Glass transition and alpha-relaxation dynamics of thin films of labeled polystyrene

0.49 MB·English

by  Rodney D. Priestley

APS/123-QED
Glass transition and alpha-relaxation dynamics of thin films of labeled polystyrene
Rodney D. Priestley, Linda J. Broadbelt, and John M. Torkelson∗
Department of Chemical and Biological Engineering Northwestern University, Evanston, IL 60208-3120, USA
Koji Fukao†
Department of Macromolecular Science and Engineering,
Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan
(Dated: February 2, 2008)
Theglass transition temperatureand relaxation dynamicsofthesegmental motionsof thinfilms
of polystyrene labeled with a dye, 4-[N-ethyl-N-(hydroxyethyl)]amino-4-nitraozobenzene (Disperse
8 Red 1, DR1) are investigated using dielectric measurements. The dielectric relaxation strength of
0 theDR1-labeledpolystyreneisapproximately65timeslargerthanthatoftheunlabeledpolystyrene
0
above the glass transition, while there is almost no difference between them below the glass tran-
2
sition. The glass transition temperature of the DR1-labeled polystyrene can be determined as a

n crossovertemperatureatwhichthetemperaturecoefficientoftheelectriccapacitancechangesfrom
a the value of the glassy state to that of the liquid state. The glass transition temperature of the
J DR1-labeledpolystyrenedecreaseswithdecreasingfilmthicknessinareasonablysimilarmannerto

5 thatoftheunlabeled polystyrenethinfilms. Thedielectric relaxation spectrumoftheDR1-labeled
polystyreneisalso investigated. Asthicknessdecreases, theα-relaxation timebecomes smaller and

] the distribution of the α-relaxation times becomes broader. These results show that thin films
t
f of DR1-labeled polystyrene are a suitable system for investigating confinement effects of the glass
o transition dynamics using dielectric relaxation spectroscopy.
s
.
t PACSnumbers: 71.55.Jv;81.05.Lg;77.22.Ch
a
m
- I. INTRODUCTION standing films of polystyrene (PS) [13, 14].
d
The dynamics of thin polymer films have been in-
n
o In recent years,intensive studies on the dynamics and vestigated by many experimental methods such as dy-
c theglasstransitioninconfinedsystemshavebeenunder- namic light scattering [15], dielectric relaxation spec-
[ takentoelucidatethenatureoftheglasstransition[1,2]. troscopy [16, 17, 18, 19, 20], dynamic mechanical mea-

1 The most promising scenario for the mechanism of the surement [21], second harmonic generation (SHG) [22],
v glass transition is based on the Adam-Gibbs theory, in and so on. In accordance with the decrease in Tg, the
0 whichalengthscalecharacteristicofthedynamicsassoci- dynamics of the α-process, which are directly associated
9 atedwithstructuralrelaxationincreaseswithdecreasing with the glass transition, become faster with decreasing
7 temperature from the liquid state to the glassy state [3]. film thickness. In previous studies by Fukao et al., di-
0 A major motivation for studies on the glass transition electric relaxation spectroscopy was applied to the in-
.
1 inaconfinedgeometrywasto measurethe characteristic vestigation of the dynamics of ultrathin polymer films
0 length scale directly using different experimental tech- andprovidedmuchinformationaboutthe relaxationdy-
8 niques [4, 5]. namics of the α-process, the β-process and the normal
0 mode in the case of polystyrene [16, 17, 23], poly(vinyl
Polymerthinfilmsareoneoftheidealconfinedsystems
:
v for such investigations because the system size, i.e., film acetate)[24],poly(methylmethacrylate)[24,25],andcis-
i poly(isoprene) [25]. Although the glass transition and
X thickness, can be easily controlled experimentally. For
dynamics of thin films of polystyrene have been inves-
this reason, many investigations were conducted on thin
r
tigated intensively, it is very difficult to obtain the di-
a polymer films with various film thickness to measure the
electric loss signal of the α-process due to the very low
glasstransitiontemperature(T )andthedynamicsofthe
g
polarity of polystyrene.
α-process,whichcorrespondstothestructuralrelaxation
The above studies on the dynamics of thin polymer
and is related to the cooperative segmental motion of
polymerchains. Forthin films supportedona substrate, films are mainly related to the average Tg and the aver-
many experimental results show that T decreases with age relaxation time of the α-process. However, it has
g
decreasing film thickness if there is no strong attractive been expected that there is a distribution or a posi-
interaction, although there have been some conflicting tional dependence of Tg and the relaxation time of the
experimentalresults[6, 7,8,9, 10,11,12]. Inparticular, α-process within polymer thin films, especially thin sup-
a very large decrease in T has been reported in freely- ported films. Ellison and Torkelson prepared multilayer
g
films of labeled and unlabeled polystyrene and success-
fullyshowedthatthereisalargedifferenceinT between
g
the regions near the free surface and near the substrate
∗Correspondingauthor: [email protected] using fluorescence measurements [26]. The Tg of a 14-
†Correspondingauthor: [email protected] nm-thick layer at the free surface is 32 K lower than the
2
bulk T , while T near the substrate is equal to the bulk deposited glass substrate. Film thickness is controlled
g g
T . It may be expected that analogous studies involving by changing the concentration of the solution and spin
g
dielectric measurements of multilayer polystyrene films speedofthespin-coater. Thethinfilmsobtainedbyspin-
can reveal the distributions of the dynamics within thin coating are annealed in vacuo for 48 hr at 303 K. After
film layers, which are consistent with the distribution of annealing, Al is vacuum-deposited onto the thin films to
T . However,suchstudies have not been previously con- serve as an upper electrode. Vacuum deposition of Al
g
ducted because no one had developed a system in which might increase the temperature of thin polymer films lo-
only one layerof a multilayerfilmis dielectricallyactive. cally. However, no dewetting of the polymer films are
As for the use of guest dipoles to enhance the dielec- observedduringthe vacuumdepositionofAl. Therefore,
tric response of a weak polar material, there are several the local heating of thin polymer films by vacuum depo-
reports in the literature [27, 28, 29, 30, 31, 32, 33]. sition, if any, would not affect the present experimental
Thus, it has been previously established that the incor- results. The thickness of the Al electrode is controlled
poration of guest dipoles into a non-polar polymer is a to be 40 nm, which is monitored by a quartz oscillator,
useful method to enhance its dielectric strength. In this andthe effectiveareaofthe electrodeS is8.0mm2. The
study, we investigate the dielectric properties of single thickness d of PS-DR1 is evaluated from the electric ca-
layerfilmsofpolystyrenelabeledwithanonlinearoptical pacitance after calibration with the absolute thickness
dyeDR1withvariousfilmthicknessesandcomparethem measured by an atomic force microscope.
