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7942 |Soft Matter, 2015, 11, 7942--7952 This journal is ©The Royal Society of Chemistry 2015

Cite this: Soft Matter, 2015,

11,7942

Calorimetric evidence for a mobile surface layer in

ultrathin polymeric films: poly(2-vinyl pyridine)

Sherif Madkour,

Huajie Yin,*

Marieke Fu

¨llbrandt

and Andreas Scho

¨nhals*

Specific heat spectroscopy was used to study the dynamic glass transition of ultrathin poly(2-vinyl

pyridine) films (thicknesses: 405–10 nm). The amplitude and the phase angle of the differential voltage

were obtained as a measure of the complex heat capacity. In a traditional data analysis, the dynamic

glass transition temperature T

is estimated from the phase angle. These data showed no thickness

dependency on T

down to 22 nm (error of the measurement of 3 K). A derivative-based method was

established, evidencing a decrease in T

with decreasing thickness up to 7 K, which can be explained by

a surface layer. For ultrathin films, data showed broadening at the lower temperature side of the spectra,

supporting the existence of a surface layer. Finally, temperature dependence of the heat capacity in the

glassy and liquid states changes with film thickness, which can be considered as a confinement effect.

1. Introduction

The characterization of the glass transition temperature, T

,of

ultrathin polymer films has been of great interest due to their

numerous applications in fields like coatings, membranes, and

innovative organic electronics. Scientifically, ultrathin films

provide ideal sample geometry for studying the confinement

eﬀects on the glass transition of polymers as film thicknesses

can be easily tuned by spin coating.

Generally, glass transition

is a topical problem of soft matter research (see for instance

ref. 2–7). Investigations on highly confined systems may help

to evidence the existing of a dynamical length scale

corres-

ponding to the glass transition, which is difficult to measure by

other approaches.

Since the pioneering work of Keddie et al.,

9,10

the thickness

dependence of the glass transition temperature has been con-

troversially discussed in literature. For the same polymer/

substrate systems, divergent results have been published. In a

recent perspective discussion by Ediger et al.,

the progress

made in the last years was discussed (see for instance ref. 12–20).

For polymers supported by a non-attractive substrate (see for

instance ref. 10, 15 and 21–27) a depression of the thermal glass

transition temperature T

with decreasing film thickness is

widely observed. This T

depression is discussed to originate

as a result of a free polymer/air surface having a higher

molecular mobility than the bulk due to missing polymer–polymer

segment interactions and also due to structural differences.

11,15

Recently, optical photobleaching experiments,

14,28

as well as

the embedding of gold nanospheres into a polymer surface,

29,30

provided some evidence for a highly mobile surface layer.

For polymers having a strong interaction with the substrate,

may increase with the reduction of the film thickness.

31–33

These experimental results were explained by the formation of

an adsorbed boundary layer, in which the polymer segments

have a lower molecular mobility; hence a higher glass transition

temperature.

For that reason, attempts are made to correlate

depression or increase of the glass transition temperature with

the interaction energy between the surface of the substrate and

the polymer g

A depression of T

should be observed for

values of g

smaller than a critical value g

, because the

influence of the mobile surface layer should be dominant in

this case. For g

the reduced mobility layer at the substrate

will dominate and an increase of T

should be expected. This

concept was critically considered by Tsui et al.,

with the

conclusion that the interaction energy between the polymer

segments and the surface of the substrate is not the only relevant

parameter. Also the packing of the segments at the interface

might play a role. In general, no correlation between g

and the

change of T

with the film thickness was found.

Nowadays,

there is growing consensus that the T

shifts observed in ultra-

thin films compared to the bulk are related to the combined

influence of the free surface (polymer–air) and the polymer–

substrate interfacial interaction.

Even though the free surface

is assumed to speed up the segmental dynamics, at tempera-

tures near T

, the effect of the polymer–substrate interaction can

either increase or decrease the dynamics, and consequently the

relaxation times of the adjacent polymer segments.

BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87,

D-12200 Berlin, Germany. E-mail: andreas.Scho[email protected];

Fax: +49-30-8104-1617; Tel: +49-30-8104-3384

Stranski-Laboratorium fu

¨r Physikalische und Theoretische Chemie/Institut fu

¨r

Chemie, Technische Universita

¨t Berlin, Straße des 17. Juni 124, 10623 Berlin,

Germany

Received 24th June 2015,

Accepted 26th August 2015

DOI: 10.1039/c5sm01558h

www.rsc.org/softmatter

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Generally, there are two diﬀerent experimental approaches

to investigate the glass transition of ultrathin polymer films. In

the first approach (also called static experiments), the tempera-

ture is ramped and a thermodynamic property (or an associated

quantity) is measured. A change in the temperature depen-

dence of this quantity is interpreted as thermal glass transition,

where a corresponding thermal glass transition temperature

) can be extracted. Examples for these methods are ellipso-

metry,

10,15

DSC

or Flash DSC,

fluorescence spectroscopy,

dielectric expansion dilatometry,

22,23,32

or X-ray reflectivity,

just to mention a few. In the second approach, techniques that

directly explore the segmental mobility, like dielectric (see for

instance ref. 19, 32 and 33) or specific heat spectroscopy

19,39–42

have been employed. In these cases, a dynamic glass transition

temperature is measured which is higher than the thermal one.

So far, all investigations carried out by specific heat spectro-

scopy did not show a thickness dependence of the dynamic

glass transition temperature, even in cases where simultaneous

dilatometric experiments evidenced a decrease of the thermal

glass transition temperature.

