Rouse 2D diusion of polymer chains in low density precursor films of polybutadiene melts

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Rouse 2D diusion of polymer chains in low density precursor films of polybutadiene melts

Claire Schune, Marc Yonger, Mohamed Hanafi, Jürgen Thiel, Laurent Guy, Thomas Chaussée, François Lequeux, Hélène Montes, Emilie Verneuil

To cite this version:

Claire Schune, Marc Yonger, Mohamed Hanafi, Jürgen Thiel, Laurent Guy, et al.. Rouse 2D diu- sion of polymer chains in low density precursor films of polybutadiene melts. ACS Macro Letters, Washington, D.C : American Chemical Society, In press, pp.843-848. �10.1021/acsmacrolett.0c00144�.

�hal-02571015v2�

density preursor lms

of polybutadiene melts

Claire Shune,

†

^,

‡

Mar Yonger,

†

^,

‡

Mohamed Hana,

†

Jürgen Thiel,

¶

Laurent Guy,

‡

Thomas Chaussée,

‡

François Lequeux,

†

Hélène Montes,

†

and Emilie Verneuil

∗

^,

†

†

^{Soft Matter Sienes and} Engineering (SIMM), ESPCI Paris, PSL University, Sorbonne Université, CNRS, F-75005 Paris, Frane

‡

^{Solvay Silia, 15 rue Pierre Pays, BP 52, F-69660} Collonges-au-Mont-d'Or, Frane

¶

^{Max-PlankInstitute for Polymer Researh,} Akermannweg 10, D-55128 Mainz,Germany

E-mail: emilie.verneuilespi.fr

Abstrat

Wetookadvantageofpseudo-partialwetting topromotethespreadingofpreursor

lms whose surfae density smoothly deays to zero away from a sessile droplet. By

followingthe spreadingdynamis ofsemi-dilutepreursor lmsofpolybutadienemelts

onsilionwafers,we measuremoleulardiusionoeientsfor dierentmolar masses

and temperatures. For homopolymers, hains follow a thermally ativated 2D Rouse

diusionmehanism,withanativationenergyrevealingpolymersegmentsinterations

with the surfae. This Rouse model is generalized to hains with spei terminal

groups.

Desribing the dynamis of polymer melts near solid surfaes is of great relevane to

mehanis,adhesion, frition orows atinterfaes asthey set the boundary onditions and

the whole dynami response . However, diret information on polymer/substrate inter-

ations an be hallenging to obtain. Indeed, the polymer dynamis at interfaes strongly

ouples polymer/substrate interations and polymer/polymer interations in the bulk 7

. In

order to isolate the polymer/substrate interations, we onduted wetting experiments on

oxidized silion wafers to promote the spreading of sub-moleular thikness polymer lms,

where all the hains are expeted to interat with the surfae. The surfaes and polymer

melts used have a high positive spreading parameter

S = γ s − (γ + γ sl )

^{, with}

γ s

^,

γ

^{, and}

γ _sl

^{the interfaialtensionsofthe solid/air,liquid/airand}solid/liquidinterfaes respetively.

In suh onditions, past experiments 7

demonstrated that a so-alledpreursor lmspreads

aroundsessiledroplets,driven byshortrangeinterationsthrough thegaininsurfaeenergy

S

^{. Its morphology also depends on the longer range} interations 8,9

. As measured by X-

ray,neutron reetivity,X-ray diuse sattering 1013

,ellipsometry 1420

,orinterferometry 21

,

thesepolymer preursorlmsare nanometerthik. Inatheoretialpointofview, restriting

to ases where only long range Vander Waalsinterations and surfae interations were at

play, Brohard-Wyart et al.

8

distinguished two wetting situations on high energy surfaes,

depending on the sign of the Derjaguin pressure

Π

^{in the lm22. If the Derjaguin pressure}

is positive, the long range interations result in an eetive repulsion of the air/polymer

and polymer/substrate interfaes, whih aims to stabilize the wetting preursor lm. This

situation is alled total wetting 23

and was widely observed in the past for various poly-

mers

10 ,1417 ,1719 ,2430 ,3033

. Suh preursor lms exhibit a step-like prole. It is expeted to

be omprised of a near-dense monolayer of moleules, exept at the utmost end of the lm

where the ompatness is gradually lost 16,17

. The preise shape and dynamis of the step

wherehaindensity deaystozeroisbelievedtoontaininformationonthe polymer/surfae

interations but the narrowness of this region inthe ase of total wetting islimiting.

