Glassy dynamics in thin films of polystyrene

0.75 MB·

by  Koji Fukao

APS/123-QED
Glassy dynamics in thin films of polystyrene
∗
Koji Fukao
Department of Physics, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu, 525-8577, Japan
Hiroki Koizumi
Department of Polymer Science, Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan
(Dated: February 2, 2008)
Glassy dynamicswasinvestigated for thinfilmsofatactic polystyrenebycomplexelectric capac-
itance measurements using dielectric relaxation spectroscopy. During the isothermal aging process
thereal part of theelectric capacitance increased with time, whereas theimaginary part decreased
8 with time. It follows that the aging time dependences of real and imaginary parts of the electric
0 capacitance were primarily associated with change in volume (film thickness) and dielectric per-
0
mittivity, respectively. Further, dielectric permittivity showed memory and rejuvenation effects in
2
a similar manner to those observed for poly(methyl methacrylate) thin films. On the other hand,

n volumedid not show a strong rejuvenation effect.
a
J PACSnumbers: 71.55.Jv;81.05.Lg;77.22.Ch

5

] I. INTRODUCTION without isothermal aging, revealed that the values were
ft ingoodagreement. Thissuggeststhatthedecreaseindi-
o electric susceptibility induced by the isothermal aging is
s Amorphous materials show a glass transition as the
totally compensatedduring the cooling process from the
. temperature decreases in the liquid state. Throughout
t isothermalagingtemperaturetoroomtemperature. This
a the glass transition, the molecular mobility due to the
m changein dielectric susceptibility has the opposite direc-
α-process is frozen and the material transforms into a
tioncomparedtothechangeduetotheaging. Therefore,
- glassy state. Polymeric glass shows structural changes
d the changeindielectric susceptibility inducedduring the
during the aging process, even below the glass transi-
n cooling process after the isothermal aging is called reju-
tiontemperatureT . Correspondingphysicalchangesare
o g venation, and hence the system is rejuvenated as far as
c observed with these structural changes [1, 2, 3]. These
thedielectricresponseisconcerned. However,duringthe
[ changes are known as physical aging, and are related to
subsequent heating process from room temperature, the
the glassy dynamics. This is regarded as an important
1 dielectric susceptibility deviates from the value observed
v propertycharacteristicofdisorderedmaterialsincluding; duringthecoolingprocesswithoutisothermalaging,and
5 polymer glasses [4, 5, 6], spin glasses [7, 8] and other
showsamaximumdeviationjustabovetheagingtemper-
9 disordered systems [9, 10, 11].
ature as if the sample remembered the isothermal aging
7
0 In our previous papers [5, 6], the glassy states of itexperiencedduringtheprecedingcoolingprocess. This
. poly(methyl methacrylate) (PMMA) show a decrease in behavioris calledmemory effect and it suggeststhat the
1 both the realand imaginaryparts of the complex dielec- thermal history is maintained as a memory.
0
tric constant with increasing time during the isothermal
8 In the case of amorphous polymers, it is well known
aging process. The glassy states show memory and re-
0 that the density of the polymers increases due to the
juvenation phenomena for thermal treatment of a con-
: isothermal aging below T , and this density change is
v stant rate mode and of a temperature cycling mode, as g
maintained even at room temperature [1]. On the other
i
X shown below. In the constant rate mode, the tempera- hand, there is no rejuvenation for the density. This find-
turechangesfromhightemperatureaboveT toanaging
r g ing appears to be inconsistent with the fact that the
a temperature, at which the sample is aged isothermally
dielectric as-susceptibility shows rejuvenation. Herein,
and the dielectric susceptibility decreases with increas-
we investigate the aging behavior of thin films of atactic
ing aging time during the process. This decrease in di-
polystyrene (a-PS) using electric capacitance measure-
electric susceptibility is associated with the relaxation
ments in order to elucidate the nature of the glassy dy-
of the system into the equilibrium states. The change
namics in polymer glasses.
