Instability of dilute poly(ethylene-oxide) solutions

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Instability of dilute poly(ethylene-oxide) solutions

Y. Layec, M.-N. Layec-Raphalen

To cite this version:

Y. Layec, M.-N. Layec-Raphalen. Instability of dilute poly(ethylene-oxide) solutions. Journal de

Physique Lettres, Edp sciences, 1983, 44 (3), pp.121-128. �10.1051/jphyslet:01983004403012100�.

�jpa-00232151�

Instability

of

dilute

_{poly(ethylene-oxide)}

solutions

Y.

_Layec

and M.-N.

_{Layec-Raphalen}

Laboratoire

_{d’Hydrodynamique}

_{Moléculaire,} Faculté des _Sciences,

6, avenue Victor Le _Gorgeu, 29283 Brest Cedex, France

(Re~u le 13 _septembre 1982, revise le 16 novembre, uccepte le 13 decembre _{1982 )}

Résumé. 2014 Nous avons étudié par diffusion de la lumière des solutions de

poly(oxyéthylène)

dans

le _{méthanol, l’eau pure} et un _mélange

_{eau-isopropanol.}

En solution

_alcoolique,

le POE est molécu-lairement _dispersé et ne

_présente

_pas d’anomalie de _{comportement.} Dans l’eau, le

_polymère

semble être sous une forme

agrégée

évoluant avec le _temps. Aux _grandes valeurs du vecteur de diffusion K,

la _fréquence

_{caractéristique}

est

_{proportionnelle}

à Kw avec w = 2,95, valeur très _proche de la valeur 3

espérée théoriquement.

Aux faibles valeurs de K, on obtient un coefficient de diffusion évoluant avec

le _temps. Cette évolution

_{s’interprète}

comme un désenchevêtrement des

_agrégats

initiaux. Abstract 2014

Using photon

correlation _spectroscopy we studied dilute solutions of

polyethylene-oxide) in solvents such as _{methanol, pure} water, or, a water _isopropanol mixture. In alcohol the

polymer is _{molecularly dispersed} and the solution is stable over a _period of time. On the other hand, aggregates seem to be _present in water and to be

_{time-dependent.}

For

_high

values of the _scattering

wave vector K the inverse relaxation time is

_proportional

to Kw where w = 2.95 which is in

good

agreement with the

_expected

theoretical value for internal motions of the coil. At the lower K values the diffusion coefficient is found to evolve with time. This evolution is

_interpreted

as a

disentangle-ment of the initial _aggregates. Classification

Physics Abstracts 36.20

1. Introduction. - Some

large

flexible macromolecules have a

_{drag reducing}

_property.

Poly-(ethylene-oxide)

(PEO)

is one such water-soluble

_{polymer largely}

used in turbulent flows

_[1-5].

The

_efficiency

in

_{drag-reduction}

is enhanced

_by

its

_propensity

for

_forming

_aggregates in solution

even at _very low concentrations

_{[6, 7].}

This _property is solvent

_dependent

but,

as far as we

_know,

no _attempt to link this

dependence

to the

_quality

of the solvent has been made. In solvents such

as methanol or

_dioxane,

PEO would be

_{molecularly dispersed [8]}

while

_aggregation

has been

confirmed

by light scattering

[8-10]

electronic

_{microscopy, viscometry [10],}

or

spectroscopic

techniques [ 11 ]

in solvents such as

benzene,

_{dimethylformamide}

or chloroform. Moreover the

situation in pure water could be further

_{complicated by}

the formation of

_complex

structures

through

hydrogen

bounding

and the formation of

_trihydrates

due to the chemical nature of the chain

_[11,

_12].

PEO solutions show a

decreasing efficiency

in

_{drag-reduction}

with

_ageing.

Some authors

[13-16]

think this is more

_likely

to be due to a

physical

mechanism like dissociation or

disen-tanglement

of

_aggregates

than to a chemical

_degradation

of the chain. PEO is a _very efficient

L-122 JOURNAL DE PHYSIQUE - LETTRES

agent when

freshly

put into solution and loses this _property as the solution becomes more and

more «

_{homogeneous »}

_{[17, 18].}

In this _paper we are

_reporting

results of

_photon

correlation _spectroscopy

_experiments

on

dilute PEO solutions over

_periods

as

_long

as two months. We have used a PEO

sample

in _pure

water, pure methanol and an

isopropanol-water

mixture. The evolution of the deduced

relaxa-tion time allows us to decide if the

_polymer

is

_{molecularly dispersed}

or _{not, and} to have an

indi-cation of the real effect of

_isopropanol

on the

_polymer

in the water solution.

2.

_Experimental

_part.