withthosepreviouslyobservedforunlabeledpolystyrene Dielectric measurements are performed using an LCR
in order to discuss the possibility of position-dependent meter (HP4284A) for the frequency range f from 20 Hz
measurementsofthedynamicsoftheα-processforamul- to 1 MHz and an impedance analyzer with a dielectric
tilayerfilm. It shouldbe notedthat this workis the first interface (Solartron Instruments 1260/1296) for the fre-
study to investigate the impact of confinement using di- quencyrangefrom0.1Hzto1MHz. Thetemperatureof
electric relaxation spectroscopy of a labeled polymer. a sample cell is changed between 273 K and 413 K at a
Thispaperconsistsofsixsections. Aftergivingexperi- constant rate of 1 K/min. The dielectric measurements
mentaldetailsinSec.II,theglasstransitiontemperature during the heating and cooling processes are performed
ofthinfilms ofPSlabeledwithDR1 isshowninSec.III. repeatedly several times. Data acquisition is made dur-
In Sec. IV, experimental results on the dielectric relax- ing the above cycles except the first cycle. Good re-
ation of the α-process of thin films of PS labeled with producibility of dielectric data is obtained after the first
DR1 aregiven. After discussingthe experimentalresults cycle.
in Sec. V, a summary of this paper is given in Sec. VI. As shown in a previous study [17], the resistance of
the Al electrodes cannot be neglected for dielectric mea-
surements of very thin films. This resistance leads to
II. EXPERIMENTS anartifactlosspeakonthehighfrequencyside. Because
thepeakshapeinthefrequencydomainisdescribedbya
Debye-type equation, the “C-R peak” can easily be sub-
In the present study, we use polystyrene labeled at
tracted. Thus, the corrected data are used for further
a low level with a nonlinear optical dye, 4-[N-ethyl-N-
analysis in the frequency domain.
(hydroxyethyl)]amino-4-nitraozobenzene (Disperse Red
1, DR1) (Fig. 1), which we refer to as PS-DR1.The PS-
DR1 is a random copolymer of neat styrene monomer
and DR1-labeled monomer synthesized following a pro- III. GLASS TRANSITION TEMPERATURE OF
THIN FILMS OF PS LABELED WITH DR1
cedure outlined in Ref. [34]. Hence, the dye molecules
DR1 are covalently attached to the polymer chains of
polystyrene. The concentration of DR1 in PS-DR1 is Figure 1 shows the real and imaginary components of
approximately 3.0 mol % and M =1.34×104 g/mol and thecomplexdielectricconstantobservedduringthecool-
w
M /M =1.65. The molecular dipole moment of DR1 ing process at the frequency of the applied electric field
w n
is approximately7.0 D [35]. It has been established that f = 100 Hz for PS-DR1 and unlabeled PS films. The
whendopedinPS,theDR1reorientationdynamicsmea- thicknessesofthePS-DR1andtheunlabeledPSfilmsare
sured by SHG are coupled to cooperative segmental dy- 360nmand298nm, respectively,andhence bothcanbe
namics and can be used as a probe of the α-process [36]. regardedas bulk systems. It is clear that below T there
g
Also, a related study demonstrated that the reorienta- is almost no difference in ǫ′ and ǫ′′ between the PS-DR1
tion dynamics of DR1 labeled to polymers are coupled and the unlabeled PS. However, the values of ǫ′ and ǫ′′
to the α-process [34]. The incorporation of DR1 from above T of PS-DR1 are much more enhanced compared
g
0.0 to 3.0 mol % label content to PS results in a linear to those of the unlabeled PS. As shown in Fig. 1(b), the
enhancement of the dielectric response, indicating that peak height of the dielectric loss due to the α-process of
dye-dye associations (dipole quenching) do not occur in PS-DR1 is approximately 65 times larger than that of
3.0 mol% PS-DR1. the unlabeled PS.