to the equilibrium is called aging. Then, the temper-
ature subsequently decreases from the isothermal aging
temperature to room temperature at a constant rate. A
II. EXPERIMENTAL
comparison of the value of the dielectric susceptibility
at room temperature after the isothermal aging to that
Thin films of atactic polystyrene (a-PS) with two dif-
ferent thicknesses, 14 nm and 284 nm, were prepared by
spin-coating from a toluene solution of a-PS on an Alu-
∗Electronic address: [email protected]; Corresponding au- minum(Al)-depositedglasssubstrate. Thethicknesswas
thor. controlledbychangingtheconcentrationofsolution. The
2
samples of a-PS used in this study were purchased from 700
aging at 340 K
Aldrich Co., Ltd. (M = 1.8×106, M /M = 1.03). heat after aging
After annealing at 70 ◦wC under vacuum fwor twno days to 695 hceoaotl ((rreeff))
removesolvents,Alwasagainvacuum-depositedtoserve 690
F)
as an upper electrode. Several heating cycles through p
C’(
and above a bulk value of T were carriedout before the 685
g
capacitancemeasurementsweretakenforthe relaxedas-
680
spun films in order to obtain reproducible results. The (a) 1 kHz, 284 nm
valuesofTg inthethinfilmswithd=14nmand284nm 675
were 350 K and 368 K, respectively. The thickness was 280 300 Te3m2p0erature 3(K4)0 360 380
evaluated from the value of the electric capacitance at
293 K for the as prepared films before measurements in 0.8 aging at 340 K
heat after aging
the same manner previously reported [12, 13]. cool (ref)
heat (ref)
The T of the two thin films differs by about 18 K.
g 0.7
According to the recent report on T of thin films of F)
g p
polystyrene,the effect of oxidationcan be a possible ori- C"(
0.6
ginofthereductionofT [14]. However,weperformedT
g g
measurements for each thin film several times and con-
0.5 (b) 1 kHz, 284 nm
firmedthatthereductionofT isnotduetotheoxidation
g
effect in the present case. 280 300 320 340 360 380
Temperature (K)
Capacitance measurements were carried out using an
LCRmeter(HP4284A)forthefrequencyf =1kHzdur-
FIG. 1: Temperature change in (a) the real part of electric
ingthecoolingandheatingprocessesbetween380Kand
capacitance C′ and (b) theimaginary part C′′ for a-PS films
273 K at a rate of 1 K/min as well as during isother-
with thickness of 284 nm for frequency 1 kHz. Temperature
mal aging at various aging temperatures T (=315 K ∼
a changesbetween380Kand273Kincludingisothermalaging
351 K). The complex electric capacitance of the sample
at 340 K.
condenserC∗(≡C′−iC′′)wasmeasuredasafunctionof
∗
temperature T and aging time t . The value of C was
w
convertedintothedynamic(complex)dielectricconstant ′
temperature and the slope of C with respectto temper-
ǫ∗(≡ ǫ′−iǫ′′) by dividing the C∗(T) by the geometrical
ature gradually changed around 365 K. Thus, there is
capacitance C (T ) at a standard temperature T . The
0 0 0 a difference between the heating and cooling processes.
value of C∗ is given by the relation C∗ = ǫ∗ǫ S and
0d This gradual change corresponds to the glass transition.
C0 = ǫ0Sd, where ǫ0 is the permittivity in vacuum, S is Furthermore, from the data for the subsequent cooling
the area of the electrode and d is film thickness. For process including isothermal aging, C′ was observed to
∗
evaluation of ǫ and C0, we use the thickness d which is increase with aging time during isothermal aging at Ta.
determined at T0 = 293 K and S = 8×10−6 m2. Inthiscase,thevalueofC′increasedby0.3%forisother-
mal aging at 340 K for 20 hours.
