Weight on - CiteSeerX

J.

Phys.

£Yance

II

Influence

Layer

7

(1997)

of Matrix Formed by a (~),

Kilt

F.T.

D.G.

Polymer Richards

(~) and

J.R.P.

Research (~) Interdisciplinary DURHAM, DHI 3LE, UK Division. (~) ISIS Science OXON, OX11 OQZ, UK

(Receiied

January

28

PACS.61.12.Ha

polymer

June

24

Science

1997;

Like Ends

Surface

(~),

Technology,

and

Laboratory,

Appleton

and

Thermodynamics

obtained

Polymer

in

1871

PAGE

Chilton,

accepted

1

University

of

Durham,

fluorosilane

groups, mixed

Didcot,

September 1997)

reflectomety

Deuteropolystyrene

Abstract. the

revised

Macromolecular

PACS.82.65.Dp

Brush Both at

a

Thompson (~~*), Hi. Webster (~)

Centre

1997;

on

Functionalised

Rutherford

Neutron

PACS.61.25.Hq

Weight

Molecular

R.W.

Bucknall

DECEMBER1997.

1871-1891

had

of

has

hydrogenous

surfaces

polymer melts; swelling

solutions; and

interfaces

functionalised

been

molar

relative

a

polymer

of 98

mass

at

10~.

each Thin

end

by

films

of

this

polymer

prepared and the blends annealed to deuteropolymer obtained by was molecular weights of the hydrogenous polystyrene matrix range of a polystyrene was preferentially located at the air-polymer has been used. In all cases the deutero far greater than that for unfunctionalised deutero polystyrene interface which extent to an was the surface depth profiles obtained, the surface hydrogenous From in the matrices. near same of the end functionalised deuteropolystyrene rich surface volume and thickness fraction excess, of end obtained function of the functionalised layer have been equilibrium concentration as a These have been compared with the predictions of scaling thedeuteropolystyrene. parameters surface layer thickness attached surface. The and brush like layers of polymers to a ory for fraction surface layer display brush behaviour which is not volume of the stretched wet average expected for end functionalised polymers on the basis of the molecular weights explored. The significantly higher than the average value is dispossibility that local grafting densities are field cussed. The shape of the surface depth profile has been fitted using a self consistent near fluorosilane the only adjustable theory using the "sticking energy" of the parameter. groups as surface fracreasonable quality were obtained and using this sticking the volume Fits of energy unfunctionalised

with

equilibrium at 413 K. The reflectometry and neutron

tions

and

(*)

@

distribution

surface

Good

normalised

surface

molar

of the

hydrogenous

matrix

for

iditions

correspondence

de

Physique

have

end

been

functionalised

have been parameters between surface agreement

between

mass

of the

calculated

excess

agreement

Author

Les

normalised

experimentally.

obtained

polystyrene

x

excess

values

volume

becomes

increases.

(e-mail: r.w.richardsfldurham.ac.uk)

1997

and

fractions

increasingly

compared is worse

with

obtained, as

the

those but

the

relative

JOURNAL

1872

DE

PHYSIQUE

II

N°12

Introduction

Attachment in

the

Steric are

two

of

polymers

polymer

chain

stabilisation such

areas

of

are

to

surfaces distant

particulate

which

have

or

from

interfaces the

under

interface

conditions

is of

where

importance

in

dispersions and the stabilisation been intensively studied for many years. adhesion [2,3j is also highly relevant are colloidal

the

majority of

many

of More

situations

units

[lj.