Thin polymer films are prepared by spin-coating from Figure2showsthetemperaturedependenceofthereal
a toluene solution of PS-DR1 onto an aluminum(Al)- partof the complex electric capacitance (C′) normalized
3
375
PS-DR1 (360 nm)
4.2 PS (298 nm) 370
cooling process, 100 Hz
3.8 365
’ 360
(cid:15) 3.4
K) 355
3.0 (a) T (g 350
2.6 345
320 340 360 380 400
Temperature (K) 340 PS-DR1
PS (Mw = 280k)
0.7 335 PS (Mw = 1.8M)
0.6 PS-DR1 (360 nm) 330
PS (298 nm) 10 100
0.5 PS (298 nm) X 65
d (nm)
0.4
(cid:15)" FIG. 3: Thickness dependence of Tg determined from the
0.3
crossovertemperatureasshowninFig.2forthinfilmsofPS-
DR1
0.2 DR1. The thickness dependence of Tg of the unlabeled PS
0.1 (b) with Mw = 2.8×105 and 1.8×106 g/mol is also plotted [16,
17]. The solid and dashed curves are obtained by fitting the
0
320 340 360 380 400 observed data points to Eq.(1) in thetext.
Temperature (K)
larger slope but has a strong frequency dependence at
FIG. 1: Temperature dependence of the real and imaginary
parts of the complex dielectric constants, ǫ′ and ǫ′′, for PS- even higher temperatures. As a result, the electric ca-
DR1(d=360nm)andunlabeledPS(d=298nm). Thedata pacitance deviates from the common straight line. As
points in this figure are obtained at f = 100 Hz during the previously discussed, the negative slope of the straight
coolingprocess. InFig.1(b),thevaluesofǫ′′fortheunlabeled line α˜ corresponds to the thermal expansion coefficient
PSmagnifiedby65timesarealsoplottedwithsquaresymbols normal to the film surface α [16, 17]. If the lateral size
n
for comparison. of the sample does not change, we have the following re-
lation α˜ ≈ 2α . Judging from the electric capacitance
n
1.000 in Fig. 1, the value of α increases drastically at 368 K.
n
Therefore,this temperaturecanbe regardedasthe T of
g
a −process PS-DR1 with d = 195 nm. The linear thermal expan-
0.995 T
g sion coefficient α evaluated from Fig. 2 changes from
n
K) 0.7×10−4 K−1 to 2.5×10−4 K−1, which agrees well with
73 0.990 the literature values of PS. The frequency dispersion of
C’(2 C′ above Tg is due to the α-relaxation process.
T)/ 0.985 Figure 3 shows the thickness dependence of Tg de-
C’( termined from the temperature dependence of the elec-
d=195 nm, heating tric capacitance as mentioned above. This figure clearly
0.980 1 MHz
shows that T decreases with decreasing film thickness.
398 kHz g
100 kHz The thickness dependence of T can be fitted using the
g
0.975 following equation:
300 320 340 360 380 400
Temperature (K) a
T (d) = T∞ 1− , (1)
g g d
(cid:16) (cid:17)
FIG.2: Temperaturedependenceofthereal partof theelec-
tric capacitance normalized by the value at 273 K for thin where the best fit parameters are Tg∞ = 369.5 ± 2.1 K
filmsofPS-DR1withd=195nmforthreedifferentfrequen- and a = 1.1 ± 0.2 nm. In Fig. 3 the thickness depen-
cies 100 kHz, 398 kHz, and 1 MHz. These data are observed dence of T of unlabeled PS is also shown. The molecu-
g
duringthe heating process. lar weights of the unlabeled PS are M = 2.8×105 and
w
1.8×106 g/mol. The values of T of the unlabeled PS
g
are determined using the same method as previously re-
tothe valueat273Kforthree differentfrequencies. The ported [16]. Comparing the thickness dependence of T
g
data are observed during the heating process. From this between the PS-DR1 and the unlabeled PS, it is found
figure, it is observedthat the normalizedelectric capaci- thatinbothcasesT decreaseswithdecreasingfilmthick-
g
tancesofthethreedifferentfrequenciesoverlapandhave ness in a reasonably similar way. At the same time, we
alineartemperaturedependence belowabout368K.On notice that there is a small difference between the two
the other hand, above this temperature the electric ca- cases. This difference may be attributed to the differ-
pacitance has a linear temperature dependence with a ence in molecular weight between the PS-DR1 and the
4
4.6
400
360 nm
4.2 195 nm
56 nm 395
26 nm
3.8 19 nm 390
’ 15 nm
(cid:15)
3.4
PS-DR1 K) 385
3.0 cooling process, 20Hz (
Ta 380
2.6
300 320 340 360 380 400 375 PS-DR1
Temperature (K)
20 Hz
0.7 370 100 Hz
360 nm Ta
0.6 195 nm
56 nm 365
0.5 2169 nnmm 10 100 1000
0.4 15 nm d (nm)
"
(cid:15) 0.3
FIG. 5: Thickness dependence of the temperature T ob-
0.2 α
PS-DR1 served at 20 Hz and 100 Hz. The dotted and dashed lines
0.1 cooling process, 20Hz correspondtothevaluesobservedinbulkstatesat20Hzand
0 100 Hz,respectively.