- 2.1 SAMPLE

AND SOLUTIONS. - We used

a commercial PEO with a

molecular

_{weight M w}

= 660

000,

_a

polydispersity M~/M~

= 1.10 _as

given by

the manufacturer

together

with some other characteristics

(Table I).

Water was twice distilled and deionized. Alcohols were

_{of spectroscopic grade}

and used without further

_{purification.}

The

_isopropanol

was mixed with water before

_being

added to the

_polymer.

All the solvents were filtered

through 0.2 J..l

membranes

directly

into the cell under a dust free

bench

Table I. - Molecular characteristics

of

the PEO

_sample

SE 70 as

_given

by

_Toyo

Soda

Manu-fiicturing Co,

Ltd.

_Tokyo,

_Japan.

(a) Low _angle

_light

_{scattering (9} = 5°) in _{water at} 25 °C.

(b)

Obtained _through the

_{equation [32] [11]}

= 3.97 x

10’~M~~cm~/gJ~]

_being

measured in benzene

at 25 ~C with a

capillary

viscometer.

(C) These two last values are obtained

by

GPC in water at 25 °C.

All

_experiments

were

_performed

at 21.5 DC.

As methanol is a bad solvent for PEO at this _temperature

_(the

_{polymer crystallizes}

near

_{19 °C),}

the solutions in this solvent were

_prepared

at 25 °C and then

_slowly

cooled to 21.5 DC. Solutions in water and in the

_{water-isopropanol}

_(90/10)

mixture were clear within 24 hours.

We took

_great

care to avoid

_degradations

of _any sort, either

mechanical,

chemical or bacterial.

Prepared

with filtered solvents and pure

polymer,

the solutions were not filtered and were

_gently

shaken

_only

when _necessary.

_They

were

_kept

in a dark room at a constant

_temperature.

The absence of bacteria in water solutions was verified.

All concentrations were chosen so that we could

_always

consider the solutions as dilute.

In such a solution where interactions can be

_neglected,

macromolecules behave as

independent

coils. The radius of

_gyration

is then related to the molecular

_{weight by R~ ~}

AfB

v

being

an

exponent

dependent

on the

_quality

of the solvent

_lying

between 0.5 in a 0-solvent and 0.6 in

a

_good

_g solvent. The concentration at which molecules

_begin

_g to interact is

C~ ~ 201320132013r,

_NA

NA RG

being Avogadro’s

number. As the

_{proportionality}

constant and

_RG

are

_dependent

on

experi-mental

_parameters

such as the

quality

of the

_solvent,

interactions or the

_{polydispersity,}

this

concentration has to be deduced from

_experimental

results. So we used the estimate of Simha

[19]

where the concentration

_{corresponding}

to

_{incipient overlap}

of

_spherical

coils is

_{c~ ~}

_1/[~]

where

_[17]

is the intrinsic

_viscosity

of the

_polymer.

All our concentrations are of the order of

2.2 THE EXPERIMENTAL TECHNIQUE AND DATA ANALYSIS

_{Quasi-elastic}

_{light scattering}

experiments

were

_performed

in the

_homodyne

mode,

using

a

_photon

correlation _{spectrometer,}

described in full detail elsewhere

_[20].

The

_{single clipped photocount}

autocorrelation function of the scattered

_light

_{C(K, t)}

was obtained

using

a 50 ns ATNE correlator. This unit has 104

channels,

the last four ones

_{being delayed by}

96

At,

thus

_allowing

a

good

determination of the

baseline.

If the diffused electric field is Gaussian

_{C(K, t)}

is related to the

_dynamical

structure factor of the

_polymer

in solution

_by

where a and B are

_parameters

which include

_experimental

features and K is the

_scattering

wave

vector

K ~ = K = 20132013

I I

sin 1,

with n

_being

the refractive index of the

_solvent,

₂₀

the

wave-/to 0 2~

g ~ o

length

of the incident

_light

and 0 the

_scattering

_angle.

If the

_sample

is

_monodisperse

and c ~

c+,

the

_dynamical

structure factor is

_{S(K, t)}

=

S(K, 0)

exp( -

T (K )

t )

and

where

_{F(K) =}

z -1

is the characteristic

_frequency

related to the translation diffusion coefficient

through

[21, 22]

f

is a dimensionless function of x =

KRG;

D is related to the

_hydrodynamic

radius

_RH

_through

the Stokes-Einstein relation for a

_sphere

kB

is the Boltzmann constant, ilo the

viscosity

of the solvent at the absolute

_temperature

T. If x

1,

the structure factor is dominated

_by

the translational motion of well

_separated

chains

RH,

f ’(x) ^_~

1 and

If x >

_1,

local

_properties

are observed and the relaxation time is

_expected

to be

_independent

of M and

_{RG (or}

_RH).