A possible reason for that is

discussed in ref. 11. Moreover by employing cooling rate depen-

dent experiments like ellipsometric,

23,25

photobleaching

Flash DSC

experiments it was evidenced that there is a limiting

cooling rate for the depression of the thermal T

. For instance,

for polystyrene the value of this limiting cooling rate was found

to be higher than 90 K min

1

This study focuses on the investigation of the dynamic glass

transition of thin films of poly(2-vinyl pyridine) (P2VP), as

contradicting results exist in the literature. In an X-ray reflec-

tivity study of P2VP films on acid cleaned SiO

surface, the

thermal glass transition temperature T

increases with decreas-

ing film thickness up to 20–50 K compared to the bulk value.

These results are also consistent with more recent data

44,45

and

were explained assuming strong interactions of the polymer

segments with surface of the substrates. Moreover, a similar

behavior was observed for thin P2VP films capped between

aluminum layers in a dielectric study.

Moll and Kumar found

only a small shift in T

for P2VP/ silica nanocomposites.

Holt

et al.

report also a study on P2VP filled with silica nano-

particles. An adsorbed boundary layer around the nanoparticles

with a thickness of ca. 4 nm was found having a two-order of

magnitude reduced mobility compared to the bulk P2VP, hence

a higher glass transition temperature consistent with findings

discussed above. A similar result was reported for poly(vinyl

acetate) filled with silica nanoparticles.

These results are in

contradiction to an investigation of P2VP films spin coated on a

highly doped Si wafer by broadband dielectric spectroscopy

where the dynamic glass transition was found to be independent

of the film thickness. Also semi-isolated P2VP chains adsorbed

on a doped Si wafer seem to resemble bulk like dynamics.

These results are also consistent with data obtained by high

speed chip calorimetry where a thickness independent T

value

for ultrathin P2VP films was found.

Paeng et al. employed

photobleaching techniques to explore the dynamics of thin P2VP

films on the cleaned native surface of a SiO

wafer.

Ahighly

mobile surface layer at the polymer/air interface was evidenced.

However, indications for a reduced mobility layer at the surface

of the substrate were also reported.

Here specific heat spectroscopy is employed utilizing

AC-chip calorimetry

to investigate the dynamic glass transi-

tion of thin P2VP films. These measurements are accompanied

by contact angle measurements in order to quantify the inter-

action of the P2VP segment with a SiO

surface used as

substrate. Additionally, broadband dielectric spectroscopy is

used to measure the molecular dynamics of the bulk material

for comparison.

2. Experimental section

2.1. Methods

Specific heat spectroscopy. Specific heat spectroscopy is

employed using diﬀerential AC-chip calorimetry.

The calori-

metric chip XEN 39390 (Xensor Integration, NL) was used as

measuring cell. The heater is located in the center of a free-

standing thin silicon nitride membrane (thickness 1 mm)

supported by a Si-frame with a window. This nanocalorimeter

chip has a theoretical heated hot spot area of about 30 30 mm

with an integrated 6-couple thermopiles and two-four-wire heaters

(biasandguardheater),asshowninref.53.Pleasenotethatin

addition to the 30 30 mm

hot spot, the heater strips also

contribute to the heated area. A SiO

layer with a thickness of

0.5–1 mm protects the heaters and thermopiles. The thin films

are spin coated over the whole chip area, but only the small

heated area was sensed and considered as a point heat source.

Pictures of the sensor can be found in ref. 41.

In principle the chip itself will contribute to the measured

heat capacity. In the diﬀerential approach to AC-chip calori-

metry, the contribution of the heat capacity of the empty sensor

(without a sample) to the measured signal is minimized. In the

approximation of thin films (submicron), the heat capacity of

the sample C

is then given by

39,40

CS¼io

C2DUDU0

ðÞ

SP0

(1)

where ois the angular frequency and i=(1)

1/2

the imaginary

unit. 

CC

+G/iodescribes the eﬀective heat capacity of the

empty sensor (C

– heat capacity of the sensor; G/iois the heat

loss through the surrounding atmosphere), Sis the sensitivity

of the thermopile, P

is the applied heating power, and DUis

the complex differential thermopile signal for an empty refer-

ence sensor and a chip with a sample, where DU

is the complex

differential voltage measured for two empty sensors. A more

detailed description of the calorimetric chip, its differential

setup and the experimental method can be found in ref. 39.

Absolute values of the heat capacity can be obtained by calibra-

tion procedures.

For the calorimetric measurement, the temperature scan

mode was used. The temperature was scanned using a heat-

ing/cooling rate of 2.0 K min

1

at fixed frequency. After

each heating/cooling run the frequency was changed stepwise

in the range of 1 Hz to 10

Hz. The selected scanning rate

and the used frequency range ensure stationary conditions for

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the measurement.

The heating power for the modulation

waskeptconstantatabout25mW, which ensures that the

amplitude of the temperature modulation is less than 0.5 K

and so a linear regime. It is important to note that the

measurements are carried out in the frame of the linear

response theory. The estimated glass transition temperatures

are dynamic glass transition temperatures and are taken in

the equilibrium state. As discussed in detail in the introduc-

tion this is diﬀerent from the temperature ramping experi-

ments carried out in DSC,

Flash DSC

or ellipsometric

studies.