′
Contrary to C , the imaginary part of the electric ca-
III. RESULTS AND DISCUSSION ′′
pacitance C was an increasing function of temperature
during the cooling and heating processes at a constant
A. Aging dynamics rate. Above 380 K a decrease in the peak was expected
due to the α-process. Further, during the isothermalag-
′′
Figure 1 shows the change in the real and imaginary ing process at 340 K, C was observed to decrease with
′′
parts of the complex electric capacitance for a-PS films increasing aging time. The change in C for aging at
withd=284nmandf=1kHz. Thetemperatureofthe 340 K for 20 hours was about 0.2 pF, which corresponds
sample was changed as follows: After several tempera- to a decrease by 3%. This fraction was an order of mag-
′
ture cycles in order to stabilize the measurements, the nitude larger than the increase in C for the same aging
temperature changed from 380 K to 273 K (cooling pro- process.
cess,dottedline)andthenfrom273Kto380K(heating Figure 2 shows the temperature dependence of the
process, solid line). The data obtained for the cooling complex electric capacitance in thin films of a-PS with
and heating processes are used as a reference data. The d = 14 nm. In this case, a similar result was obtained
sample was cooled from 380 K to 340 K(≡T ), the tem- forthe temperaturedependenceofC′ andC′′ asthatfor
a
perature was maintained at T for 20 hours, and then d = 284 nm. For thin films, the absolute value of C∗ is
a
thesamplewasagaincooleddownto273Kafterisother- enhanced. The change in C′ is more distinct due to the
mal aging (open circles). Finally, the sample was again smaller slope of C′ with respect to T. Furthermore, the
heated from 273 K to 380 K (open triangles). scatterofdatainC′ isreducedduetothelargergeomet-
′
InFig.1(a),thereferencedatashowsthattherealpart rical capacitance. The slight increase in C above 375 K
′
of the electric capacitance C is a decreasing function of was due to the existence of the α-process. In the case of
3
14880 30
14860 ahgeinagt aaftt e3r4 a1g.2in Kg 25 (a) 1 kHz, 14 nm
cool (ref) 350.8K
heat (ref) 20
14840
C’(pF) 14820 ∆C’ (pF) 1105 341.2K
14800 331.0K
5
14780 321.3K
(a) 1 kHz, 14 nm 0
14760
280 300 320 340 360 380 -5
Temperature (K) 0 200 400 600 800 1000 1200
time (min)
111100
aging at 341 K 0
100 heat after aging
cool (ref)
90 heat (ref)
-0.5
80
F) F)
C"(p 6700 ∆C" (p -1 321.3K
331.0K
50 341.2K
-1.5 350.8K
40 (b) 1 kHz, 14 nm
(b) 1 kHz, 14 nm
30
280 300 320 340 360 380 -2
Temperature (K) 0 200 400 600 800 1000 1200
time (min)
30
FIG. 2: Temperature change in (a) the real part of electric ′ ′′
FIG. 3: Aging time dependenceof thedeviation ∆C (∆C )
capacitance C′ and (b) theimaginary part C′′ for a-PS films ′ ′′ ′ ′′
ofC (t)(C (t))fromtheinitialvaluesC (0)(C (0))forvari-
with thickness of 14 nm for frequency 1 kHz. Temperature
ousagingtemperaturesforthinfilmsofa-PSwithfilmthick-
changesbetween380Kand273Kincludingisothermalaging
ness of 14 nm for f=1 kHz. The aging temperatures are
at 340 K.
350.8 K, 341.2 K, 331.0 K and 321.3 K.
d = 14 nm, the amount of the change in C′ and C′′ are B. Change in volume and dielectric permittivity
0.1 % and 3 % for the isothermal aging at 340 K for 20
hours, respectively. Apossible explanationforthe observeddependence of
′ ′′
Thissuggeststhatduringtheisothermalagingprocess C and C on the aging time during isothermal aging is
of a-PS, C′ increases with aging time, whereas C′′ de- providedinthissection. Therealandimaginarypartsof
creaseswithagingtime. Itisimportanttonotethatboth the complex electric capacitance are given as follows:
′ ′′
C and C decrease with increasing aging time for the
′ ′
isothermalaginginpoly(methylmethacrylate)[4,12,13]. C (ω,T,t) = (ǫ∞(T,t)+ǫdisp(ω,T,t))C0(T,t) (1)
It is also reported in the literature that the real part of ′′ ′′
C (ω,T,t) = ǫ (ω,T,t)C (T,t), (2)
disp 0
complex electric capacitances (dielectric constants) de-
creaseswithincreasingagingtime forpolycarbonate[15]
whereǫ∞ is the dielectricconstantatthe highfrequency
and poly(ethylene terephthalate) [16]. The observed in- ′ ′′
limit,and ǫ and ǫ are frequency-dependent contri-
′ disp disp
crease in C in a-PS is different from the decrease ob-
butionstothedielectricconstantduetotheorientational
served commonly for other polymeric systems.
