental results show that the validity ^{of the} analogy ^between polymer ^{solutions and} gels ^{is res-}

tricted to the good ^diluent systems. Measurements of the correlation time of laser light ^scattered by ^the

concentration fluctuations of polystyrene ^networks

swollen at equilibrium ⁱⁿ cyclohexane ^{are also} report- ed. The experiments ^{show that the} spectrum ^of scattered light ^{is dominated} by ^slow modes associated with the critical _process evidenced by ^Tanaka [9],

even when the systems ^{are at the} swelling equilibrium

state.

1. Experimental part.

1.1 SAMPLES.

The networks were obtained by ^radical copolymerization

of styrene ^and divinylbenzene ^{in benzene solution}

in the presence of azo-2-2’-isobutyronitrile ^{as the} initiator, ^{at 60 OC over a} period ^{of 48 h. A series of} networks of various crosslinking degrees ^{has been} prepared using different concentrations of styrene (CST) ^{and of} divinylbenzene (CDVB). ^The crosslinking degree ^{can be} qualitatively characterized by ^the equilibrium swelling degree qi ^of the network in a

good ^{solvent of the} polymeric ^chains. The values of the

equilibrium swelling degrees qiBZ and qio ^{for the series}

of polystyrene ^{networks swollen in benzene at room}

temperature (21 ^{OC ± 1} °C) ^{and in} cyclohexane ^at

34.5 OC, respectively, ^{are listed} in table I.

Table I.

Parameters of styrene-divinylbenzene ^net-

works prepared by ^radical copolymerization.

CST % ^and CDVB % ^{are the} weight concentrations of styrene ^and divinylbenzene, respectively.

qiBZ is the equilibrium swelling degree ^{of the} gels ^{in benzene}

at 21° + ¹ °C.

qio is the equilibrium swelling degree ^{of the} gels ⁱⁿ cyclohexane at 0

34.5 °C.

1. 2 TECHNIQUES. - ^1.2.1 Swelling equilibrium

measurements.

The equilibrium swelling degree qi of the polymer in the swollen networks was determined

with an accuracy of approximately ⁵ jo by ^a weighing technique described elsewhere [13].

1.2.2 Light scattering spectroscopy.

^A Spectra- Physics argon-ion ^laser (Â

^{4 880} À) ^{was used in}

conjunction ^{with a} 48 channel clipped digital ^auto-

correlator (Precision ^{Devices and} Systems ^LTD Malvern, type ^K 7023) ^for measuring ^{the autocorre-}

lation function of the scattered light intensity. ^The scattering angle ^{was varied from 200 to 1200. The} temperature ^{was held constant to within} ± 0.1 ^°C.

The experimental ^{data were} routinely processed using

the method of ^{cumulants [14-16] to provide} the average

decay ^rate T and the variance V. The latter parameter is a measure of the width of the distribution of decay

rates and is given by :

where f2 is the second moment of the distribution.

In previous papers [3, 4, 7], ^{it was shown that the} intensity scattered from elastic deformations of swollen networks is heterodyned ^{to some extent} by ^{the static} component ^{due to} microscopic heterogeneities. ^The heterodyne ^{ratio can} be checked by measuring ^the

autocorrelation function obtained by mixing ^the

scattered signal ^{with an} extemal oscillator using ^a

Michelson type interferometer.

2. Swelling equilibrium ^and phase diagram ^of polystyrene gels.

^{2.1 1} THEORETICAL PREDICTIONS.

The equilibrium ^{volume fraction} (p,, of a gel ^immersed

in a fluid is given by the condition of zero osmotic pressure. This condition can be derived from Flory’s

mean field theory together ^{with the} packing ^condi-

tion (2) ^{and is} given by [2] :

where cr is the radius of the statistical 5egment ^and V, ^is

the molar volume of the solvent. In the vicinity ^{of the}

« theta » temperature ^the Flory-Huggins interaction parameter x ^can be expanded ^{as a function of the}

T - 03B8

reduced temperature ! ⁼ T e 8 ^{’ according to the}

following relationship :

1/2 - x = t/J! (4)

where § ^{is an} entropy parameter [6].

