Atomic Force Probe of Mesoscopic Dielectric and Viscoelastic Fluctuations Near the Glass Transition
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glass transition are critically needed to test glass models. In dielectric glass formers, fluctuations in the dielectric constant on the nanometer length scale as a function of time, frequency, field and position can be related to the length scale of cooperativity. Dielectric polarization noise was studied recently in glasses [5]. In order to measure dielectric and viscoelastic fluctuations on a nanometer scale we designed an atomic force probe utilizing a piezoresistive cantilever similar to a non contact mode atomic force microscope (AFM). Preliminary results are suggestive that PVAc fluctuates between solid-like and a liquid like response just below its glass transition. THEORETICAL BACKGROUND How small a sample of structural glass would be required to see the signature of cooperativity and determine its length scale? Just below the measured Tg, most of the material relaxes or reorients much slower than the measurement time scale. Thus only a fraction of the sample of order C'(wo,T) / ,'* (co,T) can reorient during the measurement, where c' (co,T) is the real part of the dielectric constant, F'* (to,T) is the high temperature (T > Tg) dependence of s' extrapolated to T. And only a fraction of order C"((o,T) / ,'*(wo,T) can contribute to £"(co,T) or noise in a band Ato of order co in width. We assume that dipoles re-orient cooperatively on a length scale of typical 453 Mat. Res. Soc. Symp. Proc. Vol. 455 0 1997 Materials Research Society
size ý. In organic structural glasses estimates for ý based on various measurements have been in the range 2-3 um at Tg [6]. These cooperative units may be viewed for illustrative purposes as droplets [7] of typical volume ý3 and dipole moment Pd _ (ý/a)312 Po0 where a is the typical spacing between elementary dipoles which have typical moment Po. Assuming droplets re-orient independently in an applied field, the number of droplets in a sample of volume Q which contribute in Aco is given by: Qe" ((o,T) N(Am)(1)
We note that in any more complex model in which the droplets are not independent [8,9],
N(Awo) would be effectively reduced. When N(A0o) is quite small, approximately 3 [10,8], tell-tale deviations from bulk-like behavior would be expected. Namely fluctuations in C'(co,T) or noise as a function of frequency, time, sample, or thermal cycle would be observed. s (ow,T) may also exhibit fluctuations which would be smaller by approximately '"(CO,T) / E'(ca,T). Thus the sample volume required can be conservatively estimated:
Q_ ((, 3&* T)(2) E"(co, T) For glycerol at T=193K, where '"- 0.1 at 1 kHz, we find a Q - 1 x 10-16 cm 3 , e.g. a cube of about 50 um on a side. At lower temperatures or higher frequencies the volume needed increases, but the dielectric constant decreases as does signal. In polymers such as PVAc the sample volume needed would be even larger. The effective volume probed by our technique turns out to be of this order, see discussion below. EXPERIMENT Since the invention of the atomic force microscope (AFM) 1986 [11], the number of applications is growing r
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