polarizationassociatedwithmolecularmotions. The fol-
Figure 3 shows the aging time dependence of C′ and lowing relations can be derived: ǫ′ = ǫ′disp + ǫ∞ and
C′′ during isothermal aging at various temperatures T ǫ′′ =ǫ′′ . Inthe caseofa-PS,the polarityis veryweak,
a disp
∆(bCet′w(tewe)na3n2d1.∆3KC′a′(ntwd)35a0re.8dKefi)nfoedrdby=∆14Cn′(mtw.)T=hCe′(vtawlu)e−s athpeprreofxoirme;aǫt′deilsypr≪ewǫr∞itteisneaxspected. Thus, Eq. (1) can be
C′(0)and∆C′′(t )=C′′(t )−C′′(0),andthe time t =0
w w w
istheinitialtimeatwhichthetemperatureofthesample C′(ω,T,t) ≈ ǫ∞(T,t)C0(T,t). (3)
reaches the aging temperature. In Fig. 3(a), the value
′
∆C increases monotonically with aging time and the For an isothermal aging process, the density is expected
′
value ∆C at 20 hours decreases with decreasing aging toincreasewithagingtime, andhence the filmthickness
′′
temperature. InFig.3(b),itisfoundthat∆C decreases d decreases on the condition that the area of the film
′′
withincreasingagingtimeandtheabsolutevalueof∆C remains constant. Therefore, this density change causes
at20hoursdecreaseswithdecreasingTabetween341.2K an increase in C′ according to the following rate
′′
and 321.3 K. The relaxation behavior of C for isother-
mal agingat Ta=350.8K appears to be slightly different 1 ∂C′ 1∂d
from that at other Tas lower than 350.8 K. C′ ∂t =−(η+1)d ∂t, (4)
4
1.5 1.6
aging at 340 K 1.4 349.5 K
heat after aging 344.6 K
1.49 cool (ref) Liquid 1.2 339.7 K
heat (ref) 334.8 K
) 1 329.9 K
F
1.48 p 325.2 K
F) ’ ( 0.8 320.4 K
30 /p1.47 ∆C 0.6 315.5 K
1
C’ ( 0.4 1 kHz
1/
1.46 0.2
Glass1
0
Tg 0 0.5 1 1.5 2 2.5 3
1.45 log [t (min)]
w
Glass2
284nm, 1kHz
′
1.44 FIG.5: Timeevolutionofthedeviation∆C observedatvar-
320 330 340 350 360 370 380 390
iousagingtemperaturesfora-PSthinfilmswithd=284nm.
Temperature (K)
Thefrequencyof theapplied electric field is1 kHz. Thehor-
′ izontal axis is thelogarithm of aging time.
FIG. 4: Temperature dependence of the inverse of C for a
constantratemodeobservedat1kHzfora-PSwiththickness
of284nm. Theverticalaxisapproximatelycorrespondstothe
electric permittivity simultaneously for the same sample
volume V.
during the isothermal aging process.
where η is a constant and its value is almost equal to 1
C. Volume relaxation during isothermal aging
for a-PS [12]. Eq. (4) suggests that the decrease in film
′
thickness increases C for isothermal aging.