23,25

The PT-100 of the cryostat was calibrated by measuring

phase transition temperatures for five diﬀerent calibration

substances, covering the whole temperature range of the

calorimeter (173–573 K). The calibration equation obtained

was then used to correct the collected temperature data.

Contact angle measurements. The measurements were

carried out using the automated contact angle system G2 (Kru

¨ss)

employing the static sessile drop method. The used test liquids

were ethylene glycol, formamide, water and diiodomethane.

Usually, 8 drops with a volume of 3 ml were dropped onto the

surface of a thick sample film treated in a similar way as the

thin layers. The mean contact angles were calculated from

the average of at least 6 drops. The data for SiO

were taken

from ref. 41.

Broadband dielectric spectroscopy. For comparison, the

dielectric properties of a bulk sample (50 mm) were measured

by a high resolution Alpha analyzer with an active sample head

(Novocontrol GmbH). The temperature was controlled by a

Quatro cryosystem with a stability of 0.1 K. The sample for

the dielectric measurements was obtained by melting P2VP

between two gold plated brass electrodes (diameter 20 mm).

Fused silica spacers controlled its thickness to be 50 mm.

2.2. Materials and sample preparation

P2VP was purchased from Polymer Standards Services GmbH

(Mainz, Germany) with a M

of 1020 kg mol

1

and a PDI of

1.33. The thermal glass transition temperature is 373 K esti-

mated by Diﬀerential Scanning Calorimetry (DSC, 10 K min

1

second heating run). The selected polymer here is similar

to the material used in ref. 20 and allows therefore a direct

comparison of the dielectric data. For the AC-chip calori-

metry, the sensors were first mounted on the spincoater, a

few drops of chloroform were added in the center, and then

spin coated to rinse dust and organic contaminations. This

procedure was repeated twice, followed by an annealing process

of the empty chip at 473 K in vacuum for two hours to cure the

epoxy resin completely, which is used to glue the chip to the

housing.

P2VP was dissolved in chloroform with diﬀerent weight

percentages. The solutions were spincoated (3000 rpm, 60 s)

onto the central part of the sensors. The film thickness was

varied by adjusting the concentration of the solution. Note that

all spin coating processes were carried out in a laminar flow box

to minimize any possible contamination. Further, the films

were annealed at 398 K (T

ann

g,Bulk

+ 25 K) in an oil-free

vacuum for 48 h, in order to remove the residual solvent and

relax the stress induced by the spin coating procedure.

The thicknesses were measured for films identically pre-

pared on silicon wafers with a native SiO

surface, because the

film thicknesses cannot be directly measured at the sensor.

Assuming that the surface of the silicon wafer has similar

properties as the surface of the sensor, under identical spin

coating and annealing conditions, corresponding film thick-

nesses will be obtained. To proof this assumption in more

detail a XPS study is in preparation. The film thickness dwas

measured by the step height of a scratch across the film down

to the wafer surface by an AFM Nanopics 2100 (see Fig. 1).

Fig. 2 gives the estimated film thicknesses versus the concen-

tration of the solution. A linear dependence is observed, which

goes to the point of origin as expected.

Moreover, the AFM topography image (Fig. 1) reveals no

inhomogeneities and/or dewetting at the surface of the films.

Also, a low surface roughness is observed. The root mean

square (rms) roughness in the central area of the empty sensor

was estimated to be about 3.5 nm.

The roughness of the film

spin coated onto the surface of the sensor is lower and

decreases with increasing film thickness. For a film thickness

of ca. 10 nm, the roughness of the film on the sensor is

comparable with that of a film prepared on a wafer.

Fig. 1 AFM image of a scratch across a P2VP layer with a thickness of

50 nm on a silicon wafer.

Fig. 2 Estimated film thickness d versus the concentration of the solution.

The solid line is a linear regression to the data. The error bar is smaller than

symbols used.

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3. Results and discussion

The result of an AC calorimetry measurement yields a complex

diﬀerential voltage as a function of frequency and temperature,

which is proportional to the complex heat capacity (C

*) of the

film. Here the real part of the complex diﬀerential voltage U

and the phase angle fare taken as measures of C

*. At the

dynamic glass transition, U

increases stepwise with increasing

temperature (Fig. 3a) and fshows a peak (Fig. 3b).

A dynamic glass transition temperature can be determined

as either the half step temperature of U

or as the maximum

temperature of the peak of the corrected phase angle. In the

raw data of the phase angle (Fig. 3b, upper panel), there is an

underlying step in the signal, which is proportional to the real

part. Hence, the phase angle is corrected by subtracting this

contribution. According to eqn (1) and assuming that the

density of the film is the same as in the bulk, the step high

of the heat capacity at the glass transition is given by

CS;Liquid CS;Glass ¼io

C2UR;Liquid UR;Glass



SP0

md(2)

where mis the mass of the film. Therefore, U

R,Liquid

U

R,Glass

should be proportional to the thickness of the film. In

Fig. 4, DU

is plotted versus d. The expected linear dependence

is confirmed. Moreover, the data can be described by a regression

line going through the point of origin. From those results, one

might conclude that the whole sample material on the chip takes

part in the dynamic glass transition and no boundary layer with a

reduced mobility is present.

3.1. Conventional analysis of specific heat spectroscopy data

Fig. 5 gives the normalized phase angle versus temperature for

diﬀerent film thicknesses for a frequency of 160 Hz. For all

values of dthe data collapse into a common curve. This means

that the dynamic glass transition temperature is independent

of the film thickness. Similar results were obtained by AC-chip

calorimetry for PS,

19,39

PMMA,

50,58

poly(2,6-dimethyl-1,5-phenylene

oxide),

polycarbonate

andalsopoly(vinylmethylether).