Eq. (3) ^{reduces to} simpler ^{forms in the two} following limiting ^{cases :}

i) Networks swollen by ^a good solvent of the poly-

meric chains (9, ^« 1)

ii) ^{At the « 0 »} temperature (X

1/2)

Eqs. (5) ^and (6) predict ^{that for both} good ^solvent

and « 0 » regimes, ({Je(N) ’" (p*(N), ^where ({J*(N) ^is

the crossover volume fraction between dilute and semi-dilute regimes ^{for a} solution of macromolecules

having ^N statistical units. From eqs. (5) ^and (6) ^one

obtains the following relationship ^between o,, and 9eF ’

As a matter of fact the phase diagram ^of polymer

solutions ^as derived from Flory’s theory differs from that obtained from the scaling ^law approach, ^as

illustrated in figure ^{1. The} scaling ^law approach [17]

predicts ^{a crossover between a good} solvent and a « 0 » behaviour ^{at a reduced} temperature ^{i -} N - 1/2

Fig. ^1.

^Phase diagram ^{of a} swollen network. The equilibrium

curve q>e(r) ^{and the} spinodal ^curve q>(rs) ^have been calculated from eqs. (3) ^and (14) respectively. The dashed lines represent ^the phase diagram of a polymer ^{solution as} given by the tricritical theory [17].

ln the« () » domain, defined by - N-1/2 ⁱ N-1/2, ({J* ^{must be constant and} equal ^to ({J:. ^For

-r > N - 1/2

ç* ^{varies as -r- 3/5 which is in} good agreement ^with eq. (5).

Neutron scattering experiments ^have provided évidence of the behaviour predicted by ^the scaling

law approach. However, ^{the actual !} dependence ⁱⁿ

the crossover vicinity ^{is not} established, ^{and the curve} ((r) ^as derived from _eq. (3) ^{can be} considered as a

good approximation ^{for the} behaviour of swollen networks in the ^« () » domain.

It is also interesting ^{to consider what} happens ^when

T - N-l/2. For polymer ^{solutions at the concen-}

tration cp: ^{one should} expect ^{a critical} phase separa- tion. On the other hand a gel ^at swelling equilibrium

cannot break _up into two phases. ^{Therefore a further} cooling ^{of the} gel should lead to an increase of _rpe

represented by ^the straight ^line asymptotic ^{to the}

coexistence curves of polymer solutions. Figure ¹

shows that again ^{the curve} ({Je(-r) ^as derived from eq. (3) gives ^a good approximation ^{of the behaviour}

of the swollen gels ^{in this} range of temperatures.

2.2 EXPERIMENTAL RESULTS AND DISCUSSION.

Let us consider first the behaviour of networks swollen in a good ^{diluent. In table II, we have} reported ^the température dependence ^{of the} equilibrium ^volume

fraction of ^a polystyrène ^network prepared by ^anionic

method and swollen in benzène. The rate of increase of the swelling degree ^with température is very small

as expected ^from eq. (5) ^{since the value of 6 for} poly- styrene-benzene systems ^{is far below the} temperature encountered hère [18].

Table II.

Temperature dependence of ^the swelling degree for a polystyrene network swollen by ^benzene.

The sample ^{has been} prepared by ^{anionic block} copo-

lymerization using a precursor polystyrene of molecular weight McRc

⁴³ 500 and 3 molecules of divinyl-

benzene _per living ^end.

We now turn our attention to the case of a network swollen in a poor diluent. In order to draw the dia- gram r«p,) it ^is necessary ^to know the ^« 0 » tempera-

ture of the investigated systems. ^{For the} polystyrene- cyclohexane systems, ^{it is well} known that 0

34.5 °C.

