Bayer AG, Deutsches Institut fUr Kautschuktechnologie, and Continental AG. References. [1] E. Donth, 1., Non-Cryst Solids 53, 325, (1982). [2] C. Schick, E.
J Phys. IV France 10 (2000)
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Characteristic length of glass transition from calorimetry in different confinements E. Hempel, S. Vieweg, A. Huwe*, K. Otto**, C. Schick*** and E. Donth Fachbereich Physik, Universitat Halle, 06099 Halle (Saale), Germany * Fakultat fOr Physik und Geowissenschaften, Universitat Leipzig, 04103 Leipzig, Germany ** Fachbereich Chemie, Universitat Halle, 06099 Halle (Saale), Germany *** Fachbereich Physik, Universitat Rostock, 18051 Rostock, Germany Abstract. The characteristic length ~a from calorimetry describes the size of subsystems which are statistically independent from environment with respect to Fourier components of entropy fluctuation relevant for the a relaxation [1]. This paper is a review of our results in confined geometries. The lengths are determined for three different geometric situations. 1. Self-organized amorphous mobile layers between crystalline layers in semicrystalline polyethylene terephthalate PET. Parameter: layer thickness [2]. 2. Temperature modulated DSC (TMDSq of the glass former benzoin isobutyl ether (BIBE) in coated pores of different glasses. Structural effects can be separated from the glass transition. Parameter: pore size from 2.0 to 7.5 nm [3]. The characteristic lengths in confined geometries are smaller than in bulk and decrease systematically for decreasing confinement sizes. 3. Determination of the thickness of immobilized layers on spherical fillers in SBR rubbers. This experiment is twofold complementary to the usual experiment in pores: particles instead of pores, and immobilization instead of active response. Parameters: filler size and content, related by a scaling method [4].
1. INTRODUCTION Dynamic glass transition is related to dynamic heterogeneity [5]. Sophisticated experiments try to select sub-ensembles of different mobility [6,7]. A relation of dynamic heterogeneity to a spatial length seems
;a
natural. Such a "characteristic length" [1] can be identified with the average size of a cooperatively rearranging region CRR as introduced by Adam and Gibbs [8]: a CRR is defined as a subsystem which, upon a sufficient thermodynamic fluctuation, can rearrange into another configuration independently of its environment. We assume that the statistical independence can equally well be used for the CRR definition in bulk: and confined geometries for all dimensionalities and connectivities. This definition leads directly [1,9] to a calorimetric fluctuation formula for the average CRR size: Va =;~ kBTiA(lI cv)1 p8r 2 = kBTiAc p l~p8r2 (1) where all important variables on the right-hand side can approximately be determined from differential
=
scanning calorimetry DSC. In Eq. (1),
;a is the size of a CRR, Va = ; ~,
p the mass density, kB the
Boltzmann constant, A(1/cv ) the step height of the reciprocal specific heat at constant volume (approximated by Ac p / c; in this work), and 81'2 is the mean square temperature fluctuation (related to the dynamic glass transition) of one CRR [10,11]. The oTvalues from DSC are corrected for freezing. The oT values from temperature modulated DSC (TMDSC) are determined as dispersion of a Gaussian fit for the imaginary part of isochronous dynamic heat capacity cp" [12]. The details are published elsewhere [13,
;a
3]. For a large number of glass formers the characteristic length is between 1.0 and 3.5 nm with cumulations between 1.0 and 2.0 nm and 2.5 and 3.5 nm [13]. Another way to determine the responsible length scale is comparison with experiments on glass transition in confining geometries. We look for an answer to the question: Does Va. change with lengths D of confined geometries? Calorimetric experiments are presented first on mobile amorphous layers confined inside the stacks of semicrystalline poly(ethy1ene terephthalate) (PET) [2] and second on the molecular liquid benzoin isobutyl ether (BIBE) confined in porous glasses [3]. Third we investigated immobilized polymer interfaces between filler spheres and SBR 1500 rubber [4].
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2. CHARACTERISTIC LENGTH IN AMORPHOUS LAYERS [2]
3
~bulk
range of few nanothickness D in the meters [2J. Quenching the PET melt gives a completely amorphous sample. On the other hand, D can be varied to a certain extent by different crystallization procedures. Applying different temperaturetime programs, semicrystalline structures with different morphologic parameters can be produced in the whole temperature region between Tg and melting temperature
/.