300 320 340 360 380 400
Temperature (K)
FIG. 4: Temperature dependence of the real and imaginary at which the dielectric loss due to the α-process has a
components of the dielectric constants ǫ′ and ǫ′′ at the fre- maximum is shifted to the lower temperature side. In
quency20 Hzfor different film thicknesses. Fig. 5, T is plotted as a function of film thickness for
α
f = 20 Hz and 100 Hz. The temperature T is found
α
to dependstronglyonfrequencyandto increasewithin-
unlabeled PS, because the molecular weight of PS-DR1 creasing frequency. The value of T at a low frequency
α
(Mw = 1.34×104) is muchsmallerthan thatofthe unla- correspondingtotheα-relaxationtimeof100seciscom-
beledPS,andaccordinglyTgofthebulkstateofPS-DR1 parable to the value of Tg determined for the ramping
is lower by a few degrees than that corresponding to the processatarateof10K/minusingdilatometricmeasure-
unlabeledPS.Ifwetakeintoaccountthedifferencecom- mentsordifferentialscanningcalorimetry. Therefore,the
ing from the molecular weight, we can judge that the decrease in T with decreasing film thickness at a given
α
thicknessdependence ofTg ofPS-DR1isfairlycompara- frequency is associated with the decrease in Tg and the
ble to that of the unlabeled PS. faster dynamics of the α-process in thinner films.
The use ofdielectric spectroscopyrequiresthat anup-
per electrode be evaporated on top of the free surface of
the films. A consequence is that the films do not have B. Dielectric relaxation in thin films
a true free surface. However, the PS films report a re-
duction in T with decreasing film thickness similar to
g Figure 6 shows the frequency dependence of the real
techniques that allow for a free surface. Therefore, it is
andimaginarycomponentsofthecomplexdielectriccon-
believed that the free surface effects are not masked by
stants at various temperatures for thin films of PS-DR1
the addition of the top electrode as demonstrated previ-
for two different thicknesses: (a) d = 360 nm and (b)
ously [16, 18, 20].
d = 19 nm. In the real part of the complex dielectric
constant ǫ′ for the 360nm-thick-film, there is a gradual
stepfrom4.7to2.7,while inthe imaginarypartǫ′′ there
IV. DYNAMICS OF THE α-PROCESS IN THIN
is a maximum at the same frequency where there is the
FILMS OF PS LABELED WITH DR1 step in ǫ′. This frequency dependence is associated with
the existence of the α-process. The peak frequency in ǫ′′
A. Dielectric behavior at a fixed frequency corresponds to the inverse of a characteristic time of the
α-process at a given temperature. From Fig. 6 it is ob-
Figure4showsthetemperaturedependenceofthereal servedthatthe peakfrequency ofthe α-processbecomes
andimaginarycomponentsofthecomplexdielectriccon- larger with increasing temperature. This corresponds to
stantforthinfilmsofPS-DR1withfilmthicknessranging the acceleration of the dynamics of the α-process with
from360nmto15nm. Thedataareobtainedduringthe increasing temperature. At higher temperatures there
coolingprocessatfrequency20Hz. InFig.4wefindthat is also a large increase in ǫ′′ with decreasing frequency.
the contribution from the α-process is strongly affected This is usually attributed to the contributions from dc
by film thickness. As the thickness decreases, the peak conductivity due to space charges or impurities within
heightofthe dielectriclossduetotheα-processbecomes the polymericsystems. Comparingthe frequencydepen-
smaller, and at the same time the α-temperature (T ) dences of ǫ′ and ǫ′′ in Fig. 6(a) to those in Fig. 6(b), we
α
5
5.0 3.1
400.7 K
405.4 K 395.6 K
4.5 400.0 K 3.0 390.7 K
395.3 K 385.8 K
390.3 K 380.9 K
4.0 385.4 K 376.1 K
380.5 K 2.9 371.2 K
’ 375.8 K ’ 366.1 K
e 3.5 e
2.8
3.0
2.7
2.5
0.7 (a) 360nm (b) 19nm
0.08
0.6
0.5 0.06
" 0.4 "
e 0.3 e 0.04
0.2
0.02
0.1
0 0
-1 0 1 2 3 4 5 6 -1 0 1 2 3 4 5
log 1 0 [f (Hz)] log 1 0 [f (Hz)]
FIG.6: ThedependenceofthecomplexdielectricconstantonthelogarithmoffrequencyatvarioustemperaturesaboveT for
g
thin films of PS-DR1: (a) d = 360 nm and (b) d = 19 nm. Solid curvesare calculated by Eq. (2).
TABLE I: Fitting parameters of the HN equation for PS-DR1 with various film thicknesses: relaxation strength ∆ǫ, shape
parametersαHN,βHN,andrelaxation timeτ0. Here,theexponentβKWW intheKWWrelaxation functionisevaluatedusing
therelation β =(α β )1/1.23 [44].
KWW HN HN
d (nm) T (K) ∆ǫ αHN βHN τ0 (sec) βKWW
19 390.7 0.33 ± 0.02 0.46 ± 0.02 0.48 ± 0.10 (3.1±0.5)×10−4 0.29±0.06
26 389.8 0.96 ± 0.01 0.69 ± 0.02 0.52 ± 0.02 (1.8±0.1)×10−2 0.43±0.24
360 390.3 2.14 ± 0.01 0.80 ± 0.01 0.57 ± 0.01 (2.32±0.04)×10−2 0.53±0.08
and β are the shape parameters, and τ is the relax-
HN 0
TABLEII:Thevaluesoftheparametersresultinginthebest
ation time of the α-process. The solid curves in Fig. 6
fit of the relaxation times of the α-process τ to Eq. (3) for
are obtained using Eq. (2) with the best-fit parameters.
thin films of PS-DR1 with various film thicknesses (d = 360
In Fig. 6 it is found that Eq. (2) can well reproduce
nm, 26 nm and 19 nm).
the frequency dependence of the observeddielectric con-
d (nm) log10[τ˜0(sec)] U (103 K) T0 (K) m stant. Examples of the best-fit parameters of the HN-
360 −11.8 ± 0.6 1.6 ± 0.2 318 ± 4 99 ± 11
equationat 390K are listed in Table I. In this table, the
26 −13.3 ± 0.5 2.1 ± 0.2 306 ± 3 92 ± 8
exponent β is also listed, on the assumption that
19 −14.6 ± 1.0 2.3 ± 0.4 294 ± 7 97 ± 17 KWW
the relaxation function φ(t) is given by the KWW equa-
tion φ(t) = exp(−(t/τ)βKWW). The value of β can
KWW
be evaluated by the relation β = (α β )1/1.23
find that the peak height of the loss peak in ǫ′′ due to KWW HN HN
and is a measure of the distribution of the relaxation
the α-process for d = 19 nm is much smaller than that
times [44].
for d = 360 nm and that the peak shape and the peak
position also change with decreasing film thickness.