At the

first glance the results obtained here are in accordance with

the dielectric data given in ref. 20 and 50 but disagree with

findings discussed in ref. 38 and 48.

To analyse the data in more detail, Gaussians were fitted to

the normalized phase angle as depicted in inset A of Fig. 6.

From such analysis, the maximum temperature of the normal-

ized phase angle is estimated at the given frequency and the

relaxation map can be constructed (see Fig. 6). Within the

Fig. 3 Real part (a) and phase angle (b) of the complex diﬀerential voltage

of a thin P2VP polymer film (347 nm) measured at a frequency of 160 Hz.

The contribution of the underlying step in the heat capacity in the raw data

of the phase angle (upper panel) was subtracted from the all over curve

(lower panel).

Fig. 4 DU

versus the film thickness dfor a frequency of 160 Hz. The solid

line is a linear regression to the data. For low film thickness the error is

somewhat larger. Therefore the data points for the lowest film thickness

might deviate slightly from the regression line.

Fig. 5 Normalized phase angle of the complex diﬀerential voltage versus

temperature measured for thin P2VP films at a frequency of 160 Hz for

selected thicknesses of 400, 347, 216, 85, 50, and 22 nm.

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experimental error of 3 K, the data for all film thicknesses

collapse into one chart. As mentioned above, this is in agreement

with AC-chip calorimetry studies on other polymers.

19,39–42,58

The temperature dependence of the relaxation rates can be

described by the Vogel/Fulcher/Tammann (VFT) equation

59–61

log fp¼log f1A

TT0

(3)

where f

and Aare fitting parameters and T

is called ideal

glass transition or Vogel temperature, which is found to be

30–70 K below the thermal T

. For all film thicknesses the data

can be described by a common VFT-fit (see Fig. 6). Due to the

limited frequency range of the specific heat spectroscopy, the

prefactor f

was taken from the dielectric results (see below)

and kept constant during the fit procedure.

In Fig. 6, the data for a bulk sample measured by dielectric

spectroscopy are included as well. Further, the temperature

dependence of these data can be described by the VFT equation

where the estimated value for the Vogel temperature T

is close

to that estimated from the thermal data (see caption Fig. 6).

The dielectric and thermal data overlap more or less, which

is a bit uncommon for most materials. The thermal and

dielectric data usually exhibits a systematic shift, as previously

found for diﬀerent homopolymers,

41,42

and also for low mole-

cular compounds.

The inset B of Fig. 6 compares dielectric data measured for

thin films of P2VP with the VFT fit line extracted from the

specific heat spectroscopy data. The dielectric data are the

averaged data in the thickness range of 172 nm down to

8 nm, taken form ref. 50. The free surface was implemented

by the use of insulating colloids as spacers. For more details see

ref. 50. Both sets of data, where samples have one free surface,

agree nicely with each other and both sets of relaxation have the

same temperature dependence. A similar behaviour should be

expected for mechanical measurements, which are hard to

conduct in the case of ultrathin films.

3.2. Contact angle measurements

To characterize the interaction of the P2VP segments with the

SiO

surface of the substrate contact angle measurements were

carried out. It is assumed that a silicon wafer with a 500 nm

native SiO

layer has the same surface properties than the used

AC-chip. The estimated contact angles obtained for the diﬀerent

test liquids which are summarized in Table 1.

The total surface energy g

Total

of a sample is expressed by

Total

where g

and g

are the dispersive and polar

components of the surface energy, respectively.

63,64

The measured

contact angles y

for the liquid iare related by the Owens/Wendt

theory,

65,66

which is a combination of Young’s relation with Good’s

equation (for details see ref. 67) to the polar and dispersive

components of the surface energies of the solid and liquid by

1þcos yi

ðÞgL;i

2ﬃﬃﬃﬃﬃﬃﬃﬃ

gLW

L;i

q¼ﬃﬃﬃﬃﬃ

qﬃﬃﬃﬃﬃﬃﬃ

L;i

qﬃﬃﬃﬃﬃﬃﬃﬃ

gLW

L;i

qþﬃﬃﬃﬃﬃﬃﬃﬃ

gLW

q(4)

where g

and g

are the dispersive and polar components of the

surface energy of the polymer or the substrate (S = P2VP, SiO

). The

values for the surface tension of the test liquids were taken from

ref. 63. Using at least 3 test liquids, an Owens/Wendt plot accord-

ing to eqn (4) is created and the polar and dispersive components

of the solid surface energy are estimated by linear regression.

Results are presented in Table 2.

The rule of Fowkes

was applied to estimate the interfacial

energy g

between P2VP and SiO

, which reads

gSP ¼gAþgB

ðÞ2gLW

AgLW



2þgP

AgP





(5)

Fig. 6 Relaxation rates versus inverse temperature for diﬀerent film

thicknesses estimated from the normalized phase angle (open symbols):

circles – 405 nm, squares – 349 nm, up sited triangles – 230 nm, down

sited triangles – 216 nm, stars – 150 nm, asterisks – 120 nm, left sited

triangles – 85 nm, hexagons – 50 nm, right sited triangles – 22 nm,

crosses – 10 nm. The solid circles are data from dielectric spectroscopy for

a bulk sample. Lines are fits of the VFT equation to the corresponding data

with following parameters. Dielectric data (dashed line): log(f

[Hz]) =

12, A= 779 K, T

= 315.4 K; thermal data (solid line): log(f

[Hz]) = 12,

A= 774.6 K, T

= 317.8 K. The dotted line gives the thermal glass transition

temperature measured by DSC. Inset (A) gives the normalized phase angle

for a film with a thickness of 347 nm at a frequency of 160 Hz (solid line).