...... 2 tI
'V>
E
e
;a
11 ......................................................
g
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In polyethylene terephthalate (PET) the glass transition can be observed in bulky amorphous regions or, for semicrystalline samples, in mobile amorphous layers with
1
~
Tm' The morphology for definition of D was determined with small angle X-ray scattering (SAXS), DSC, NMR, and Raman spectroscopy [2]. A narrow correla-
O+------T------~----~---
o
1
2
3
morphology D I om
;a
tion between characteristic length and the morphological layer thickness D was obtained for the differently prepared series (Fig. 1). The characteristic length in the mobile amorphous layer is always smaller than in bulk and decreases for smaller D.
Figure 1. Characteristic length ~a from calorimetry as a function of amorphous-layer thickness D for semicrystalline PET prepared by different crystallization regimes (.1, V
,+, ).
3. MOLECULAR LIQUID CONFINED IN POROUS GLASSES [3] The characteristic lengths of the molecular liquid benzoin isobutyl ether (BIBE) confined in porous glasses were also determined by calorimetry. The glasses with pore diameters of 7.5,5.0 and 2.5 nm are commercial products (GeITech). Additionally, a glass with pore diameter of 2 nm was prepared by spinodal decomposition. All porous glasses were coated with dimethyl hexamethyl disilane and dimethyl aminotriethyl silane, respectively. TMDSC experiments were made at a frequency v = Cl) /21C = 16.7 mHz. Surface effects for BIBE are shifted in temperature and can, therefore, easily separated [3J . ...... A correlation between the characteristic length
2
8 10 12 6 pore diameter D I om 4
14
;a and
the pore diameter D was again
obtained (Fig. 2). Note that ;a(D) < D, ;a.(D)
;~ulk, the characteristic lengths begin to decrease at D values larger than ;a in bulk. We think that the optimization of the fluctuating acteristic lengths
pattern for dynamic heterogeneity is disturbed by the confinement. The hard confinement cannot participate at the optimization in the liquid, of course, so that additional free volume is produced leading to smaller cooperativities. -A complementary experimental situation yields lengths of immobilized boundary layers whose thickness is of the same order of magnitude as the characteristic length. Inversely, our results can also be considered as a certain order-of-magnitude confirmation of the characteristic lengths ;acalculated from the calorimetric fluctuation formula (1). Acknowledgements The authors are grateful to DFG Sonderforschungsbereich 418, BMBF, Fonds Chemische Industrie FCI, Bayer AG, Deutsches Institut fUr Kautschuktechnologie, and Continental AG.
References [1] E. Donth, 1., Non-Cryst Solids 53, 325, (1982). [2] C. Schick, E. Donth, Phys. Scripta 43, 423 (1991). [3] E. Hempel, A. Huwe, K. Otto, F. Janowski, K. SchrOter, E. Donth, Thermochimica Acta 337, 163 (1999). [4] S. Vieweg, R. Unger, E. Hempel, E. Donth, 1. Non-Crystal. Solids 235-237, 470 (1998). [5] G. Diezemann, R BOhmer, G. Hinze, R Sillescu,1. Non-Crystal. Solids. 235-237, 121 (1998). [6] U. Tracht, M. Wilhelm, A. Heuer, R Feng, K. Schmidt-Rohr, H.W. Spiess, Phys. Rev. Lett 81,2727 (1998). [7] H. Sillescu, 1. Non-Cryst. Solids 243, 81 (1999). [8] G. Adam, 1.H. Gibbs, J. Chern. Phys. 43, 139 (1965). [9] E. Donth, Relaxation and Thermodynamics in Polymers. Glass transition (Akademie-Verlag, Berlin, 1992). [to] E. Donth, 1. Polym. Sci B34, 2881 (1996). [11] E. Donth, Acta Polymerica 50,240 (1999). [12] 1. Korus, E. Hempel, M. Beiner, S. Kahle, E. Donth, Acta Polymeric a 48,369 (1997). [13] E. Hempel, G. Hempel, A. Hensel, C. Schick, E. Donth, 1. Phys. Chern., in press. [14] E. Donth, Glasiibergang (Akademie-Verlag, Berlin, 1981) p. 111. [15] M. Arndt, R. Stannarius, R Groothues, E. Hempel, F. Kremer, Phys.Rev. Lett 79, 2077 (1997).