In the present paper we oer to study the wetting of polybutadiene melts on oxidized

silion wafers, whih experiene onjoining interations that tend to squeeze the preursor

lm (

Π < 0

^{): a motionless droplet oexists with the preursor lm. This regime is alled}

pseudo-partial wetting and was evidened for high polarisability polymers . We will

show that depositing polybutadiene droplets onsuh surfaes is away toprepare preursor

lms of low density, whih smoothlydeay overan extended lateral region. We willhara-

terize the preursor lmproles and dynamis by ellipsometryand showthat the hains in

the lm obey a diusion equation. The variations of the diusion oeient with the lm

thikness are extrated from the ellipsometry data and its evolution with the molar mass

will be takled for homopolymers and polymers with spei terminalgroups. In addition,

for homopolymers, the eet of temperature onthe diusion willbe studied and translated

in termsof ativation energy.

Thepolymermeltsusedinthisstudyare1,4-polybutadiene(PBd1,4),hydroxyl-terminated

1,4-polybutadiene(PBd-OH), and1,2-polybutadiene(PBd1,2). Molarmasses

M n

^rangebe-

tween900and40000g/mol 44,45

. Theglasstransitiontemperature

T g

^{ofPBd1,4andPBd-OH}

is lose to

−100

^{C and lose to}

−30

^{C for PBd 1,2. It does not signiantly depend on the}

molarmassintherangetested 44,47

,whihallowstoworkinthe10Cto73Crangewhilebeing

atlargetemperaturedistane to

T _g

^{. Thepreursor lmsspreadingaroundthe dropletswere}

haraterized with an ellipsometri mirosope (EP3, Aurion) using nulling ellipsometry

with590nm wavelengthof10nmbandwith, 65

◦

inideneangle,andveminutestimereso-

lution. Sessiledropletsofradius

r d

^{omprisedbetween}

40

^and

250 µ

^{m,andvolumebelowthe}

nanoliter, were deposited onpiranha leaned 44

oxidized silion wafers,with aninitialoxide

layer thikness

e

^{measured from 2 to 4 nm depending on the wafer used. The} experiments wereperformedinanhermetiellunderaweakowofnitrogen,ataxedrelativehumidity

of 11

%

^{, and at dierent}temperatures. As the siliathikness

e

^{isknown, the polymer on-}

tributionto the optial path shiftan be dedued fromellipsometry measurements and the

loalpolymerthikness

h

^anbedetermined. Thisthiknessisanaveragedthiknessoverthe pixel area of the ellipsometri mirosope, whih is around64

µ

^m

²

^{. The polymer thikness}

h

^{maybesmallerthan amoleularsize and inthat ase the polymer layerisina non-dense}

still an be used 43,48

. Noise redution is ahieved by taking advantage of the quasiirular

shape of the droplets: thiknesses are angularly averaged over 10

◦

angles entered to the

droplet enter. Deposition method,experimental set-up, and data analysis were detailedin

apreviousstudy 43

. Weensured thevolatilityofthe polymer meltsanbenegletedand the

absene of volatile pollutes by heking that nothing transfers to the surfae from a drop

keptslightlyaboveit. Atomiforemirosopyshowed thepreursorlmshavenotexture.

43

The typial spreading of a preursor lm of PBd 1,4 around a sessile droplet of radius

r d ≃ 100 µ

^{m at short times is shown in Fig. 1. A few minutes after the deposition of}

h (nm)

0 2

0.5 1.5 1

100

m

(a) t = 5 min (b) t = 30 min

(c)

d

Figure1: Thikness mapsmeasured by ellipsometryof apreursor lmof PBd 1,4of

M n = 1900

^{g/mol at (a) 5 min and (b) 30 min after the deposition time of the droplet. ()}

Corresponding thikness proles as a funtion of the distane to the droplet edge

r − r d

^,

angularly averaged over a 10

◦

angle entered at the droplet enter. Blak lines: t to

solutions of Eq. 1 with

D ¯ = 1.6 µm ² /

^{s and}

h ¹ = 0.6

^{nm. Silia layer thikness is}

e = 2.2

nm and

T = 20

^C.

the droplet, the ontat line stops while a lm spontaneously spreads around the droplet.