.

Figure ^{2 shows the} (p,,(,r) diagrams ^{for two} polysty-

rene networks prepared by ^radical copolymerization

and swollen in cyclohexane. The full lines represent the curves calculated from _eqs. (3) ^and (4), adjusted

at the theta temperature. ^{The values of ({JeO} required

for this adjustment ^have been obtained from _eq. (7)

where we have used the rpeF values experimentally

determined for networks swollen in benzene and x

0.43 [19]. ^These experimental ^{values have been} reported ^on the calculated curves -r«({Je). ^{The corres-} ponding ^{value of i leads to 0 = - 90} °C. This value

can only be considered as indicative, ^{since it has} been obtained by assuming ^the validity ^of eq. (4),

which is restricted to small values of i.

It can be seen on figure 2 that the experimental

volume fractions of polystyrene-cyclohexane gels

exceed largely the theoretical ones. This result can be

explained ^either by ^{a lack of} validity ^{of the} packing

condition (2) ^{in the «} 0 » domain or by ^a collapse

1034

U. U.2 U.3

Fig. ^2.

Temperature-volume ^{fraction curves for} polystyrene

networks swollen at equilibrium by benzene and cyclohexane. ^The full curves have been calculated from _eq. (3) : ^{te. R} 43, à R 37.

The dashed lines drawn through ^the experimental points ^{have been} arbitrarily extrapolated ^to the calculated curves.

of the elastic chains of the network. The latter possi- bility ^{can be} excluded, ^{since neutron} scattering experiments ^have demonstrated that the elastic chains of polystyrene networks swollen by cyclohexane ^are unperturbed gaussians and that the deswelling ^{of the}

networks with decreasing ^solvent quality ^{is not}

affine in the mesh size of the network [20]. Therefore,

the variation of _pe in the ^« 0 » domain results pri- marily ^{from a mutual} interspersion ^{of the chains.}

There is no available interpretation ^{of this} phenome-

non which has been discussed in more detail recent-

ly [5].

The interspersion degree ^{of a network} swollen in

cyclohexane ^can be estimated from a comparison ^of

the equilibrium ^{volume fraction measured at the 0}

temperature and that calculated under the packing

condition assumption.

Figure ^{3 shows in a} log-log scale the variation of 9,,, for a series of networks as a function of the corres-

ponding equilibrium ^volume fractions in benzene

at 21 °C. On the same figure ^{we have} plotted ^{the curve}

calculated from _eq. (7). Inspection ^{of this} figure ^reveals

that the degree ^of interspersion ^{does not} vary consi-

derably ^{from one} gel ^to another, although ^the para- meters of the crosslinking ^{reaction are} quite ^different (cf. ^Table I).

The degree ^of interspersion ^{which can be charac-}

terized by the ratio between experimental ^{and calcu-}

lated values of _{(Pel is} found equal ^{to 2.8 + 0.5..}

Fig. ^3.

Equilibrium volume fraction in cyclohexane ^{at 34.5 °C}

versus the equilibrium volume fraction in benzene at 21 °C for a

series of networks prepared by ^radical process. The full line has been calculated from _eq. (7). ^The dashed line drawn through ^the experimental points ^{has the same} slope.

3. Light spectroscopy.

3.1 THEORY.

It has been shown both theoretically ^and experimentally

that the correlation function of light scattered from

thermally ^excited longitudinal fluctuations of swollen networks has the form of an exponential decay. ^The decay ^rate for fluctuations of wavevector K is given by :

where Dc ^{is the} cooperative ^{diffusion constant} equal

to the ratio of the longitudinal osmotic elastic modulus

El ^{to the} frictional coefficient 0 of the network in the fluid medium

Two experimental situations have been considered up ^{to now :}

-

The first situation refers to networks swollen

at equilibrium ^{in a} good ^{solvent of the} polymeric

chains. Under such conditions, D, ^can be written as :

where 1 ^{is the} viscosity ^{of the solvent and} RH ^the hydrodynamic ^{radius of the} chains of the network.