The dashed line is a fit of a Gaussian to the data. The solid line is the

averaged value of the given data points. Inset B compares dielectric data

for ultrathin P2VP films measured with one free surface taken from ref. 50

with the VFT-fit taken from the AC-chip calorimetry. The dielectric data

are averaged data in the thickness range from 172 nm down to 8 nm

because the data for all film thicknesses collapse into one chart.

Table 1 Contact angle values of the test liquids for poly(2-vinyl pyridine).

Data for SiO

were taken from ref. 41. The errors result from the average of

measurements on 6 drops

Water Formamide Ethylene glycol Diiodomethane

P2VP 67.510.9165.510.8146.611.1140.010.91

SiO

61.011.0148.211.0139.010.6128.911.21

Table 2 Total surface energy g

Total

and its dispersive g

and polar g

components for P2VP and the SiO

surface of the silicon wafer

Total

[mJ m

2

[mJ m

2

[mJ m

2

]

P2VP 39.5 29.8 9.7

SiO

47.0 44.6 2.3

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where A and B refer to the substrate and the polymer,

respectively.

Using eqn (5) the total interfacial energy between P2VP and

SiO

is 4.1 mJ m

2

. According to ref. 35 this is a strong

interaction between the polymer segments and the surface of

the substrate. Therefore an adsorbed layer with a reduced

mobility should be formed at the surface of the substrate in

agreement with results published in ref. 48. Likewise for other

polymers, which interact strongly with the substrate, an increase

of the glass transition temperature should be observed. But

however, no change in dynamic T

was observed here by specific

heat spectroscopy. One possible reason for this result might be

the high molecular weight of the used P2VP. As it was shown in

ref. 31 and 71 the formation of the reduced mobility layer

depends on time and the diﬀusive mobility of the polymer

chains. For a high molecular weight the chain mobility is lower

than for a lower one. It might be that under the selected

experimental condition the annealing time above T

was not

long enough to form a reduced mobility at the substrate, which

is thick enough to influence the dynamic glass transition of the

whole film.

Attempts to correlate the change in the glass transition

temperature with the interaction energy between the substrate

and the polymer surface g

are made in ref. 35. In Fig. 7, the

diﬀerence of the glass transition temperature for 20 nm thick

films and the bulk value versus the interfacial energy are plotted

for polystyrene and poly(methyl methacrylate) spin coated on

modified octadecyltrichlorosilane (OTS) surfaces according to

ref. 35. For g

o2mJm

2

a depression of the glass transition

temperatures should be observed while for g

42mJm

2

increase of T

should be observed. In this figure, data for

diﬀerent polymer substrate combinations, with comparable

film thicknesses, taken from the literature, were added.

(A similar figure but with less data points is given in ref. 68

too.) This concept is able to describe the variation of the T

with

interaction energy for polystyrene and poly(methyl methacrylate)

on the modified octadecyltrichlorosilane surfaces. Also for some

other polymers like polycarbonate on SiO

or AlO

x32,41

or poly-

(ethylene terephthalate),

this correlation seems (partially)

valid. However, it is not generically true for all polymer/substrate

combinations.

For instance, for polysulfone, the interaction energy between

the segments and the substrate surface was estimated to be

= 5.45 mJ m

2

, taken from ref. 33. This value is much larger

than the value of polycarbonate/AlO

, where a similar increase

of the glass transition temperature of about 5 K (for a ca. 20 nm

thick film) was found. However, the corresponding point

for polysulfone is located far away from the correlation line

between the polymer–substrate interaction energy and the

change in the glass transition temperature. However, by taking

the Vogel temperature, T

, as a measure for the thermal glass

transition temperature, the correlation between the change in

the glass transition temperature and the polymer–substrate

interaction energy

31,35

seems to be fulfilled.

For poly(vinyl acetate) films prepared on diﬀerent surfaces,

this correlation is found to be invalid as well. Data for polystyrene

samples having diﬀerent molecular weights were also added;

whereas the interaction energy between the AlO

surface of the

substrate and the polystyrene segments is taken from ref. 31.

These data points are located also far away from the correlation

line between the polymer/substrate interaction energy and the

change in the glass transition temperature. The observed depen-

dence on the molecular weight is in contradiction to the assump-

tion that the interaction energy between the polymer segments

and the surface of the substrate is the only parameter, which

determines the value of the glass transition temperature of

ultrathin polystyrene films as well. This regards also the observed

time dependence of the depression of T

In conclusion, the

polymer/substrate interaction energy seems to be not the only

parameter, which is responsible for the change in the thermal

glass transition temperature with the film thickness for ultrathin

films. Packing eﬀects and/or densifications of the reduced mobi-

lity layer at the surface, which can be time and molecular weight

dependent, might also play a role. This is discussed also in detail

in ref. 31.