Thislearly indiatesthatPBdexhibits pseudo-partialwettingondition onoxidizedsilion

wafer, whih is onsistent with the literature . As seen in Fig. 1(), the preursor

lmis onnetedto the dropletat aonstant nanometri thikness

h ¹

^{and itsheightprole}

smoothly dereases from

h ¹

^{towards zero. This onstant pinning height at the lm/droplet}

onnetion isalwaysobserved (see SI3 44

)and not orrelated tothe molar mass. It averages

to

h ¹ = 0.6 ± 0.4

^{nm forPBd 1,4. Similarpreursor lmthikness proleswere obtained for}

allPBd 1,4 44

, PBd 1,2 50

and PBd-OH. Remarkably, thikness values stand below both the

Kuhnlength

b = 0.96

^{nm andthe bulkgyrationradius}

R g = 1.67 nm

^{forPBd1900g/mol51.}

It thus raises the question of the polymer density in preursor lms, as pointed out in the

literature

7,10,16,32

.

Followingthe path of Johner and Semenov 52

on onned polymer hains, we derive the

surfae-averaged thikness inthe preursor lm, based on topologialonsiderations in two

ases: (i) when polymer segments overthe entire siliasurfae and (ii) at the dilute limit,

whenthe2Doilsare separatedenoughsothatthey donotinteratwitheahother. Chains

are onsidered as ylinders of length

Nb

^{and diameter}

d

^{, where}

N

^{is the number of Kuhn}

segments per polymer hain, so that the moleular volume writes

V c = Nbπd ² /4

^{. The}

diameter

d

^{an be estimated by balaning}

V _c

^{with the moleularvolume}

V = M _K N/ρN _A

^,

where

M K

^{is the molar mass of the Kuhn segment,}

ρ

^{the density of} polybutadiene, 44

and

N A

^{the Avogadro onstant. We nd}

d = p

4M K /(ρN A bπ) ≃ 0.53

^nm.

In ase (i),the surfae averaged thikness

h d

^{equals the hain volume}

V c

^{divided by the}

projeted area oupied by ahainonthe surfae

S d = Nbd

^yielding

h d = ^π 4 d ∼ 0.45

^{nm for}

PBd. When

h > h d

^{,thelmisdense. When}

h ≤ h d

^{,somesiliasitesareunoupied. Inase}

(ii), many siliasites are unoupied and the projeted area of a hain writes

S ^∗ = πR ² _g, 2 D

^,

R _g, 2 D

^{being the 2D gyration radius. The} surfae-averaged thikness of a 2D oil is then

h ^∗ = V c /S ^∗

^{. It is similar to the overlap} onentration

c ^∗

^{in solution, with the unoupied}

silia sites playing the role of the solvent. When

h < h ^∗

^{, the lm is 2D dilute. Above}

h ^∗

^,

it is 2D semi-dilute and the hains overlap. For polymer hains onned in 2D with some

overlapping allowed, Johner and Semenov theoretially showed that the variation of

R g, 2 D

with

N

^{amounts to a power law with exponent}

ν

^{varying with}

N

^between

1/2

^and

3/4

^:

Rg ² _D = 2bN ^ν

^. Consequently, thikness

h ^∗

^{weakly dereases with}

N

^:

h ^∗ ∼ (d ² /16b)N ^{1−2 ν}

^.

For the mass range of our study, we nd

h ^∗

^{< 0.03 nm, whih is at the detetion limit for}

thiknesses. The preursor lm thiknesses

h

^{measured by} ellipsometry verify

h ^∗ < h < h d

whih indiates that the hains in the preursor lms are in the 2D semi-dilute regime.

Furthermore, at any given time, we observe that, as the distane from the droplet

r − r d

inreases, the thikness

h

^{dereases and vanishes at large distane, whih we interpret as a}

derease in polymer density untilthe lmompletely dilutes.

