Letter pubs.acs.org/JPCL
Fragility of an Isochorically Confined Polymer Glass Chuan Zhang,† Yunlong Guo,† Kimberly B. Shepard,† and Rodney D. Priestley*,†,‡ †
Department of Chemical and Biological Engineering and ‡Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *
ABSTRACT: We report the effect of isochoric confinement on the dynamic fragility of a polymeric glass-former, that is, polystyrene (PS). Utilizing silica-capped PS nanospheres as a model system, the fictive temperature (Tf) and the isochoric heat capacity (Cv) are measured as a function of diameter via differential scanning calorimetry. By examining Tf as a function of cooling rate for each sample, the isochoric fragility (mv) is obtained, which decreases significantly as the diameter of the nanospheres is reduced from 260 to 129 nm. Hence, the temperature dependence of structural relaxation near the glass transition is weakened with isochoric confinement.
SECTION: Glasses, Colloids, Polymers, and Soft Matter
N
tal16,17 and computational18,19 results have generally supported the notion that confinement of glass-formers with nonattractive interactions leads to a reduction in the isobaric fragility. To date, studies have exclusively measured the nominally isobaric fragility, usually at atmospheric pressure (P), of confined polymer, presumably due to experimental difficulties. However, it is possible to define an isochoric (constant volume) fragility, mv, which may be related to mp via the following relationship:
anoscopic confinement can lead to a dramatic change in the properties of confined polymers. Of particular interest has been the impact of confinement on the glasstransition temperature (Tg) of thin polymer films in both the supported1−4 and free-standing geometries.5−8 For the specific case of polystyrene (PS), the most extensively characterized polymer, Tg has been observed to decrease with confinement for supported films on a noninteracting substrate1−3 and for free-standing films.5,8 The depressed Tg of PS thin films has been purported to be a result of free surface effects that act to locally reduce the requirement for cooperative segmental motion.2,8−11 Consistent with this viewpoint are local direct measurements of a reduced free surface layer Tg2,7 and the observation that PS films with no free surface display no change in Tg with size.3 Because there still remains significant interest and debate about the origins and existence of the Tg-confinement effect for PS thin films,12 one approach to push forward our understanding of the behavior of confined polymers is to investigate other manifestations of the glass transition, for instance, the dynamic fragility. The dynamic fragility index (m) describes how fast dynamics change for glass-forming liquids as Tg is approached.13,14 Mathematically, m is defined as: ⎡ d log τ ⎤ ⎥ m=⎢ ⎢⎣ d(Tg /T ) ⎥⎦ T=T
⎛ ∂ log τ ⎞ ⎛ ∂V ⎞ ⎟ (T = Tg) ⎟ ⎜ mp = mv + ⎜ ⎝ ∂V ⎠T ⎜⎝ ∂(Tg /T ) ⎟⎠ P
when both are evaluated at the same thermodynamic point. The first term on the right-hand side of eq 2, that is, the isochoric fragility, describes the intrinsic effect of temperature on structural relaxation, as volume is held constant. Hence, mv measures how much of the dynamics near the glass transition is governed by thermal activation. The second term on the righthand side of eq 2 describes volume (i.e., congestion) effects on dynamics as temperature and pressure are held constant. If τ is independent of volume at temperatures close to Tg, then mp = mv, which implies that there would be no volume contribution to the temperature variation of structural relaxation. If τ remains invariant as a function of temperature at a constant volume, then mv would be zero, and thus there would be no energetic (thermal) contribution to the temperature variation of structural relaxation. For bulk polymeric materials, mv has not been determined experimentally but rather calculated using PVT data and the appropriate equation of state22 or via cross-
(1)
g
where τ is the relaxation time and T is temperature. The most common experimental method to access m is via dielectric relaxation spectroscopy (DRS). The seminal DRS study on the effect of confinement on isobaric (constant pressure) fragility (mp) in supported (Al-capped) PS thin films was conducted by Fukao and Miyamoto, in which they observed a sharp decrease in mp for film thicknesses