droplets subjects recent usq of copoly-

emulsion

polymer attachment and the compatibilisers of immiscible homopolymers [4-6j. Although each of these areas has mers as been discussed from their particular viewpoint, each has a major factor in common, the I.e. attached polymer forms a "brush like" layer at the surface or interface. A polymer brush is defined the layer formed by the attachment of polymer molecules by one anchoring point as (generally at one end of the molecule) to a surface or interface. Beginning with the seminal Alexander [7] and de Gennes [8] much has been paid to such brush layers attention papers by both experimentally and theoretically. Clearly the ability of the anchoring group to function effectively is paramount, however the of the surrounding by which the brush matrix nature molecules also influences surrounded the arrangement the polymer segments adopt in the are brush layer. The scaling description developed by de Gennes [8] is particularly transparent in setting influence of surrounding and areal density ii. e. of molecules matrix number unit out the per of interface) of attached grafted molecules the of the molecules from extension area or on the plane of Subsequently, analytical expressions have been developed for the attachment. distribution of segments normal to the interface molecular when low weight solvents constitute the surrounding matrix [9]. Scaling law descriptions were preceded by the Self Consistent Field (SCF) approach developed by Scheutjens and Fleer [1,10,11]. The major difference (apart from numerical exactness) from the scaling laws is that there is no a priori profile assumption of the shape of the concentration of polymer normal to the grafted surface, this is determined by the various contributions to Although such SCF the free calculations be computationally intensive, they have energy. can been brought to a high degree of sophistication and a notable extension to grafted polymers surrounded by a polymeric matrix has been made by Shull [12]. The studies of polymer brushes majority of experimental have been polymer made on molecules grafted to solid substrates [13-22] (generally silicon or mica). A significant amount of the published work has dealt with the results from the force force-distance balance where the obtained has been compared with that predicted by the various theories [23-29]. A parcurve ticularly relevant study was carried out using small angle neutron scattering on porous silica containing grafted polymer [30] ~,hich followed closely on earlier work where polymer stabilised colloidal dispersions were used [31, 32]. Notwithstanding the pertinence of such results to "real" situations, it is evident that the of the profile of polymer normal to extraction concentration the surface is by no straight forward. means Where the grafted surface is planar, the number of applicable techniques multiplies and in the data be analysed easily. Ellipsometry, ATR FTIR and neutron and some cases can more X-ray reflectometry [33, 34] may all be and have been applied to solid or liquid surfaces. Ion (e.g. Forward Recoil Spectrometry (FRES) and Nuclear Analysis beam methods Reaction (NRA) being high vacuum methods be applied to solid samples [20,35] and in this respect can Determination techniques of SIMS and XPS. of volume fraction similar to the "classical" are profiles of adsorbed or grafted polymer melts in amorphous matrices has generally been done Reflectometry (NR) methods. The majority of such by either ion beam analysis or Neutron interface, only two are substrate-polymer concerned with grafting at the solid describe studies Clarke et al. [17] have used the widest equilibrium grafting at the air-polymer interface. range where

such

BRUSH

N°12

LAYER

OF

FUNCTIONALISED

POLYMER

AT

EACH

END

1873

molecular weights in their investigation of the effect of matrix weight on the layer profile. However only one grafting density, a, was used and they point out that the ungrafted polymer is in conditions used do not correspond to equilibrium grafting, I-ewhere Indeed, Liu et al. [21j suggest that at the grafting density equilibrium with the bulk mixture. from ideal used, the grafted chains must be distorted Nonetheless, these results statistics. showed highly grafted the polymer finite that in these had volume matrix systems, a even fraction surface. at the grafted volume discussed the near surface fraction depth profiles obtained In an earlier paper [36] we for a fluorosilane terminated deutero-polystyrene mixed hydrogenous polystyrene. with The molecular

of

brush

fluorosilane

forces

group results

attachment

air-polymer

the

at

interface

because

of its

low

surface

theory. We discuss here the energy were of deuteropolystyrene and the role influence of placing fluorosilane both ends the at groups Throughout the following of the molecular weight of the hydrogenous polystyrene matrix. interface and only equilibrium grafting is discussed discussion, grafting is to the air-polymer from the self field analysis are values and hence "sticking energies" extracted consistent true oftheoretical rather "forced" predictions with data in the absence than values to give agreement of equilibrium grafting. and