Our observations on PBd 1,4 show that the pseudo-partial wetting regime drastially

diers fromwhat wasmeasured in theliterature for polymers intotal wetting. In the latter

ase, the ontat line of the droplet ontinuously advanes and the preursor lm exhibits

a step-like prole of quasi-uniform thikness in the nanometer range ending with a sharp

step

10,1418 ,20,24,25,2730

, or in some ases terraed proles 53 56

. Dierent models were devel-

opedtoreovertheexperimentallmproleandtimeevolutionofitslateralextension. Inthe

ase ofasinglestep prole,Joanny and deGennes 57

derived the thikness proleofthe lm

thatthey relatedtoadiusionoeientinhydrodynamiregime

D(h) = −(h ³ /3η).dΠ/dh

^.

In the ase of terraed lms with layers of moleular thikness, de Gennes and Cazabat 58

desribed the evolution with time of the lateralextension of dierentlayers, but this model

only works at suiently long times and fails for single layers and/or semi-dilute or dilute

layers 53,56

. In a preursor lm of vanishing thikness, a hydrodynami desription is not

expeted to be valid: moleules are dilute and at likea two dimensional gas. In that ase,

the theoretial diusion oeient is onstant:

D = kT /ξ

^{, with}

ξ

^{the frition oeient of}

the moleules on the surfae

20 ,53 ,54,56,59

.

Here, none of these theoretial frameworks were used a priori. Instead, in order to

haraterize the spreading dynamis of the polybutadiene hains inour preursor lms, the

∂ t h(r, t) = 1

r ∂ r (rD(h) ∂ r h(r, t))

⁽¹⁾

with

r

^{the distanetothe dropletenter. Fromour} experimentalproles,the apillaryterm

desribed in the literature 6063

was found negligible. The variations of the diusion oe-

ient

D(h)

^{with polymer thikness were reovered by spatially} integrating the experimental thikness proles

h(r, t)

^{between two times separated by a time interval}

∆t

^{26 ,64. We hose}

to onsider the diusion oeient as an average of the diusion oeients measured at

t ¹ = 30

^{min and with}

∆t < t ¹

^{. This value of}

t ¹

^{allows a suient lateral extension of the}

preursor lmfor allmolar masses, so it an be aurately deteted. The value of

∆t

^{is of}

minor inuene. For PBd 1,4, the resulting variations of the diusion oeient with the

Figure2: Evolutionof the diusion oeient

D

^{with thikness}

h

^{for PBd 1,4 at}

T = 20

^C.

From top to bottom:

M n =

^{900, 1900, 5400 and 39100 g/mol. Grey area: thikness region}

where

D

^{isaveraged toobtain}

D ¯

^.

thikness are presented in Fig. 2. Within experimental auray, we see that the diusion

oeient is independent of the polymer thikness for the dierentmolar masses tested. In

the following, we dene

D ¯

^{as the average of}

D(h)

^{in the} semi-dilute regime, for

h

^ranging

between 0.1 nm and

h d

^{. The solution of Eq. 1 with}

D ¯ = 1.6 µ

^m

²

^{/s and the boundary}

onditions

h(r = r d , t) = h ¹ = 0.6

^{nm and}

h(r > r d , t = 0) = 0

^{for a preursor lmof PBd}

1,4 1900 g/mol is suessfully omparedwith the experimental data onFig. 1.

Hene, a thikness independent diusion oeient impliesthe hains dynamisis inde-

pendent of the polymer surfae density even though hains overlap: this suggests hains-

terations. From a theoretial point of view, gas lattie models 7,6569

and simulations at

the mirosopi sale 64 ,7073

have been widely used in the literature to desribe the growth

of moleular lms and predit their density prole. Popesu et al.

73

showed that the lm

density prolemainlydepends on

W ⁰

^{, the strengthof the} inter-hainsattration. From this work, our smooth thikness proles would orrespond to

W ⁰ < 0.4 kT ≃ 2.5 kJ/mol

^{. We}

willseethatthisvalueisnegligiblewithrespettothehain/surfaeinterationswemeasure.