3.3. Derivative analysis of specific heat spectroscopy data

As discussed above, all AC-chip calorimetry studies on ultrathin

films of homopolymers, including P2VP used in this work

concluded that the dynamic T

is thickness independent, in

many cases, contradicting the findings of other studies using

diﬀerent characterization techniques. For P2VP, one shall

expect to see a rather strong reduced mobile layer as speculated

from the contact angle measurements, shown above. The

reduced mobile layer for this polymer has also been detected

by other methods, e.g. X-ray reflectivity

and diﬀerent BDS

studies.

46,48

On the other hand, also the existence of a high

mobile free surface layer has been evidenced for P2VP.

Fig. 7 Diﬀerence of the glass transition temperature for ca. 20 nm-thick

films and the corresponding bulk value versus the interfacial energy. The

open symbols for poly(methyl methacrylate) (squares) and polystyrene

(circles) are taken together with the (dashed) correlation line from ref. 35.

The grey dotted lines gives DT

= 0 and critical value for g

. The data for

polycarbonate (PC, diamonds) are taken from ref. 32 (AlO

) and ref. 41

(SiO

). The asterisks represent data for polysulfone (PSU) taken from

ref. 33. The value for PET (left pointed triangle) are taken form ref. 69.

The data for poly(vinyl acetate) (PVAC, triangles) prepared on the indicated

surfaces are taken from ref. 70. The values for polystyrene (PS, green stars)

are drawn from ref. 71. P2VP (solid circle) – this work.

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7948 |Soft Matter, 2015, 11, 7942--7952 This journal is ©The Royal Society of Chemistry 2015

To resolve the systematic contradiction of AC-chip calorimetry

from the other characterization method, an advanced analysis

of the calorimetric data might be useful.

From the technical point of view, there are a few problems

with the conventional data analysis of AC-chip calorimetry.

Firstly, the theoretical treatment of the method assumes that

the reference and the sample sensor are identical. In that

theoretical case, one shall expect to see a constant baseline at

zero level for the diﬀerential voltage for all frequencies and

temperatures. Because of the fact that the sensors are not

completely identical, an extra contribution will be added up

to the signal coming from the film. This extra contribution to

the diﬀerential voltage is not large but depends on both

temperature and frequency. It can be ignored for relatively

thick films (450 nm). However, for thinner films, the diﬀerence

between the two empty sensors is in the same order of magni-

tude as the measured U

, which might induce artifacts.

The other problem in estimating the dynamic glass transi-

tion temperature from the maximum position of the phase

angle is related to the fact that the measured phase angle has

also an underlying contribution that is proportional to the step

of the heat capacity.

This eﬀect will not aﬀect the T

peak

position for thick samples. However, for ultrathin films

(o20 nm), the values of the phase angle become small and

comparable to the noise level of the instrument.

Thus, the

correction and estimation of the phase angle cannot be done

unambiguously.

For these reasons here the temperature dependence of the

complex diﬀerential voltage is analysed in more detail for some

selected sample thicknesses, which was investigated with

an optimized sensitivity. First, the sensitivity of the lock-in

amplifier of the AC-chip calorimeter was set to be between two

and three times the value of U

of the sample at 160 Hz and

the corresponding T

g,160 Hz

, to assure an optimal signal and a

reduced noise. Second, pairs of empty sensors were first

measured in the identical frequency and temperature range

as for the samples to obtain the excess contribution of the

sensors. Third, after the measurement of the films spin coated

on one of the analyzed empty sensors, the real part of the

complex voltage obtained for the two empty sensors was sub-

tracted from the corresponding U

recorded for the films. This

procedure leads to a corrected U

Instead of analysing the temperature dependence of the

phase angle, the derivative of the corrected real part of the

complex voltage versus temperature was employed. Since U

changes step-like at the dynamic glass transition, its first

derivative will result in a peak. The temperature of the peak

maximum can be taken as the dynamic glass transition tem-

perature at 160 Hz. The derivative method will also allow

estimating dU

/dTwhich is related to dc

/dTfor both the glassy

and the liquid state. To calculate the derivative of the corrected

real part of the complex voltage was adjacent-point averaged

(over 300 points; for the two thinnest films over 500 points) in

the whole measured temperature range. This will result in a

smoothed signal. To have equidistant points, U

(T) was inter-

polated (1000 points). After that the derivative was calculated.

It is worth to mention that the diﬀerence in the smoothing

methods and parameters was previously reported to result

in about 2 K diﬀerence in the T

values, which is within

the uncertainty of the measurement.

The advantage of this

method is strong when analyzing measurements of ultrathin

films, where the signal is weak and changes of the phase angle

are hardly to detect. For films thinner than 15 nm, one can

usually still see a small step in U

, yet it is not unambiguously

to determine where the step starts and ends. Moreover, in a

first crude approximation the derivative can be considered as a

representation of the relaxation time spectra.

Four new samples were prepared (10 nm, 20 nm, 85 nm and

220 nm) and the measurements were analyzed as described above.

Fig. 8 shows the derivative calculated as described versus

temperature for three diﬀerent sample thicknesses at a frequency

of 160 Hz. For each value of the thicknesses a well-defined peak is

visible indicating the dynamic glass transition. With decreasing

thickness a systematic shift of the dynamic glass transition to

lowertemperaturesisobserved.This shift up to 7 K is essentially

larger than the error of the AC-chip calorimetric measurement.

The derivative method was also applied to the other samples

prepared previously and a dynamic glass transition tempera-

ture at 160 Hz was estimated from the maximum position of

the derivative. These data were plotted in Fig. 9 versus the

thickness of the film. The dynamic glass transition temperature

of the bulk sample is taken as the average value of the dynamic

glass transition temperature for the five samples with the

highest thicknesses.