discussed

in

of self

terms

consistent

field

Background

Theoretical

scaling law predictions for the thickness of the grafted layer and follow of the self description field approach. consistent a The scaling analysis considers grafted polymer molecules with a statistical step length, a, and degree of polymerisation, N, the tails of which are in with surrounding "solvent" of contact behaviour defined in terms of the grafting degree of polymerisation, P. Regimes of different are pervaded by the individual grafted molecules density, a. When this is low and the volumes The grafted molecules viewed as chains have ideal do not overlap, the grafted statistics. are mushroom being N~/2a, this is also the thickness, h, mushroom like regions, the radius of the defines this region is a < N~~ Above this value of a of the layer. The limit to a which upper stretch and the layer thickness molecules begin to overlap but initially they do not the grafted PN~~/~ is still the ideal value of N~/2a. This region is defined by an upper grafting density of volume P~ ~/~) even though the excluded interactions For higher grafting densities (up to a have screened polymeric matrix, the molecules molecules between the grafted out by the are As the grafting density of the need to satisfy space filling stretch because requirements. to increasingly expelled from the region occupied chains become approaches 1, then the matrix the "dry" brush by brush layers. In this regime it is anticipated that the brush layer thickness We

outline

here

this

with

brief

the

=

is

m~

Naa.

The

ii)

0


~'~ 50

O

OO

150

/~

Depth Fig. PSH

of

fraction

Volume

4.

relative

molar

profiles

mass

1.075

obtained M.

~c~

fitting

from

values

are

a)

to

0.297

200

250

neutron

b)

0.15

300

reflectometry

c)

0.09

d)

data

for

DPSF2

in

0.049.

of DPS in the three highest should be small. Mixtures molecular weight PSH polymers 20% /w. made, DPS The the highest probability of the being with mixture content were circa w surface molecular weight was 1.075 M and segregation being evident was that where the matrix volume fraction profiles obtained compared in Figure 5 to those for DPSF2 containing the are approximately the same composition. Evidently, DPSF2 is adsorbed to a mixtures at average fluorosilane end groups and significantly higher extent and this can only be attributable to the interface. Furthermore. conclude the polymer attached by ends air-polymer that is its the to we only clearly SIMS and XPS functionalised end earlier experiments [41j on a polymer at one groups

show

that

there

is

an

excess

concentration

of

fluorine

atoms

at

the

surface.

adsorption isotherms (z~ f(~o~) in Figure 6 have a marked molecular weight dependence, although in all cases the general behaviour initial in z~ which is the increase same, i.e. an rapidly approaches a plateau value. This behaviour is predicted by self consistent field theory, below. Somewhat behaviour dependence of ~s on ~o~ (Fig. 7). similar is shown for the see Although there is no evidence of a plateau value being approached for these data, a marked dependence on the molecular weight of the PSH matrix is also evident and again this behaviour field theory which we discuss fully below. is predicted by self consistent more The

Discussion

particular molecular weight matrix the volume fraction profiles show the same general a qualitative shape as the equilibrium volume fraction increases (Fig. 4). Similarly, when approxof DPSF2 is present in each of the PSH matrixes, the imately equal equilibrium concentration (Fig. 5). However, when volume fraction profiles for profiles again have the same characteristics similar surface values compared, that for DPSF2 in the lowest molar mass PSH the are excess matrix (52 K) is evidently different, Figure 8. Thus we may be in a regime where expulsion of polymer from the brush layer is not so strong and the the matrix of the brush layer nature For

JOURNAL

1880

PHYSIQUE

DE

N°12

II

1.O a ~

~ O-B oJ

Z

c

~ °

O.6

c

o

r

(

O.4

~

Q~

rm=

~

~~~~,

",-

O.2

~ >

~~

~°

~'~°

De/th

~~~

(approximately) Fig. 5. Volume fraction profiles of DPSF2 and DPS at the unfunctionalised same a) 1.075 X 10~, b) 330 X 10~, equilibrium volume fraction. Relative molar of PSH matrices masses unfunctionalised DPS in PSH c) 106 X 10~, d) 52 X 10~. Dashed lines pertain to of relative matrices 10~. 10~ molar and 330 10~, 106 1.075 X X masses, X 80 o A

+ ~

60

ASH ASH ASH ~~~

°

~

~ t~

/ o


then

grafting density located at the surface, The

we

values

h

~K

a°

(10)