Figure 3 shows that for PBd 1,4 at

20

^{C, the diusion oeient}

D ¯

^{of the polymer}

hains onthe surfae is inversely proportional to the hain length. This result holds above

the 3D bulk entanglement length of the polymer

N _e ^{3 d} = M e /M K = 18

^{51 ,74. When the}

temperature is inreased to

73

^{C, the power law}

D ¯ ∼ N ⁻¹

^{is maintained and the values of}

D ¯

^{are larger. The PBd hains of the preursor lms thus follow a} two-dimensional Rouse

diusion mehanism 51,75

, revealing that they do not enounter obstales or entanglements:

inthe rangeofmolar massestested,the hains dynamisinthe present2D semi-dilutelms

doesnotinvolveanyentanglements. ThisresultisinagreementwiththereenttheoryofLee

etal.

76

,whihpreditsthattheentanglementmassdrastiallyinreaseswithonnement(in

h ⁻³

^{). It alsoagrees with}measurementsofthe mehanialproperties ofultra-thinsuspended

polymer lms.

77,78

The temperaturedependene istestedby tting

D ¯

^{toafritionmodelwithanArrhenius}

equation 26 ,27

:

D(N, T ¯ ) = kT Nξ K

= kT

Nξ K, ∞ e ^{E a /RT}

⁽²⁾

where

ξ K

^{is the frition oeient of a polymer segment on the surfae, whih depends on}

temperature, fritionatinnite temperature

ξ _K, ^∞

^{andativation energy}

E _a

^{. Theativation}

energy orresponds to the energy barrier that polymer Kuhn segments have to overometo

move from one site on the surfae to another. As seen in Fig. 4(a), by plotting

DN/(kT ¯ )

as a funtion of

1/T

^{for PBd 1,4, all the data ollapse on a single master urve, allowing}

10 7 10 9

N N ^3d _e

Figure 3:

D/(kT ¯ )

^{as a funtion of}

N

^{. PBd 1,4: at 20C, at 73C. Lines : t to Eq. 2}

with

E a = 29.7

^{kJ/mol and}

ξ K, ∞ = 10 ^{−15 . 4}

^{kg/s. PBd-OH: at 20C, at 73C. Lines:}

ts to Eq. 3with

ξ _OH ^{20 C} = 10 ^{−8 . 3}

^{kg/s and}

ξ ⁷³ _OH ^C = 10 ^{−10 . 9}

^kg/s.

to extrat a unique ativation energy

E a = 30 ± 5

^{kJ/mol. In Fig. 4(b), the power law}

N ⁻¹

^{is found to be robust when plotting}

De ¯ ^{E a /RT}

^versus

N

^{for all} temperatures. We nd

ξ K, ∞ = 10 ^{−15 . 4±0 . 9} kg/s

^{. At 20C,}

ξ K = 10 ^{−10 . 1±1 . 8} kg/s

^{. ForPBd1,4, the moleulardiusion}

isthusathermallyativatedRousemehanism. ThesurfaeKuhnsegmentativationenergy

E a

^{anbeonvertedintoanequivalentspreadingparameter}

S eq

^{byaountingforthesurfae}

ofaKuhnsegmentontatingsilia,i.e.

b × d

^{. Thisyields}

S eq = E a /(N A bd)

^{andnumerially}

S eq ≃ 100 mJ/m ²

^{. Thishigh valueof}

S eq

^{isonsistent withthe existeneofapreursor lm,}

whihdevelops inthe ase of high energy surfaes 79

.

ForPBd-OHpreursorlms,thediusionoeientvalueswere extratedatathikness

h = 0.2

^{nm. As shown inFig. 3, the variationsof}

D ¯

^{with the hain length forPBd 1,4 and}

PBd-OHoverlapatlarge

N

^{, butthe}

N ⁻¹

^{salingislostatsmall}

N

^{forPBd-OH.Toaount}

for this observation, we note that the frition oeient of hydroxylated terminalsegments

is expeted to be dierent from the homopolymer:

ξ K 6= ξ OH

^{. Assuming additivity of the}

frition oeients, Eq. 2is modied intoEq. 3:

D(N, T ¯ ) = kT

(N − 1)ξ K + ξ OH

(3)

By tting the diusion oeient values of PBd-OH to Eq. 3, we obtain high frition

oeient ratios:

ξ OH /ξ K ∼ 65

^{at 20C and 73C.} Hydroxylated terminal groups thus ex-

47

10 20 36 56 73 T(°C)

(a) (b)

De ^Ea/RT / (kT) (s/kg) D.N / (kT) (s/kg)