Here,weusethe followingempiricalequationofǫ′ and
ǫ′′ as a function of frequency:
ǫ∗ =ǫ +iσ˜ω−m+ ∆ǫ , (2) C. Relaxation time of the α-process
∞ ǫ0 [1+(iωτ0)αHN]βHN
where ω = 2πf, ǫ is the permittivity in vacuo and ǫ Figure 7 shows the Arrhenius plot of the α-process of
0 ∞
is the permittivity at a very high frequency. The second thinfilmsofPS-DR1withd=19nm,26nm,and360nm.
term is a contribution from space charge [37], and this The vertical axis is the logarithm of 1/2πτ, where τ is
contributioncanbe attributedto pure dc conductivity if therelaxationtimeoftheα-processandisevaluatedfrom
m = 1. The third term comes from the α-process, and therelation2πf τ =1,wheref isthe frequencyat
max max
its empirical form is usually calledthe Havriliak-Negami which ǫ′′ has a loss peak due to the α-process at a given
(HN)equation,where∆ǫistherelaxationstrength,α temperature. The curves are evaluated using the Vogel-
HN
6
4
360 nm
26 nm 1.6
3 19 nm
360 nm
1.4
s)] 2
(
pt [1/20 1 1.2 +01.69nm
log1 0 max 1.0
-1 " 0.8
e"/
+0.3
e
-2 0.6 26nm
2.45 2.5 2.55 2.6 2.65 2.7 2.75
1/T (10-3 K-1)
0.4
FIG. 7: Arrhenius plot for the α-relaxation process in thin 360nm
0.2
films of PS-DR1. The logarithm of 1/2πτ vs. 1/T for three
differentthicknessesd=19 nm(△),26nm((cid:3)),and360 nm
(◦). The curves are obtained using the VFT law. The sym- 0
bol+correspondstodc-conductivitieswhichareevaluatedat -4 -3 -2 -1 0 1 2 3 4
0.1Hzford=360nminFig.10andareshiftedalongthever- log [f/f ]
10 max
ticalaxissothatwecancomparethetemperaturedependence
of dc-conductivityto that of 1/τ .
FIG. 8: Dependence of the normalized dielectric loss of PS-
DR1 on the logarithm of the normalized frequency. The two
Fulcher-Tammann (VFT) law: axes are normalized with respect to thepeak position dueto
theα-process,correspondingtoǫ′m′ax andfmax. Thenumbers
U given in the right margin stand for the film thickness. The
τ(T)=τ˜0exp , (3) data for d = 19 nm and 26 nm are shifted up by +0.6 and
(cid:18)T −T (cid:19)
0 +0.3, respectively, for clarity. Different symbols correspond
where τ˜ is a microscopictime scale for the α-process, U todifferenttemperatures: (a)ford=360 nm,datapointsat
0
405.4 K, 400.0 K, 395.3 K, 390.3 K, 385.4 K, 380.5 K, and
isanapparentactivationenergy,andT istheVogeltem-
0 375.8Kareplotted(b)ford=26nm,404.9K,399.7K,394.7
perature[39]. Foreachfilmthicknessitisfoundthatthe
K,389.8K,384.9K,380.1K,and375.1K(c)ford=19nm,
relaxation time of the α-process obeys the VFT law. At
400.7 K, 395.6 K, 390.7 K, 385.8 K, 380.9 K, 376.1 K, and
the same time, there is a distinct thickness dependence
371.2 K
of τ, that is, the relaxation time of the α-process be-
comes smaller with decreasing film thickness at a given
temperature. The best-fit parameters of the VFT law
for thin films of PS-DR1 are listed in Table II. It is
0.30
clearthatthe Vogeltemperature decreaseswithdecreas- 19 nm
ing film thickness, which is consistent with the fact that 26 nm 360 nm
0.25 360 nm
T decreases with decreasing film thickness as shown in
g
Fig. 3. The fragility index m, which is a measure of the 0.20 391 K
26 nm
non-Arrheniustemperaturedependenceoftherelaxation
times,isalsoevaluatedfromthetemperaturedependence s) 0.15
F(
of the α-relaxation time according to the following defi-
19 nm
nition: 0.10
m = dlog10τ(T) , (4) 0.05
(cid:20) d(T /T) (cid:21)
g T=Tg 0
-12 -10 -8 -6 -4 -2 0 2
where Tg is defined so that τ(Tg) = 100 sec [40]. log [t (s)]
10
FIG.9: ThedistributionfunctionF(s)oftherelaxationtimes
D. Profile of the α-loss peak
oftheα-processat391KforthinfilmsofPS-DR1. Thevalues
are calculated by Eq. (6) with the best fit parameters of the
Inordertoobtainthethicknessdependenceofthepro- HN equation. The dotted curverepresents theresult for d =
fileofthedielectriclossspectrum,theobservedlosspeaks 360 nm, the dashed curve that for d = 26nm, and the solid
ofǫ′′atvarioustemperaturesarenormalizedwithrespect curvethat for d = 19 nm.