Figure 4 shows the temperature change in the inverse Asdiscussedintheprevioussection,therealpartofthe
ofC′ observedduringtheconstantratemode. Theverti- complex electric capacitance changes with aging time in
calaxis approximatelycorrespondsto the volume ofthis accordance with the volume change. Figure 5 shows the
′ ′
systemif the area remainsconstant. Therefore,in Fig. 4 agingtimedependenceofC relativetothevalueofC (0)
a temperature dependence of the volume characteristic forthinfilmswithd=284nm. Thehorizontalaxisisthe
′
of amorphous polymers can be observed. As the sample logarithmofagingtime. Figure5clearlyshowsthat∆C
is cooled down from a high temperature to a lower one increases with the logarithmic law with respect to the
through T , the initial liquid state changes to a glassy aging time for the long time region. Further, there is no
g
state (Glass 1) and then the glassy state is converted tendencytosaturateinthistimeregion. Weevaluatethe
into asecondglassystate (Glass2)during anisothermal slope of this aging time dependence using the following
aging. This temperature dependence of volume can typ- equation:
ically be measured using dilatometric measurements for ∆C′(t ) = A˜logt +B (for large t ) (5)
amorphous polymers. w w w
′′
On the other hand, Eq. (2) shows that C includes Here, from the value of A˜, the aging rate of the volume,
′′
two different contributions from ǫ and C . For the
disp 0 A, for thin films of a-PS can be evaluated as follows:
isothermal aging, C is expected to increase with aging
0
time, because the density increases, i.e., the film thick- A˜ 1 d∆C′
ness decreases, as shown above. Therefore, the decrease A = C′(0) = C′(0)dlogt , (6)
′′ w
in C with aging time suggests that the imaginary part
of dielectric constant, ǫ′′ , decreases with aging time whereforagivenfrequencyC′(0)isthevalueofC′ atthe
disp
and that its contribution can overcome the contribution timeatwhichthetemperaturereachestheagingtemper-
fromthe increasein C0. For PMMA, which has a strong ature. Figure 6 shows the temperature dependence of A
polar group in the chain, it has been reported that both for thin films with two different thicknesses d = 14 nm
real and imaginary parts of the dielectric constant de- and 284 nm. In the present temperature range, the ag-
crease with aging time during the isothermal aging pro- ing rate A was found to be larger in d = 284 nm than
cess [4, 6]. in d = 14 nm. In this figure, it is clear that the rate
The results observed in a-PS can be explained as fol- Aincreaseswithincreasingagingtemperatureandobeys
lows: for the isothermal aging process, the decrease in the Arrhenius law: A = A exp(−U/k T), where k is
0 B B
film thickness is observed as the increase in C′, whereas the Boltzmann constant, U is the activation energy and
thedecreaseintheimaginarycomponentofdielectricper- A is a constant.
0
mittivity is observed as a decrease in C′′. Therefore, the It shouldbe discussedwhat is the molecular originas-
presentmeasurement onthe electric capacitanceof a-PS sociated with the volume change during the aging pro-
willprovideinformationonthechangeinvolumeanddi- cess. Below T there should be no contribution due to
g
5
that the isothermal aging increases the density. For the
-6.5 ′
subsequentheating process,∆C changesalongthe path
′
traced by ∆C for the preceding cooling process after
-7.0
′
isothermalaging,andthen∆C reachesamaximumjust
g Ae-7.5 aqbuoenvtelyTade(Screeeasoepsenaptpriraonagclheisn)g. Tzehreo.vaTluheisobfe∆hCav′iosrubcsaen-
lo-8.0 14 nm1, 010 k HHzz be interpreted as follows: the fact that the sample expe-
20 Hz riences aging at T by the way of the preceding cooling
-8.5 284 nm, 1010 k HHzz processismemorizaedwithinthesample,andthememory
10 kHz is recalled during the subsequent heating process.
-9.0 ′′
2.9 3.0 3.1 3.2 The temperature dependence of ∆C is different from
1/T(103K) ′
that of ∆C , as shown in Fig. 7(b). For the cooling pro-
′′
cess from 380 K, ∆C remains almost zero, and then
FIG. 6: Dependence of the logarithm of the coefficient A on ′′
∆C decreaseswithincreasingagingtimefortheisother-
1/T for various frequencies and thicknesses. The values of f ′′
mal aging. ∆C subsequently increases with decreasing
are 20 Hz,100 Hz, and 1 kHz, and thevalues of d are 14 nm
temperatureandreacheszeroat273K.Inthiscase,there
and 284 nm.