10 ¹ N

-1

E _a ^1,2 Ea

1/T (K ^-1 ) x 10 ^-3

Figure4: (a)Redueddiusionoeient

DN/(kT ¯ )

^asafuntionof

1/T

^{. Theblaksymbols}

representthe dierentPBd 1,4hain lengths andorresponds tothose in(b). Hollowwhite

symbolsare forPBd1,2: N=15, N=33. Dashed lines: ts toEq. 2:

E a = 29.7

^kJ/mol

and

ξ K, ∞ = 10 ^{−15 . 4}

^{kg/s for PBd 1,4, and}

E _a ^{1 , 2} = 47.7

^{kJ/mol and}

ξ _K, ^{1 , 2} ∞ = 10 ⁻¹⁷

^{kg/s for}

PBd 1,2. (b)

De ¯ ^{E a /RT} /(kT )

^{as a funtion of}

N

^{allows to ollapse all the data for PBd 1,4}

ona master urve. Blak line: power law with exponent -1. Colorsale: temperature.

periene higher frition on silia. Consequently, the dynamis of a short PBd-OH hain is

slowed down ompared to a PBd 1,4 hain of equivalent length. For long PBd-OH hains,

the Rouse motion of the hains is asymptotiallyreovered (Fig. 3).

For PBd 1,2 the Rouse saling of

D ¯

^with

N ⁻¹

^{holds and the moleular diusion is}

also thermally ativated (Fig. 4). We nd a higher ativation energy than for PBd 1,4:

E _a ^{1 , 2} = 48 ± 5

^{kJ/mol, asobserved inFig. 4(a). At20C,}

ξ _K ^{1 , 2} = 10 ^{−8 . 5±2 . 9} kg/s

^{. The value of}

the surfae ativation energy thus reveals the spei polymer/substrate interations, that

our measurements allow to quantify. A higher surfae ativation energy reets stronger

interationsbetweenthe homopolymersegmentsandthe substrate,whihisthe aseofPBd

1,2 through itsvinyl side groups.

80 ,81

In this paper, we show that polybutadiene melts are observed to be in pseudo-partial

wetting ondition on oxidized silion. Studying the spreading dynamis of subnanometer

thik lms allows to probe polymer/interfae interations. We show that the hain density

hains are mainlyin a2D semi-dilute state inthese lms. From the experimental preursor

lm proles, we extrat the variations of the diusion oeient

D

^{of the polymer hains}

on the surfae, that we nd independent from density. This result suggests littleor no in-

terations inbetween polymer hains of the preursor lms, omparing to polymer/surfae

interations. In addition, we nd that the diusion oeient is inversely proportional to

molar mass, whih is the signature of a two dimensional Rouse diusion. This result holds

for molar masses belowand above bulkentanglement mass, highlighting the non-entangled

statein2Dofthehainsinthepreursorlm. Hene,theRousemehanismatstakeinvolves

the sole fritionof Kuhn segmentswith the siliainterfae. Byvarying thetemperature, we

are able to determine a surfae ativation energy on silia for the Kuhn segment of buta-

diene homopolymers with varied hemistry. A greater surfae ativation energy was found

when vinyl side groups were present, whih reveals greater interations with silia. For

hydroxy-terminated polybutadienes, variations of the diusion oeient with molar mass

were suessfullyaounted for by modelling the hain frition asthe sum of frition oe-

ientsof eah of itsKuhn segment.

http://dx.doi.org/10.1021/asmarolett.000144

This doument is the unedited Author's version of a Submitted Work that was sub-

sequently aepted for publiation in ACS MaroLetters, opyright ©Amerian Chemial

Soiety afterpeer review. To aess the nal editedand published work see:

http://pubs.as.org/artilesonrequest/AOR-PHU2RMYUQAWBBYFEJQ59

Polymer haraterizations, additionalexperimental speiations, and preursor lmthik-

ness proles. Movie: ellipsometriimages for PBD1,2Mn=1650 g/mol.

Referenes

(1) Vogt, B. D. Mehanial and visoelasti properties of onned amorphous polymers.

Journal of Polymer Siene,Part B: PolymerPhysis 2018, 56, 930.

(2) Myshkin, N.; Kovalev,A. Adhesion and surfae fores in polymer tribology. A review.

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