Then the relation

₍₃₎

_gives

us

Now,

if the

_sample

in solution is

_{polydispersed}

_(molecular

_{polydispersity}

or

_aggregates)

then the

dynamical

structure factor and therefore the autocorrelation function are no

_longer

_single

exponentials

but

where

_G’(f)

is the normalized distribution function.

The

_experimental

_points

can be fitted

_by

the method of moments

_{[23]. Expanding}

_{exp( - T t)}

L-124 JOURNAL DE _{PHYSIQUE -} LETTRES

where F =

G(T )

r dF is _an

averaged

time constant which is related to the

_z-averaged

trans-f

_

lational diffusion coefficient

_{by D~}

=

TIK

2.

The

_{moments ~~ _}

(T -

F)’

G(r)

dr characterize the

_{non-exponential}

behaviour of the correlation function. The ratio

_{1l2/ r 2}

is a measure of the

polydispersity

of the

_sample.

But for

_large

_{polydispersities}

or

_broad

distributions the

_analysis

is no

longer

exact

_[24].

So,

as a first _step, we will use in this _paper

~Z/T 2

_only

as a

_{qualitative approach}

to the

_{polydispersity, giving}

us an indication of the width of

G(T)

which is related to the molecular

weight

distribution

_through

r =

DK 2

and D -

RH 1 ~

M - v.

Each

_experimental

curve has been

_least-square

fitted to a

_{single exponential}

_{(Eq. (2))}

and to

a cumulant function

(Eq. (7))

_up to the third moment. The

_quality

of the fit is estimated

_by

the factor

_Q

I i I

8i

being

the deviation of the ith

experimental point

from the calculated value. If

the si

are

ran-domly

distributed,

Q

is

_equal

to one.

3.

_Experimental

results. - 3. 1 SOLUTION

IN METHANOL. - In methanol the

_highest

concen-tration used is 0.54 x

10- 3

_gig.

Whatever theoretical function is used to fit the correlation

function,

RH

is found

_to

be

indepen-dent of the concentration and of

_the

_{scattering angle}

over the full _range studied

_{(30~ 9 135~).}

From the values of

_Q

and

_921T2

_(Table

_II),

it seems clear that the

_{single exponential}

is not

a _very

_good

fit and that our

_{polymer sample}

has some

_{polydispersity}

which is somewhat

larger

than the value

_{given by}

the manufacturer. This _apparent

_discrepancy

could also be due to a

very small amount of

_aggregates

in our solution.

Let us now turn to the radius of

_gyration.

If we take the

_only

Mark-Houwink relation we are

aware of for the PEO-methanol _system

_[25].

and _put it in the

_Flory-Fox

relation

_[26]

we obtain an

_approximate

value for

_RG

Table II. -

Experimental

parameters obtained

_{by fitting}

autocorrelation

_function

- PEO in

Taking 0

= 2.5 x

1023,

_RG

= 315

A

is obtained for _a molecular

weight

of 660000. With

the

_experimental

value

_RH

= 200

A,

the ratio

p =

R~/RH ~

1.58,

which

is,

surprisingly,

in

fairly good

agreement with theoretical

_{predictions [27].}

On the other

hand,

with this value of

_{RG, x}

=

KRG

1 over the entire _range of diffusion

angles

afld there is no contribution of internal motions to the correlation function.

We

_repeatedly

measured the diffusion coefficient at the same concentration over a

period

of about two months. D shows neither

variation,

nor evolution with

time,

thus

_showing

the

_high

stability

of the PEO molecule in methanol. We can conclude that there is

little,

if _any,

aggre-gation

of the PEO in

_methanol,

_confirming

_previous

results

_[8],

and that the molecule is

_quite

stable.

3.2 IN TWICE DISTILLED, DEIONIZED WATER. - The concentration studied

was 0.28 x

10-3

g/g.

For all measurements the fit to

_{equation (7)}

leads to a

_quality

factor

_Q

> 0.75. The

_departure

from the

_{single exponential}

is

_{considerably larger}

than in

methanol,

although decreasing

with time. We can conclude from this that the «

_{polydispersity »}

is

_higher

in water than in methanol.

Figure

1 shows the variation of In

_{(-rK 2)-l}

with In K for the same solution after times

varying

between two

_days

and two months.

Fig.

1. -

(rK 2) --

1

versus K. PEO _M,,,, = 660 000, c = 0.28 _x 10-3

g/g in water.

_Age

of the solution : A 2 _days; 0 9

_{days; >}

18 _days; A 22

_{days; 0}

37

_{days; +}

49

_days.