′
isalargescatterinthevaluesofC ,becausethethickness
is284nmandthegeometricalcapacitanceC isnotlarge
0
the α-process, and hence it can be expected that the β- enough. Figure 7(d) shows the temperature dependence
′′
process should be the most probable candidate for the of∆C duringtheconstantratemodeford=14nm. For
′′
molecular origin for the physical aging. However, in the d= 14 nm, the scatter of C is suppressed, therefore; it
′′
literature the activation energy for the β-process in at- isclearthatthevalueof∆C reacheszeroat273Kafter
actic polystyrene was estimated to be 38 kcal/mol [17] cooling from Ta. This result suggests that the system is
or 30 kcal/mol [18], which are larger than the activa- rejuvenatedasfarasthe dielectricresponseisconcerned.
′′
tion energy evaluated from the temperature dependence Forthesubsequentheatingprocess,∆C decreasesalong
ofthe aging rateA. Therefore,the presentresultcannot the curve observedduring the preceding cooling process,
be regardedas an evidence that the β-process is directly andreacheszeroaftershowingaminimumjustaboveTa.
′′
associated to the physical aging, although the α-process Because the temperature dependence of ∆C is primar-
′′ ′′
can be excluded from the candidate for molecular origin ily attributed to that of ǫ , it follows that ǫ exhibits
for the physical aging. Probably, the β-process is indi- a memory and rejuvenation effect. A similar effect has
′ ′′
rectly related to the volume change during the physical been observed for ǫ and ǫ in the case of PMMA [4, 6].
aging process. Combining the results observed for ∆C′ and ∆C′′, it
is concluded that the volume of a-PSfilms decrease dur-
ing isothermal aging, and the deviation from the refer-
D. Memory and rejuvenation in thin films ence value is maintained below the aging temperature.
On the other hand, dielectric permittivity also decreases
′ during isothermal aging, and the deviation of the dielec-
Figure 7 shows the temperature dependence of ∆C
and ∆C′′ observed during the cooling process with tric permittivity from the reference value is totally re-
isothermal aging at T and the subsequent heating pro- juvenated at lower temperatures. The existence of the
a
volume change observed in the present measurement is
cessforf=1kHzina-PSfilmswithd=284nm((a),(b))
and 14 nm ((c), (d)). In this case, ∆C′(T) (∆C′′(T)) is consistentwiththe factthatthereareseveralreportsre-
′ ′′ latingtothe changeinvolumeordensitydue tophysical
evaluated as the deviation of C (T) (C (T)) from the
reference values C′ (T) (C′′ (T)) at the same tempera- aging [1]. Based on the volume, the system does not ap-
ref ref
′ ′′ pear to be rejuvenated, however, the dielectric response
ture T. For the reference value C (C ) to the cool-
ref ref
ing process including isothermalaging,we used the data to the ac-electric field is fully rejuvenated.
measured for the preceding cooling process without any In disordered systems, similar memory and rejuvena-
isothermalaging,andforthereferencevaluefortheheat- tion effects are often observed during the aging process.
ing process after the isothermal aging, we used the data In spin glasses,magnetic ac-susceptibility shows a mem-
measured for the preceding heating process. oryandrejuvenationeffectduringtheconstantratemode
Figure 7(a) shows that as the temperature decreases and the temperature cycling mode. A possible mecha-
from 380 K to 340 K, ∆C′ remains almost zero, and the nism for this effect has been extensively discussed by a
deviation ∆C′ increases as the aging time increases dur- number of researchgroups [19, 20, 21, 22, 23, 24, 25].