to the peak position for each temperature in the case of
7
three different film thicknesses, as shown in Fig. 8. For In order to extract the dc-conductivity, the dielectric
clarity, data points of d = 19 nm and d = 26 nm are loss ǫ′′ in Fig. 6 are replotted as ωǫ ǫ′′ vs. logf, where
0
shifted along the vertical axis by +0.6 and +0.3, respec- ωǫ ǫ′′ corresponds to the real part of conductivity σ′, as
0
tively. From Fig. 8 it is found that the width of the showninFig.10. InFig.10,itisfoundthatσ′ obeysthe
α-loss peak clearly increases with decreasing film thick- power-lawω1−m inthe lowerfrequency regionandtends
ness. Thissuggeststhatthedistributionoftherelaxation to approach a constant value with decreasing frequency.
timesbecomesbroaderwithdecreasingfilmthickness. At This constant value corresponds to the dc-conductivity.
the same time, there is a contributiondue to the dc con- For d = 360 nm, the value σ′ at 0.1 Hz in Fig. 10 can
ductivity in the low-frequency side, which may disturb be regarded as the dc-conductivity because the slope in
the evaluationof the distribution of the relaxationtimes thelowfrequencyregionissmall. Ontheotherhand,for
of the α-process. In order to avoid this problem, we use d = 19 nm, σ′ still decreases with decreasing frequency
the best-fit parameters of the HN equations α , β in the low frequency region around 0.1 Hz, and hence
HN HN
and τ and then evaluate the distributions of τ. it is impossible to evaluate the dc-conductivity from the
0
Here, the distribution function F(log τ) of the relax- present data for d = 19 nm. The dc-conductivities ob-
e
ation times τ is defined by the following relation: tained thus for d = 360 nm are plotted in Fig. 6 after
shifting themalongthe verticalaxissothatwecancom-
+∞ F(log τ)d(log τ) pare the temperature dependence of dc-conductivity to
ǫ∗(ω)=ǫ +∆ǫ e e . (5)
∞ Z 1+iωτ that of 1/τ. In Fig. 6 it found that there is a fairly
−∞
good agreement between the two data. Therefore, the
If we assume that the shape of the dielectric loss peak is present results are consistent with previous results that
described by the HN equation, the distribution function dc-conductivityhasasimilartemperaturedependenceof
F(log τ) can be calculated analytically as follows: the segmental motion [41]. For detailed comparison, the
e
data at much lower frequencies are highly required.
1
F(s) = [1+2eαHN(x0−s)cosπα +e2αHN(x0−s)]−βHN/2
HN
π
×sin β tan−1 eαHN(x0−s)sinπαHN ,(6) V. DISCUSSION
(cid:20) HN (cid:18)1+eαHN(x0−s)cosπαHN(cid:19)(cid:21)
In1994,Torkelsonandcoworkersinvestigatedtherota-
where s = logeτ [24] ans x0 = logeτ0. Figure 9 shows tional dynamics of DR1 doped at 2 wt.% in polystyrene
the distribution of α-relaxation times for three different using SHG and dielectric relaxation spectroscopy [36].
film thicknesses at 391 K, which is evaluated using Eq. TheyfoundthatbothSHGanddielectricrelaxationspec-
(6). Itisfoundthattherelaxationtimeoftheα-process, troscopy yielded almost the same average time constant
which is related to the peak position of the distribution, hτi, and that above T the values of hτi fit well to the
g
isshiftedtoasmallertimewithdecreasingfilmthickness, Williams-Landel-Ferry (WLF) equation with appropri-
andatthesametime,thefullwidthatthehalfmaximum ate WLF constants [42], which indicated that the rota-
of the distribution becomes broader, increasing from 2 tional reorientation dynamics of DR1 are coupled to the
decades (for d = 360 nm) to 8 decades (for d = 19 nm). α-relaxation process of PS.
As shown in the previous section, the dielectric loss
peakcanbeobservedaboveT usingdielectricrelaxation
g
E. Conductivity component spectroscopy for thin films of PS-DR1. In our measure-
ment, we observe a very large dielectric loss above T
g
Figure 6 shows that there is a contribution of conduc- compared to the unlabeled PS. In PS-DR1, DR1 chro-
tivity due to the motion of space charge such as ions in- mophores are attached covalently to the main polymer
cluded in polymer materials in the low frequency range. chain,while DR1dyesweredopedinPSinRef.[36]. Al-
Inordertoanalyzethiscontributioninthelowfrequency though there are covalent bonds between DR1 and PS
region, we use the second term of the right-hand side of in the present case, the rotational reorientation relax-
Eq. (2): ǫ′′ ∼ σ˜ω−m. Making data fit to this equation ation times of the labeled DR1 can still be described by
forvariouscotnempǫe0ratures,we canobtainthe temperature the VFT law, which is the same as the WLF equation,
dependence of σ˜ and m for d = 19 nm and 360 nm. It as shown in Fig. 7. This is consistent with results in
isfoundthatmisapproximatelyindependentoftemper- Ref.[36]. Therefore,the rotationalreorientationdynam-
ature and is equal to 0.82 ± 0.02 for d = 360 nm and ics of DR1 chromophores attached to the polymer main
0.48 ± 0.01 for d= 19 nm. If ǫ′′ has a ω dependence chain, which must be the microscopic origin of the di-
con
given by ω−m, the real part of ac-conductivity σ′ is pro- electriclossobservedinthe presentstudy, areequivalent
portional to ω1−m. Hence, we obtain the ω dependence to the cooperative segmental motions of PS, that is, the
of σ in the low frequency region as follows: α-relaxation process.