For small film thicknesses, the value of the dynamic glass

transition is below this average value and further decreases

with decreasing film thickness. Because a decrease of the

dynamic glass temperature is considered as the influence of a

free surface,

this result can be considered as an evidence for a

free surface with a higher molecular mobility from calorimetric

measurements.

It should be shortly summarized why the traditional and the

derivative based data analysis give diﬀerent results. Firstly, in

the phase angle two diﬀerent quantities with well-defined

Fig. 8 Derivative of the corrected real part of the complex diﬀerential

voltage with regard to temperature versus temperature for the indicated

film thicknesses at the frequency of 160 Hz. For sake of clearness the

curves were shifted along the y-scale.

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physical meanings are mixed up, the real and the loss part of

the complex diﬀerential voltage. The correction of the phase

angle for the real part of the complex voltage cannot be done

unambiguously especially for low film thickness as discussed

above. Secondly, the derivative of the real part of the complex

diﬀerential voltage can be considered as an estimation of

the underlying relaxation time spectra.

This means both

quantities weight the underlying dynamics in a diﬀerent way.

This fact is unimportant for thick films but might become

relevant for low film thicknesses. A closer inspection of Fig. 5

that also the phase angle measured for higher thickness seem

to be located at somewhat higher temperatures which is con-

sistent with the derivative analysis.

Some further evidence for a mobile surface layer comes from

the shape of dU

/dT versus temperature. A more detailed

inspection of Fig. 8 reveals that the width of the derivative for

a thin film (see for instance 10 nm) is broader than that

measured for a larger thickness. This fact is illustrated in more

detail in Fig. 10, where the derivative for a 10 nm and a 40 nm

thick film are compared. Therefore, the derivative is normal-

ized with respect to both its intensity and peak temperature.

Fig. 10 reveals that the peak for the 10 nm thick film is much

broader than that for the 40 nm one. Firstly, compared to the

40 nm thick layer, the film with a thickness of 10 nm shows a

considerable broadening at the lower temperature side. In the

sense of distribution of relaxation times, this corresponds to an

increased contribution of relaxation modes having shorter

relaxation times. With decreasing film thickness, the influence

of a surface layer with a higher mobility will increase. There-

fore, in addition to the decrease of the dynamic glass transition

with decreasing film thickness, the broadening of the relaxa-

tion spectra on the low temperature side gives further evidence

for the existence of a surface layer with a higher molecular

mobility at the polymer air interface.

Besides the broadening of the spectra at the low temperature

side for the thin film for the 10 nm thin film there is also

a broadening of the derivative at temperatures above the

dynamic glass transition temperature. This broadening at the

high temperature side of the spectra is due to relaxation modes

having a reduced mobility. As shown by the contact angle

measurements, discussed above, the P2VP segments should

strongly interact with the SiO

surface of the sensor, which

should result in slowing down of the molecular dynamics of the

polymer segments close to the surface. Therefore, the broad-

ening of the spectra at high temperatures is assigned to

polymer segments, which are in interaction with the SiO

surface of the sensor. A corresponding broadening was

observed by dielectric spectroscopy employing nanostructured

electrodes.

A closer inspection of the data for the 10 nm thick

film reveals that there is a small shoulder at TT

Max

=28K

(T= 424 K). This shoulder is found at the same temperature

frequency position, where for the nanocomposites of P2VP with

silica nanoparticles, discussed in ref. 48, the relaxation process

is observed, which was related to the fluctuations of P2VP

segments adsorbed at the surface of the silica particles. This

coincidence provides further evidence that a reduced mobility

layer is formed at surface of the calorimeter chip. Probably, due

to the high molecular weight of the used P2VP, the formation of

this reduced mobility layer will take longer time. Under the

employed experimental conditions, it is likely that the thick-

ness of this layer is small and will not influence the dynamic

glass transition behavior of the whole film. For future work,

additional investigations are planned where the annealing time

and temperature, during film preparation, are varied in broader

ranges. This includes further a variation of the molecular

weight because it was shown for instance that for polystyrene

the change of the glass transition temperature depends on

molecular weight due to a changed adsorption kinetics.

It is well known that the specific heat capacity in the glassy

state has a stronger temperature dependence than in the

liquid,

which means (dc

/dT)

Glass

4(dc

/dT)

Liquid

. Close to

the glass transition c

(T) can be approximated by linear depen-

dencies in both the glassy and liquid state. In the derivative

representation, this is reflected by constant values of the

derivative dU

/dTwhich corresponds to dc

/dTindependent

of temperature below and above the dynamic glass transition.

The inset of Fig. 11 depicts the derivative versus temperature

for a relatively thick film of 347 nm. For this film, which

can be considered as bulk-like, the expected relationship

Fig. 9 Dynamic glass transition temperature measured at 160 Hz versus

film thickness d. The dashed line is the average value of the five data points

with largest thicknesses. Fig. 10 Normalized derivative (dU

/dT)/(dU

/dT)

Max

versus temperature

at a frequency of 160 Hz for a 10 nm (open squares) and a 40 nm

(open stars) thick film.