ing isothermalagingat340 K (See open circles). During In spin glasses, memory and rejuvenation effects have
the cooling process, after the isothermal aging, the de- beeninvestigatedthroughthemeasurementsofmagnetic
viation decreases and then approaches a constant value, ac-susceptibility. A number of experiments clearly show
but not zero. As a result, most of the deviation ∆C′ in- theexistenceofastrongrejuvenationeffectinagingphe-
duced during the isothermal aging remains even at 273 nomenathroughtheso-calledtemperature-cyclingmode,
K. This result is thought to be associated with the fact where the aging temperature is maintained at T for the
1
6
35
1.0 (a) 1kHz, 284nm (c) 1kHz, 14nm
30
0.8 25
rejuvenation
∆C’ (pF) 00..46 ∆C’ (pF) 1250
10
aging
350.8K
0.2 cool 5 cool:
heat heat:
0 0
280 300 320 340 360 380 280 300 320 340 360 380
Temperature (K) Temperature (K)
0.2 0.5
(b) 1kHz, 284nm (d) 1kHz, 14nm
0 0
-0.2 aging
-0.5
F)-0.4
2C" (10p--00..86 rejuvenation ∆C" (pF)--11..50
∆
-2.0
-1.0
cool 350.8K:
-1.2 heat -2.5 cool:
heat:
-1.4 -3.0
280 300 320 340 360 380 280 300 320 340 360 380
Temperature (K) Temperature (K)
′ ′′ ′ ′′
FIG. 7: Temperature dependence of the deviation ∆C (∆C ) of the component of the complex electric capacitance C (C )
from the reference values observed for the cooling process including at an isothermal aging at 350.8 K and the subsequent
heating process for thin films of a-PS with d = 14 nm and f = 1 kHz((a) and (b)) and 100 Hz((c) and (d)).
first and third stage and at T (smaller than T ) for the are measured simultaneously during the isothermal
2 1
second stage. At the beginning of the second stage of aging process, it can be expected that for spin glasses
the temperature-cyclingmode,theimaginarypartofthe the magnetic ac-susceptibility will show a rejuvenation,
′′
magneticac-susceptibilityχ returnstotheinitialvalue whereas the magnetization is not rejuvenated.
ac
′′ ′′
for χ at the beginning of the first stage, although χ
ac ac
decreases during the first stage. However, it should be
noted here that the magnetic ac-susceptibility is associ-
ated with a time scale, defined by tω = 2π/ω (where ω IV. SUMMARY
is the angularfrequency ofthe ac-magneticfield). There
is a relationship between the time scale and the length
Herein, we investigated the aging dynamics for thin
scale [24], therefore, the magnetic ac-susceptibility is as-
films of atactic polystyrene through measurements of
sociated with the length scale ξ(t ). The experimental
ω complex electric capacitance using dielectric relaxation
results suggestthatthe dielectric ac-susceptibility shows
spectroscopy. The results obtained in this study are
a rejuvenation effect, whereas the volume of the system
summarized as follows:
changeswith increasingagingtime andshows no rejuve-
nation. Although these findings appear to be inconsis-
tent, this can be explained as follows. Similar to mag-
1. During the isothermal aging process at a given ag-
netic ac-susceptibility, the dielectric ac-susceptibility is
ing temperature the realpartofthe electric capac-
associatedwith alength scaleξ(t )defined by the angu-
ω itance increases with aging time, while the imagi-
lar frequency ω of the applied electric field. The volume
nary part decreases with aging time.
or density is a macroscopic physical quantity and has a
characteristic length scale significantly larger than ξ(tω) 2. The aging time dependences of the real and imag-
forthepresentfrequencyrange. Thissuggeststhat,even inary parts of the electric capacitance are mainly
if the volume changes during the isothermal aging pro- associatedwiththe changeinvolumeorfilmthick-
cessandthechangeismaintainedatlowertemperatures, ness and dielectric permittivity, respectively.
the dielectric response to the applied electric field is not
influenced by the change in volume. Therefore, the di- 3. Memory effect can be observed for both ac-
electric ac-susceptibility can be rejuvenated during the dielectric permittivity and volume. On the other
cooling process after the isothermal aging process. hand, a strong rejuvenation effect can be observed
If both magnetic ac-susceptibility and a macroscopic for the ac-dielectric permittivity, but not for the
physical quantity such as the remaining magnetization volume.
7
V. ACKNOWLEDGMENTS the Japan Society for the Promotion of Science and for
Exploratory Research (No. 19654064) and Scientific Re-
The authors thank K. Takegawaand Y. Saruyama for search in the Priority Area “Soft Matter Physics” from
usefuldiscussions. This workwassupportedby aGrant- the Ministry of Education, Culture, Sports, Science and
in-Aid for Scientific Research (B) (No. 16340122) from Technology of Japan.
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