Above T , the reorientationdynamics of DR1 coupled
g
ω0.18 : d=360 nm with the α-process have a very large contribution to the
σ′ ∼ (7)
(cid:26) ω0.53 : d=19 nm. dielectricsusceptibility,asshowninFig.1. Inmanypoly-
8
10-9 10-10
405.4 K 400.7 K
400.0 K 395.6 K
395.3 K 390.7 K
390.3 K 385.8 K
m) 10-10 385.4 K m) 10-11 380.9 K
S/ S/
y ( y (
vit 10-11 vit 10-12
cti cti
u u
d d
n n
o o
c 10-12 c 10-13
(a) 360 nm (b) 19 nm
10-13 10-14
-1 -0.5 0 0.5 1 1.5 2 -1 -0.5 0 0.5 1 1.5 2
log [f (Hz)] log [f (Hz)]
10 10
FIG. 10: Thefrequency dependenceof thereal part of theconductivityat various temperaturesfor PS-DR1with d= 360 nm
(a) and 19 nm (b). The value of the vertical axis is evaluated from the frequency dependence of the imaginary part of the
dielectric ac-susceptibility using therelation σ′=ωǫ0ǫ′′.
creasingfilmthicknessforPS-DR1inasimilarmanneras
0.06
2.6 unlabeled PS. The reduction in Tg with decreasing film
2.4 U=68.1 kJ / mol thicknessisbelievedto berelatedtoalayeratthe upper
00..0045 log[f(Hz)]max 1011122.....46802 wTAgilt-ceholendctetrcriorbeduaetseipnsogmlyfiomlrmeerttoihnittchekrenfaaecvsese,rwathgiteehdlaayynreeardmuwiccietshdoaTfgtrh.eedTufihclumesd,,
leading to a decrease in the average film T .
1.2 g
3.2 3.3 3.4 3.5
" 0.03 1/T (10-3K-1) In a previous report by Fukao et al., it has been re-
e
ported that the fragility decreases slightly with decreas-
0.02 15 nm ing film thickness in thin films of PS on the basis of
X 3.8 thecombinedresultsofdielectricrelaxationspectroscopy
20 Hz
andthermalexpansionspectroscopy[23]. Inarecentpa-
50 Hz
0.01
100 Hz per, a slight decrease in the fragility index from 150 to
323 Hz
110 was also observed using dielectric relaxation spec-
0 troscopy when the thickness was decreasedfrom 286 nm
200 240 280 320 360 400
to 8.7 nm [20]. The fragility index of PS-DR1 as a func-
Temperature (K)
tionoffilmthicknessisshowninTableII.Althoughthere
isalargeerror,theobservedresultsarequalitativelycon-
FIG. 11: The dielectric loss as a function of temperature for
differentfrequencies20Hz,50Hz,100Hzand323Hzforthin sistentwiththepreviousresultsofunlabeledpolystyrene.
films of PS-DR1with d = 15 nm. The data below 360 K are The shapes of the dielectric loss and the distribution
magnified by 3.8 times. The arrows indicate the location of of relaxation times of the α-process for thin films of PS-
the α-process. The inset shows the Arrhenius plot for the
l DR1 areshowninFigs.8and9. The bestfitparameters
α-process.
l of the HN equation are listed for thin films of PS-DR1
with various film thickness at 390 K in Table I. It is il-
lustrated in Figs. 8 and 9 that the distribution of the
meric systems with large polarity such as PMMA and α-relaxationtimes becomesbroaderwithdecreasingfilm
PVAc, it is impossible to determine Tg using capacitive thickness,whichindicates thatthe thicknessdependence
dilatometry [17, 43]. However, as shown in Fig. 2, Tg of the distribution of the α-relaxation times in PS-DR1
can be successfully determined by capacitive dilatome- is the same as that of unlabeled PS. The broadening of
try in the case of PS-DR1. Furthermore, the thickness the distribution of the α-relaxation times with decreas-
dependence of Tg in thin films of PS-DR1 can also be ing film thickness may result from a region at the upper
determined and is found to be consistent with that of Al-polymer interface with dynamics different from bulk
unlabeled PS. From this result we can conclude that the dynamics. This hypothesis will be tested in a forthcom-
rotational reorientation dynamics of DR1 are an excel- ing paper [45]. We note that the distribution of PS-DR1
lent sensor for the α-process in thin films of PS, and the is narrower than that of unlabeled PS at a fixed thick-
resultsobtainedinthinfilmsofPS-DR1canbecompared ness: β = 0.53 for PS-DR1 with d = 360 nm and
KWW
with those of unlabeled PS. β = 0.435 for unlabeled PS with d = 408 nm [17].