~~

layer and the DPSF2 surface volume fraction logarithmic plot of Figure 10. Note that even for the highest PSH matrix and for the highest concentration of DPSF2 in the the mixture, volume fraction reaches unity, the maximum is hence 0.8 and average never complete expulsion of the matrix polymer from the adsorbed layer does not take place. For the DPSF2 volume fraction the scaling relation observed is average The

have

volume

average

linear

a

fraction

of

dependence on molecular weight

a

in

DPSF2 the

the

in

double

rw

~AV Whereas

for

the

surface

volume

fraction

the

excess

polymer

in

the

near

a~'~~~~'~~

(II)

have

we

~s Since

lK

~K

a°

~~*°.°~

profile expressed

surface

by: ~~

/~ ~ AV

and z

~

~

Na'

(12) in

volume

fraction

terms

is

given

BRUSH

N°12

LAYER

OF

FUNCTIONALISED

POLYMER

AT

EACH

END

1883

O° O A

+ x

PSH PSH PSH PSH

MW MW MW MW

1.075M 330K 100K 52K

~

lO~' lO~~

lO~~

(a)

~

lO° O A

+ x

PSH PSH PSH PSH

1.075M 330K 100K 52K

MW MW MW MW

°

~

04 ~

~

~

a

lO~~

lO~~

lO~~

(b) Surface Fig. 10. grafting density. For

°

fraction

volume

both

plots

the

(a) solid

and line

average is the

layer

brush linear

least

volume squares

(b)

fraction fit

to

the

as

a

function

of

data.

then Naa

~AV For

stretched

the

wet

brush

regime, h

~K

~

~Av which

data

agrees

do

confidence.

not

exactly display

with any

the scaling dependence

~K

observed on

j'

aQ~ (Eq. (3));

P,

the

a~/~ for

the

matrix

(13) experimental

data,

molar

that

mass,

equation we

can

(II). discern

Our with

JOURNAL

1884

DE

PHYSIQUE

N°12

II

.o ~

~ O-B ~J

2 ~ ~

0.6

c

-_

)

,

',

0.4

~

'

',

~

',

~

'---_

0.2

~

Z

~'~0

2

3

4

z/R~ Fig.

Volume

ii.

tionalised

at

profiles

fraction end

one

under

equilibrium

Self

Consistent

and for

conditions

obtained

from

both

ends

at

equal

normalised

neutron

reflectometry

(solid line) surface

blended

for with

deuteropolystyrene funchydrogenous polystyrene

excess.

Analysis

Field

A detailed description of the SCF theory for the dry brush, I.e. polymer brushes surrounded by matrix polymer of equal degree of polymerisation was first developed by Shull [12j, more has been extended recently the where there is a from wet situations transition treatment to dry brush characteristics It is this establish the of the appropriate point at to nature to [42]. interface attachment of the DPSF2 to the air-polymer since although both ends of the polymer interface affinity for this why both should have there is no a priori attach thus reason an forming some sort of looped configuration. Shull has discussed the volume fraction profiles of demonstrates polymers attached by one (tail configuration) or both ends and he [43j that loop profile than tail configurations. This has to be configurations produce a comparison narrower /Rg). of equal normalised surface of conditions polymer In Figure 11 we made under (z~ excess profiles for DPSF2 in PS and for a mixture containing deuteropolystyrene fraction plot volume surface with the same fluoro silane the normalised group at one end only. For both cases excess fraction profile for the DPSF2 0.56. Clearly the volume containing blend is much is narrower that for the single end functionalised polymer and thus the dominant configurations of than molecules both DPSF2 those with ends the air-polymer interface. We acknowledge the at are of DPS there is a small probability that the adsorption due that is in the to segments some molecule indicated by the volume fraction profiles in Figure and middle of the the z~ 5 as rw

values

in

explicitly at so

the that

lattice

6 to must

for

for

II

Table

polymer are adsorption

10

be

of the

surface

smaller

small.

polymer

polymer kBTfl is the

air

unfunctionalised times

with

an

net

free

region.

those

However

for

DPSF2

the

values and

their

of z~

for

contribution

unfunctionalised to

the

total

subsequent discussion using the SCF analysis is adsorbing moiety at each end with both of them being located An quantity is the adsorption important parameter, fl, defined when the adsorbing end is confined decrease to the first energy between adsorption parameter is related to the difference This

Because

interface.