Thus, ^the measurement of D, provides direct infor- mation on the mesh size of the network.

The second experimental situation is realized by

cooling suddenly ^a network swollen at equilibrium ^{in a}

good ^{diluent. If the} cooling ^{is fast} enough ^{so that the}

diluent cannot diffuse out of the gel, ^{one observes}

a critical behaviour associated with a phase separation

of the binary mixture of the network and the diluent.

The time correlation function of the concentration fluctuations in the network, ^near phase separation

has been calculated by ^Tanaka using ^{either a mode} coupling theory [10] ^{or the classical} Flory’s theory [9].

In the hydrodynamic regime (Kj « 1) ^{the autocorre-}

lation function decays exponentially in time with a rate constant given by :

where ’1g represents ^the viscosity ^{of the} gel ^{fluid. In}

our investigation the swollen networks ^were washed

continuously to extract the free polymer ^{so that} tlg

must be the viscosity ^{of the solvent.}

The correlation length ÇH (ÇH > RH) represents the distance over which the movements of the unit segments ^are correlated. At a certain temperature T,, which corresponds ^{to a} metastable spinodal tempe-

rature, ÇH diverges. ^{This is} equivalent ^to saying ^that

the longitudinal ^modulus El ^{vanishes at} 7s ^{as can be} ascertained from a comparison ^of eqs. (9) ^and (11).

In the mean field theory ^of Flory, ^the divergence

takes form :

The spinodal temperature T. is defined through ^the

condition

where w is the osmotic pressure of the gel. ^From Flory’s expression ^{of the free} energy and the condi- tion (13) ^{one obtains the} following relationship

between the volume fraction of the gel ^{and the} spinodal

interaction parameter ^X,

The spinodal ^curve representing ç ^{as a} function of Ts - 03B8

Ts = s0 ^{has been plotted on figure 1. In the good}

diluent régime (qJ ^« 1), eq. (14) ^{reduces to :}

The comparison ^of eqs. (5) ^and (15) shows that in the

good ^diluent regime ^the spinodal ^{curve is affine to the} equilibrium ^curve.

However the work reported ^{here refers to a different} experimental ^{situation where} instead of cooling ^the gel at constant volume fraction, ^{one describes the} equilibrium ^{curve. Under these} conditions, ^one should expect ^a smooth variation of 1-IK’ corresponding ^to

the temperature dependence of RH (cf. eq. (10)).

3.2 EXPERIMENTAL RESULTS AND DISCUSSION.

We have measured as a function of temperature ^the autocorrelation function of light scattered from three

polystyrene networks swollen in cyclohexane. ^The

results were as follows :

3.2.1 Shape of ^the autocorrelation function.

Significant departures ^{from the} exponential shape

were observed, contrary ^{to the case of} networks, swollen to the same extent in a good ^diluent.

The relaxation time distribution ^can be characte- rized through ^{the variance which, as mentioned in the} experimental ^{section, reflects the width of the distri-} bution, although ^{it is not} possible ^to give ^a quantita-

tive assessment of the distribution function. The

experimental ^{values of the variance measured at}

différent temperatures ^{for the three} investigated gels

are reported ^{in table} III. It is immediately ^{seen from}

table III that the variance increases when the tempe-

rature is lowered. Moreover, ^{at a} given temperature the variance increases with the crosslink density.

Table III.

Variances ^{as a} function of temperature

for polystyrene ^{networks swollen in} cyclohexane.

Two other important ^features of the autocorrelation function must be underlined.

First, the average decay ^{rate is} proportional ^{to K2}

in the investigated range of scattering angles.