KWW
From Fig. 3 it is observed that T decreases with de- This maybe relatedto the fact thatthe rotationalreori-
g
9
entation dynamics of the DR1, which are coupled with U= 68±3 kJ/mol, which agrees very well with the value
the α-process,areobservedby dielectricrelaxationspec- reportedfortheunlabeledPS[20]. Atpresent,wecannot
troscopy. provide an unambiguous answer as to whether the addi-
Figure 6 we shows that there is a decrease in the tional relaxation process observed in the current study
strengthof the α-relaxationprocess with decreasingfilm results from interfacial effects or a simple or primitive
thickness; ∆ǫ changes from 2.14 to 0.33 with decreasing dynamical process. Studies are currently underway to
film thickness from 360 nm to 19 nm. This thickness determine whether or not it is an interfacial effect.
dependence of ∆ǫ is commonly observed in thin films of Here, it should be noted that the DR1 chromophore
other polymeric systems such polystyrene, poly(methyl covalently attached to the main chain in PS-DR1 is a
methacrylate), poly(vinyl acetate) and so on [18, 24]. In bulkygroup. Therefore,thereisapossibilitythatthelo-
a previous reportby Fukao et al., a simple model for the cal structure of the amorphous PS chains deviates from
decreasein∆ǫinthinfilmswasproposedandcanbeap- that of the unlabeled PS and its deviation affects the
pliedtothinfilmsofPSlabeledwithDR1. Inthemodel, dynamics of the polymer chains observed by dielectric
it is assumed that there is a motional unit in which n relaxation spectroscopy. However, we believe that such
dipolemotionsmoveorrotatecooperatively. Inthiscase deviation, if any, has almost no effect on the segmen-
∆ǫ is given by the following relation: tal motions of PS-DR1, because the α-dynamics and its
thickness dependence are consistent with those of unla-
Nµ2
∆ǫ = , (8) beled PS, as shown in our study. In addition, previous
3kBT studies conducted using DR1 as the dye either doped
or covalently attached to the polymer yielded average
whereNisthenumberofthe motionalunitsandisgiven
α-relaxation times in agreement with those determined
by N =N×n,andµis the totalstrengthofdipole mo-
0
using other techniques.
ments included in a unit and is given by µ=nµ . Here,
0
µ is the strength of a single dipole moment attached
0
to polymer chains, N is the total number of dipole mo-
0
VI. SUMMARY
ments in the system and it is assumed that there is no
correlation between the motional units. Using N and
0
µ , we can rewrite Eq.(9) as follows: We investigated the glass transition temperature and
0
relaxation dynamics of the α-process of thin films of
∆ǫ = nN0µ20. (9) polystyrene labeled with a dye DR1 using dielectric re-
3k T laxation measurements. The results can be summarized
B
as follows:
Therefore, if the number of dipole moments within the
motionalunitisdecreasedwithdecreasingfilmthickness, 1. The dielectric strengthof DR1-labeled polystyrene
the decreasein ∆ǫ inthinner films canbe accountedfor. is approximately 65 times as large as that of unla-
The idea of a decrease in the number of dipole moments beled polystyrene above the glass transition, while
movingcooperativelyisconsistentwiththatbasedonthe there is almost no difference between them below
existenceofacooperativelyrearrangingregion(CRR)[3]. the glass transition.
In supported ultrathin films of unlabeled PS, it has
been reported that there is an additional relaxationpro- 2. The Tg of DR1-labeled polystyrene can be deter-
cess (α -process) in addition to the α-process [17, 20]. minedwellasacrossovertemperatureatwhichthe
l
The α -process is located at a lower temperature than temperature coefficient of the electric capacitance
l
that of the α-process. This process was assigned to re- changes from the value of the glassy state to that
laxation dynamics of the surface region in PS films, and of the liquid state. The Tg thus obtained decreases
has an Arrhenius type of temperature dependence with with decreasing film thickness in a manner similar
an activation energy of 71 kJ/mol [20]. A recent study to that of unlabeled polystyrene thin films.
investigating the relaxation processes of thin supported
3. As for the dielectric relaxation spectrum of the
polystyrene films using dielectric spectroscopy also ob-
DR1-labeled polystyrene, the α-relaxation time
servedanadditionalrelaxationprocessbelowT withan
g becomes smaller and the distribution of the α-
Arrhenius temperature dependence [46]. The activation
relaxation times becomes broader, as thickness de-
energyoftheadditionalprocesswas15-25kJ/mol. How-
creases.
ever, the additional process was attributed to a simple
or primitive dynamical process that acts as a precursor These results show that there is a distinct contrast
totheglasstransitioninultrathinfreestandingfilms. In between the relaxation strength of the α-process of
the present study, an α-process is observed in ultrathin PS-DR1 and that of the unlabeled PS and that thin
l
PS-DR1 films (d < 20 nm) at temperatures lower than films of DR1-labeled polystyrene are a suitable system
that of the α-process, as shown in Fig. 11. From the in- for investigating confinement effects of the glass transi-
vestigation in Fig. 11, it is found that the α -process of tion dynamics using dielectric relaxation spectroscopy.
l
thin films of PS-DR1 can also be describedby anArrhe- Therefore, we expect that we will be able to observe
niustypeofactivationprocesswiththeactivationenergy the dynamics of the α-process only from the labeled
10
layer in a multi-layer system of PS-DR1 and unlabeled and DMR-0520513), a Grant-in-Aid for Scientific Re-
PS, and to obtain information on the dynamics of the search(B)(No.16340122)fromJapanSocietyforthePro-
α-process at any position normal to the film surface. motion of Science, a DFI fellowship (R.D.P.) and a NSF
We will report the results on such position dependent EASPI fellowship (R.D.P.).
measurements of the α-dynamics in the near future [45].
Acknowledgements
This work was supported by the NSF-MRSEC Pro-
gramatNorthwesternUniversity(GrantsDMR-0076097
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