DPS.

than of this

all

BRUSH

N°12

LAYER

8

OF

POLYMER

FUNCTIONALISED

O

o

A

+ x

PSH PSH PSH PSH

EACH

AT

END

1885

100K 0.3 100K 0.05 52K 0.05 52K

0.2

c

.° 0.6 ~$ o

t

1~'~

o

o

~

~

2

o

>

°

o

o

0.2

~'~0

2

3

4

6

5

z/R~ Fig.

12.

data

for

each

is

Fit

of self

PSH

two

consistent

theory

field

calculated

matrices.

Relative

molar

parameter

of the

functionalised

mass

of each

volume matrix

fraction

and

the

profile (line) volume

to

fraction

experimental of

DPSF2

in

noted.

the

interaction

(x))

such

end

with

the

surface

(x()

and

with

the

bulk

that; fl

=

(X$

X$) + I-I

In(a/Rg).

(14)

Equation (14) was originally derived for polymer molecules with one sticky end, and not withconfinement standing the fact that the will be different for polymers with two sticky ends, term alteration Within this equation is applicable without discussed here [44j. to the polymers being x() is adjustable and exhibits significant control on the form of the volthe SCF theory, (x) fraction profile normal to the surface or calculated by interface. Volume fraction profiles ume least fitted to the the SCF theory for polymers with two sticky ends non-linearly squares were x(). Typical fits are shown in Figure 12 experimentally obtained profiles by adjusting (x) x() which resulted for the DPSF2 degree of polymerisation was and the value of (x) average 3.8 ~ 0.I and the value of fl which results is circa 1.05. Figure 12 exhibits the charactersame which have been for other SCF profile generally istics observed the the I.e. systems, crosses of the and than experimental volexperimental points is usually somewhat broader the curve fraction fraction profile. The surface volume calculation is in good obtained from the SCF ume Clarke [17j suggested that the broadening of the SCF due agreement with the data. was curves combination chain of using average and the large perturbation of the real chain statistics to a by the surface to which polymers were A further statistics adsorbed. confirmation of looped configurations of DPSF2 dominating is shown in Figures 13 where the results of attempting to fit the experimental volume fraction profiles with both one and two end functionalised solutions those than equations are shown. Clearly the single end fits are considerably to the SCF worse for a molecule attached by both ends. Figure 14 shows a comparison of the surface volume fraction of DPSF2 from the reflectometry data compared with the SCF theory calcuobtained values and the two sets of values are qualitatively in agreement in their lated variation with ~ and their magnitude although absolute These also apply agreement is not obtained. comments

1886

comparison

the

to

tween

normalised

of

experimental

and

self

JOURNAL

DE

surface

excess

field

consistent

weight. We

PHYSIQUE

values

II

Figure

as

values

calculated

N°12

15

shows, the

disparity

z~/Rg becoming

of

greater

bewith

experimental ii?] that observed Clarke al. for similar in their behaviour by carboxylic et to very However, no comacid terminated polystyrene grafted to the native oxide layer of silicon. values from SCF theory weJ.e made, and consequently we parisons with surface cannot excess with both ends functionalised whether the trend observed here polymers is unique to say or field approach due to increased configurational symptomatic of failures in the self consistent

increasing profiles are

molecular

matrix

distortion

in

PSH

the

of

matrices

remarked

higher

that

earlier

weight.

molecular

could

It

and

calculated

the

argued

be

the

that

self

used here, and that molecule inappropriate for the DPSF2 more relevant models of SIMS reflectivity data for exist. In comparison and recent neutron may a carboxylic acid terminated polystyrene and linear di and triblock copolymers of vinyl pyridine different and polystyrene, Liu et al. [21j compared many models concluded that and one no model produced profiles which were in markedly better data than any with other agreement model. what their However results do show is the screening of excluded volume interactions in the bulk melt is equally boundary such as a wall or operational in the region of a perturbing field

consistent

calculation

is

surface.