For the

_higher

K

values, T’~ ~

K "’ where w = 2.94 ± 0.02. In that _range, the z-1 behaviour

is in

_{quite good}

_agreement with the theoretical

_{predictions [21]}

and with

_{previous experimental}

results on

_polystyrene

of very

_high

molecular

_weight

₍₁

to 2 x

10’)

in benzene

_[28]

_(w

= 2.85 ±

0.05)

or in trans-decalin

[29]

(w

=

2.78).

For lower values

_{of K, (rK}

_2)-l

is constant and

_equal

to the translation diffusion coefficient D.

Assuming

that Stokes law is

valid,

we can deduce from the values of D the evolution of

_RH

with

_time,

as

_reported

in table III and

_plotted

in

_figure

2. This evolution is

_correctly

described

by

a relation such as

RH x

= 280

A

_represents the

hydrodynamic

radius

RH

_at the final _state of the solution and

depends solely

on the molecular

weight

of individual molecules.

_{RH 7}

+ #

is the initial state

depending

on the molecular

_weight,

on the concentration c and in all likelihood on the

history

L-126 JOURNAL DE _{PHYSIQUE -} LETTRES

Table III. - Evolution

of

the parameters with time - PEO

in water -

c = 0.28 x

10- 3

_g/g.

Fig.

2. -

RH versus t. Same solution as in

_figure

1.

of the

_polymer.

_y describes the evolution with time and

_depends

on

_M,

c and the nature of the solvent.

The

_Flory-Fox

relation

_together

with one of the Mark-Houwink formulae for PEO in water

_[30]

leads to

_RG

= 430

A

and

RG/RH

= 1.53 for _a

Mw

= 660 000.

These results indicate that the

_degradation

of the PEO with time could

_be,

in

fact,

only

a

dissociation,

the molecular

_weight

of the

_{initial aggregates}

_being

of the order of 2.5 x

106

or more if we assume

_{R~ ~}

M o.6.

It _may be worthwhile

noting

that the solution can be considered

as dilute even with these

_high

molecular

_{weight particles,}

the concentration c

being

of the order

of

_{c~ /3}

in this case.

’

3. 3 IN THE WATER-ISOPROPANOL MIXTURE

_{(90/ 10).}

- The manufacturer recommends the

adding

of small amounts of ethanol or

_isopropanol

in water to _prevent

_{sample degradation.}

We have studied such a

_solution,

10

_%

of

_{isopropanol being}

added to water.

Measurements gave a constant value for r over the entire _range of

_{scattering angles}

and

over a

_{forty days}

_{period, leading}

to

and

In all cases

_Q

> 0.75 and

_{~2ir2 ~}

0.3,

which is

_comparable

with the values obtained for these factors with the solutions in methanol.

It is worthwhile

_noting

that the

_hydrodynamic

radius obtained in this case is _very similar to

the

_limiting

value obtained in _pure water.

_So,

this would tend to _prove that the action of

iso-propanol

is a stabilization of the

_molecule,

the associations which exist in _pure water

_being

hindered.

4. Conclusion. -

Using

a non destructive

technique,

we have shown that alcohols have a

dis-persing

effect on

PEO,

which dissolved in this case into isolated molecules. On the other

_hand,

in

water, aggregates exist

_initially.

The evolution with time is a

_{disentanglement}

of the

_molecules,

mechanical or chemical

_{degradation being}

avoided. The

_ability

to form

_aggregates

_depends

probably

on molecular

weight.

Here we have found that at a

_MW

= 660

000,

the initial

aggre-gates could be formed

_by

about four molecules. However this is

_by

no means

_{contradictory}

with the fact that a

_weight

of 12 x

10’

has been evaluated for the associated form of the PEO

WSR 301

_{(M~ ~}

3 x

106)

in _pure water

_[31],

which _represents

_packs

of about

_fifty

molecules. The

_study

of the

_dependence

on molecular

_weight

and concentration of the dimension of the

aggregates

and of their evolution with time is

_{currently taking place.}

Such a

_phenomenon

could have

_important

_consequences for the mechanical and

_rheological

behaviour of these solutions. For

_example,

the

_efficiency

of PEO in

drag-reduction

may be

enhanced

_by

the _presence of _very

_high

molecular

_weight

structures such as networks in « dilute » solutions

_[17].

The addition

_{of isopropanol}

or methanol as

_suggested

_by

the manufacturer

modi-fies the structure of the

_polymer

in solution and

_changes

the

_{rheological properties}

of the solution and the

_efficiency

of PEO in

_{drag-reduction}

_[18].

The kinetics of

polymer

dissolution is another

_{important technological problem}

which could be related to this

_study.

Acknowledgments.

-

The authors are

_pleased

to _{express their thanks} to

_professor

C. Wolff for valuable discussions and comments. We

_{acknowledge partial}

financial _support from the D.R.E.T.

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