Second, the average decay ^{rate is reduced} by ^{a factor}

of 2 when a reference beam is superposed ^{on the}

scattered intensity ^{on the} photomultiplier. This result

permits ^{us to conclude that the scattered} intensity

from the network concentration fluctuations domi-

nates the scattering from static inhomogeneities ^{of the} gel, contrary ^{to what} is observed in networks swollen

by ^a good ^diluent [3]. ^{In this} regard, ^one may remark that the polymer concentration increases considerably

in passing ^{from a} good ^{diluent to a} poor diluent of the network. This _{may lead} to a better homogeneity

of the gel.

3.2.2 Temperature dependence of ^the decay ^rate.

Figure 4 shows the variations of ri K2 as ^a function of

temperature.

1036

Fig. ^4.

Decay ^rates rjK2 of concentration fluctuations of

polystyrene networks swollen in cyclohexane.

The decay ^rate decreases with temperature ^and appears ^to vanish at a temperature Tc (Tc 0), ^which depends ^{on the} crosslinking degree ^of the networks.

Below Tc ^the gel ^becomes strongly opalescent. ^This opalescent ^{state is} stable with respect ^to time, ^{at least}

on the scale of months.

3.2.3 Hydrodynamic correlation length.

^An apparent hydrodynamic correlation length jh ^{can be}

determined from the decay ^rate by using ^the following relationship :

In the good ^{diluent limit,} light scattering probes respiration ^{modes of the network and} jh ^is equal ^{to the} hydrodynamic ^radius RH of the mesh of the network.

On the other hand, ^{if the} spectrum is dominated by

critical fluctuations, jh differs from RH. Furthermore,

the actual viscosity coefficient involved in _eq. (16)

may be different from that of the _pure solvent since the gels ^are rather concentrated in the theta regime.

However, ^if one assumes in a first approximation

the same temperature dependence ^{for both} coefficients, then jh ^and ÇH ^{will also} exhibit the same temperature

dependences.

The variation of jà ^{versus T, as} determined from ^the

average decay ^{rates in} conjunction ^{with the} tempera-

ture dependence ^{of the} viscosity ^{of the} cyclohexane

are reported ^on figure ^{5. In} the whole temperature range, the correlation length jh ^{of a} given gel ^exceeds largely ^the hydrodynamic ^radius RH ^{of the chains of}

networks swollen to the same extent in a good ^diluent.

For instance jà = ^{200 A for the R} 43-cyclohexane

Fig. ^5.

Temperature dependences ^{of the} apparent hydrodyna-

mic correlation length ^of polystyrene networks swollen by cyclo-

hexane. The dashed lines have been drawn arbitrarily through ^the points.

gel ^{in the} high temperature range whereas RH - ²⁰ A

for the R 35-benzene gel ^of equivalent ^{volume fraction.}

Figure ^{5 reveals also a small but} nevertheless signi-

ficant inflexion of the curve çH(T) ^{in the} temperature range close to the « 0 » temperature. ^{In this} regard

one must take note that this ef’ect occurs in the _range of temperatures ^{where the} change ^{of volume fraction}

due to the interspersion ^{is the more} pronounced.

The observed divergence ^{below the « 0 »} tempera-

ture demonstrates the existence of a critical behaviour which must be associated with a phase separation. ^The

critical temperatures ^{can be} determined from the plots

of H ^{1 versus T} (Fig. 6). ^{In order to} demonstrate the

Fig. ^6.

Plots of the inverse of the apparent hydrodynamic

correlation length ^versus temperature ^for polystyrene ^networks

swollen by cyclohexane. The full lines have been drawn arbitrarily

through ^the points.

temperature dependence ^{of jQ in a} quantitative way

we have represented ⁱⁿ figure ^{7 a} log-log plot ^of ç

versus the reduced tem erature T- T for the net- versus the reduced

p T ^{for the net-}

works R 40 and R 43 swollen in cyclohexane. ^{The data}

relative to both gels ^{fit the same} straight ^{line of} slope 2/3. ^{As for the} gel ^R 35, ^{the data of} figure ^{6 seem to}

indicate that H ¹ varies like T. However, ^{it must be} pointed ^{out that no data are} available for this sample

in the vicinity ^of Tc. Furthermore, ^for T » Tc ^some background contribution _may be significant. ^{To be} complete ^it should be mentioned that the variance associated with the distribution of relaxation times is also roughly ^a unique ^function of (T - Tc)/Tc.