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(dc

/dT)

Glass

4(dc

/dT)

Liquid

is fulfilled. However, Fig. 11 shows

further that with decreasing film thickness, this relationship

changes. For a film with a 220 nm thickness, (dU

/dT)

Glass

(dU

/dT)

Liquid

holds; whereas for a thinner film with a thick-

ness of 70 nm the relationship is reversed (dU

/dT)

Glass

(dU

/dT)

Liquid

. This is not only observed for the considered

thicknesses, but also for the other thicknesses as well (see Fig. 8

and 10). Obviously, confinement eﬀects influence the tempera-

ture dependencies of the specific heat capacity in the liquid and

glassy state. Such change in the temperature dependence of

specific heat capacity before and after the dynamic glass

transition region was able to be observed at relatively high

thicknesses, above 220 nm in the present study. The critical

thickness is possibly molecular weight dependent, which needs

further quantitative measurements. It was already reported that

for PS with M

= 1400 kg mol

1

, a change in the temperature

dependence of specific heat capacity at the glass transition

occurred from several hundred nm.

In the glassy state, c

(T)

originates from vibrations. The same vibrations are also

responsible for the temperature dependence of the thermal

expansion. The specific heat capacity and the thermal expan-

sion coeﬃcient are linked to each other.

It has been reported

previously that the thermal expansion coeﬃcient in the glassy

state for thin films decreases with the film thickness.

75,76

These findings are quite similar to the results found here for

P2VP. Moreover, quasielastic neutron scattering experiments

for thin films of polystyrene and polycarbonate

77,78

showed that

the mean square displacement hr

idecreases with decreasing

film thickness. Also a direct investigation of the vibrational

density of states in the frequency range of excess vibrations

characteristic for the glassy state (Boson peak) show a decrease

of the intensity of the Boson peak with decreasing film thick-

ness for polystyrene for relatively high thicknesses of

100 nm.

79,80

This behavior is equivalent to a decrease of the

mean square displacement. Using a harmonic approximation

ican be related to a force constant f

by f

B1/hr

A decrease of the mean square displacement can therefore be

explained by an increase of the force constant. This means a

change from a soft to hard potential. Taking as well as

anharmonic contributions into account, the change of the

temperature dependence of the specific heat capacity in the

glassy state might be explained by a hardening of the potential

of the vibrations. However, it is worth to note that the change of

the specific heat capacity in the glassy and liquid state might

also be explained by a three layer model which also applies

here.

To diﬀerentiate between both possibilities, additional

investigations on a broader range of samples and diﬀerent

polymers are required. Such studies are under preparation,

which will also including a more quantitative discussion.

4. Conclusion

Specific heat spectroscopy employing diﬀerential AC-chip

calorimetry in the frequency range from 1 Hz to 10

Hz with

a sensitivity of pJ K

1

was used to study the dynamic glass

transition behavior of ultrathin poly(2-vinyl pyridine) films with

thicknesses from 405 nm down to 10 nm. To characterize

the interaction of the P2VP segments with the surface of the

substrate, contact angle measurements was utilized along with

AFM investigation to study the topology of the films. Broad-

band dielectric spectroscopy was used to obtain the molecular

dynamics for the bulk sample.

AC-chip calorimetry delivers the real part and the phase

angle of the complex diﬀerential voltage as a measure of

the complex heat capacity as function of temperature and

frequency simultaneously. The data were analyzed by two

diﬀerent methods. In a rather traditional data analysis,

the dynamic glass transition temperature is estimated from the

maximum position of the measured phase angle. These data

showed no thickness dependence of the dynamic glass transition

temperature down to ca. 22 nm, within in the error of the

measurement of 3K.Thisresultisinagreementwithdielectric

data obtained for samples having one free surface, yet still in

disagreement to other literature data. Therefore second method

was established which is based on the first derivative of the real

part of the complex diﬀerential voltage with regard to tempera-

ture. These data show a decrease of the dynamic glass transition

temperature with decreasing thickness of about 7 K. This decrease

canbeexplainedasaresultoftheinfluenceofsurfacelayerwitha

higher molecular mobility. Moreover, for thin films the data

showed a broadening at the lower temperature side of the

dynamic glass transition, which can be considered as a further

prove for a surface layer.

Moreover, contact angle measurements showed that the

P2VP/SiO

interaction was rather a strong one, 4.1 mJ m

2

which suggests that an absorbed layer of reduced mobility

should exist at the polymer/substrate interface. An absorbed

layer was evidenced for films below 50 nm, through another

broadening of the peak with the appearance of a shoulder at

the higher temperature side of the spectra that superimposes

with the fluctuations of P2VP segments adsorbed at the surface

of the silica particles, as reported in literature.

Fig. 11 Derivative (dU

/dT)/dversustemperature at a frequency of 160 Hz

for a 220 nm (open diamonds) and a 70 nm (open triangles) thick film. The

inset shows the same for a film with a thickness of 347 nm.

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Finally, evidence was provided the temperature dependence

of the specific heat capacity in the glassy and the liquid state

changes depends on the film thickness. These changes were

observed for relatively high film thickness of some 100 nm and

can be considered as confinement eﬀects. For the glassy state

these changes are in agreement with several neutron scattering

studies and can be explained by a hardening of the potential of

the vibrations, and thus the existence of a reduced mobile layer,

in agreement of the three layer model. Nevertheless additional

investigations are required.

Acknowledgements

The authors gratefully acknowledge the financial support

from the German Science Foundation (Deutsche Forschungs-

gemeinschaft, SCHO-470/20-1 and SCHO-470/20-2) is highly

acknowledged.

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