possibility

relatively large fluorosilane aggregate in the surface plane. groups of higher local grafting regions much density, a, than the average case we above and As calculated much lower. the values regions where is consequence average some a a that for a dry brush and an undeformed brush height may be somewhere between stretched brush, leading to the apparent behaviour stretched brush. In rebuttal of this point wet as a fluorosilane less bulky than of the short blocks used it can be said that the are groups some studies of Moreover, small angle anchors other brush behaviour in in [21j. separate neutron as of DPSF2 and PSH we have evidence of scattering experiments on micelle mixtures no seen formation, the radius of gyration was that of unperturbed the polystyrene composition over Consequently, we are of the opinion that surface aggregation of range 5 < c/(i~w/w) < 20. fluorinated groups is negligible. A

that

is

dependence

The

heights

height

brush

of the

on

unexpected

is

a

Klein

literature.

the

in

weights of

molecular

matrix

in

have

reported

comparisons

such

the

could

this

In

and

9000

330

regrettably

and

there

are

other

few

al. [45j used NRA to determine molecular weight 000. In the lower

brush

et

matrix

anticipated because the brush was swollen by the lower was as a a molecular weight matrix an exponent of 0.54 was molecular weight matrix. For the higher the brush being in a transition interpreted being due region from obtained which to was as a) (where dependence stretched there is of h the the screened swollen region to no on non a). From values of h and a reported by Kramer et al. [lsj, for a polystyrene dry brush (h (molecular weight 250 000) end capped with a few segments of polybutadiene surrounded by a PSH with a molecular weight of 575 000 an exponent of 0.6 was obtained, significantly matrix exponent

of 0.33

obtained

rw

different

either

from

the

screened

stretched

or

although the values of h in Table loop configurations the relevant Rg value attached of polymerisation of N/2 by one

is

h

m

3Rg/2

in

Table

Very recently

high excess

and

low

(z~/Rg)

are

Gs

One

cases.

Rg

should

be

that

end.

In

this

point

DPSF2, of polymer

of

case

the

that

because

Rg

be

may

of

the

molecules is

with 60

circa

I

germane

dominant

degree

a

and

thus

II.

Shull

[42] has

molecular are

brush

II

that

weight

obtained

for

extended matrices the

wet

the

SCF

calculation

and

distinctive

brush

and

dry

the

to

relations brush

region

crossover

for

regimes.

the For

normalised wet

brush

between surface

regime

BRUSH

N°12

LAYER

OF

POLYMER

FUNCTIONALISED

AT

EACH

END

1887

~

©

~0. ? ~ o C

o

4

~l O

©

E

O

O-I

~

O ~

?

°

°

>

0

2

3

4

5

3

4

5

Z/R~

j~) 0.8 ~

©

E

£

O-G

~ o C

.°

0.4

t a

~l ~

o

0.2

~

o

~

o

>

~'~0

2

Z/Rq

jb) I-o ~

~ ©

0.8

? ~

°

0.6

c

o W o

p

0.4

uo

~

o

E

°

°

~

o

>

0

2

3

Fig. 13. "sticky" of

molar

Attempted ends mass

to

the

106

fit

volume X

10~.

5

4

z/R~

C

of

SCF fraction

Equilibrium

equations

profiles bulk

for

polymers

obtained volume

for

with

DPSF2

fractions

of

and

one

in

a

DPSF2

hydrogenous are

two

(solid line)

polystyrene

a) 0.08; b)

0.165:

matrix

c)

0.24.

JOURNAL

1888

PHYSIQUE

DE

II

N°12

.o O O

O-B x

+

0.6 o

x

~~~ ~~~~

~'~0.0

Experimental

14.

(solid lines) using

self

values consistent

O-I

field

O.3

O.2

surface

of

52K

PSH

x

Fig.

1.075M

PSH

O

0.2

p~

DPSF2

volume

fraction

theory

with

of

sticking

a

DA

compared

DPSF2

of1.05

energy

with

those

calculated

kBT.

.o

o

~

O-B n

n

a

af0.6

~

~

~

*~

n

O

x

A

O.2

+ x

~'~O.O

Fig. to

Normalised

15.

experimental

with XP polymer