Fig. ^7.

Log-log plot ^{of the} apparent hydrodynamic correlation

length ^{versus reduced} temperature (T - Tc/Tc ^for samples ^{R 43} and R 40. The slope ^{of the} straight ^{line is} 2/3.

The observed behaviour corresponds surprisingly

well to what is expected ^{close to a critical} phase separation. The critical exponent associated with the

slowing ^{down of the} fluctuations is equal ^to 2/3 ^as predicted by ^the theory of critical point singulari-

ties [21]. ^{Moreover the} critical fluctuations are still dominant at temperatures far above the ^« 0 » tempe-

rature (T - Tc ~ 30 °C). ^{Such a} behaviour has also been observed in binary liquid ^mixtures [21].

The above results are in _many respects ^{similar to} those obtained by ^Tanaka [8-12] ⁱⁿ polyacrylamide gels ^{and must} be associated with the same process. In

the latter study, the critical exponent ^was found equal

to 1/2. The différence between this value and our

experimental determination 2/3 may be due to différent

experimental conditions, ^{since in the Tanaka’s} experi-

ments the gels ^{were cooled at a constant volume frac-} tion, contrary ^{to this} study ^{where the} gels ^{were investi-} gated ^at swelling equilibrium. ^{In this} regard ^{one must}

remember that the spinodal ^curve represented ^on figure ^{1 has} been calculated for homogeneous ^close packed ^{networks. It was shown in the first} part ^{of this} paper that the actual polymer concentrations of networks swollen by ^{a theta solvent were much} larger

than the concentrations corresponding ^{to the} packing

condition. The resulting interspersion ^{of the chains}

should favour large concentration fluctuations which would not require any extension of the chains. Fur-

thermore, ^{it is now} well established that swollen networks exhibit generally large swelling ^inhomo- geneities ^{due to non random} crosslinking [22, 23, 3, 4].

This may result in a broadening ^{of the} spinodal ^line

and give ^{rise to} critical fluctuations in a large range of temperatures ^and polymer concentrations.

4. Conclusion.

The results of the present study provide confirmatory ^{evidence of the} analogy ^between

a polystyrene ^{network swollen at} equilibrium ⁱⁿ

benzene and the equivalent polymer ^{solution at the}

crossover concentration, ^{between dilute and semi-} dilute regimes. ^The measurements of swelling equili-

brium of polystyrene ^networks prepared by ^radical copolymerization ^{and swollen in} cyclohexane ^show

that the interspersion ^{of the} elastic chains previously

evidenced in anionically prepared ^{networks at room}

temperature [5] ^is large in the whole temperature range.

The degree of interspersion ^{does not} vary considerably

with the crosslinking degree.

In the ^« 0 » domain the spectrum of scattered light

is dominated by ^{the critical} fluctuations associated with an internal phase separation. ^The slowing ^down

of the fluctuations when the temperature ^of phase separation ^is approached ^is characterized by ^{a critical} exponent equal ^to 2/3, ⁱⁿ agreement with the classical theories of critical phenomena. This behaviour is different from that observed by ^{Tanaka in} polycryla-

mide gels ^{in the} vicinity of the metastable spinodal

temperature. ^{In this} regard, ^{it would be} interesting ^to

compare the temperature dependences ^{of the corre-}

lation length associated with critical fluctuations of a

gel, obtained under equilibrium ^{and non} equilibrium

conditions respectively.

Acknowledgments.

^The authors would like to thank R. Okasha for the preparation ^of the networks.

References

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