Technical Comments

Materials with Negative Compressibilities

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Science  10 Jul 1998:
Vol. 281, Issue 5374, pp. 143
DOI: 10.1126/science.281.5374.143a

Ray H. Baughman et al. studied materials with the seemingly paradoxical property of negative compressibility in one or more dimensions (1). The biological literature is just beginning to recognize that this phenomenon might be occurring when proteins and other biologically important species are subjected to pressure. A recent study by Cleryet al. (2) showed that butyryl cholinesterase went from a native-like structure to a molten globule-like structure when the protein was subjected to pressure (P). This intermediate, on the way to unfolding, has a larger volume than does the native structure. The data, obtained by polyacrylamide gel electrophoresis under P, reveal that the hydrated radius of the molten globule is greater than that of the native enzyme.

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Negative linear compressibilities occurring in certain “rare” crystal phases were described and implications suggested by Baughman et al. (1). This phenomena, however, is also exhibited by a rather wide class of common compounds containing alkyl chains. The crystalline orthorhombic “Rotator-I” (R I) phase of n-alkanes exhibits a significant negative linear isothermal compressibility βL(min) = (1/b)(db/dP) = −1.2 × 10−4 bar−1, with βL(min)/βV = −1.4 and βL(max)/βV = 2.2, (2) yielding a negative area compressibility in the b-c plane. The corresponding thermal expansion coefficient is also negative. The compressibilities, thermal expansion coefficients, and heat capacity are strongly temperature-dependent in the R Iphase; the above-quoted values are for the high-temperature range of the phase. The R I phase is not confined to the pure n-alkanes, but exists over an even wider temperature (T) range in mixtures (such as waxes) (3), as well as derivative molecules containing alkyl chains including long-chain alcohols and olefins (4). TheR I phase lies between the rotationally disordered hexagonal R II phase at higherT and the orthorhombic herringbone crystal phase at lowerT. The R I phase is characterized byT-P–dependent freezing out of the rotational disorder, which leads to these unusual elastic and thermal properties.

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Response: Sirota and King base their comment on the observation of negative linear compressibilities for a rotator phase of C21H44 and C23H48 (1). These properties are “rare” for these n-alkane wax molecules, because the required phases are stable over a narrow T interval (9.2°C and 3.6°C, respectively) close to the melting T, which is a small fraction of the total solid-state stability range (1). In contrast, the phases we described earlier (2) that have negative linear compressibilities are stable over T ranges varying from typically several hundred degrees for the organic phases to nearly 800°C for a ceramic.

The importance of this property observation for the rotator phase is in the mechanism resulting in the reported negative linear compressibility and the possibility of generalizing this mechanism to identify materials useful for applications. The mechanisms we described (2) for obtaining negative linear compressibilities are enthalpic in origin—so they can in principle operate to arbitrarily low T. On the other hand, the presently described mechanism for explaining this property of the rotator phase is entropic, which implies that the negative linear compressibilities are inherently a high T property of the rotator phase.

Our static-lattice, molecular mechanics calculations (3) for odd-carbon n-alkanes show that linear compressibilities are all positive at low T (where entropic effects can be ignored). Each chain in the rotator phase has four nearest-neighbor chains that are slightly closer than the two next-nearest-neighbor chains in a polyethylene-like structure (1,4). We believe that thermally introduced disorder in relative orientation (about the chain direction) pushes apart these nearest-neighbor chains and opens space which is filled by a closer approach of the next-nearest-neighbor chains—thereby providing both positive and negative thermal expansion coefficients. Pdecreases orientational disorder because this disorder increases volume. Thus, a negative linear compressibility appears in the direction that provides a negative thermal expansion. This model correctly predicts the near equality of the ratio of observed (1) thermal expansion coefficients (−1.4) and the ratio of observed linear compressibilities (−1.5) for the two axes orthogonal to the chains in the above rotator phases. Also in agreement with this model, we predict a similar ratio (−1.7). We made this prediction by using the molecular mechanics method to calculate the changes in axial dimensions resulting from misorienting well-separated chains in a defect-free n-alkane lattice (by rotation about the chain axis).

We have used the entropic mechanism concept and observed thermal expansion data to identify materials likely to have negative linear compressibilities. For example, poly(2,5-di-n-dodecyl-1,4-phenylene) shows a large negative thermal expansion coefficient orthogonal to the chains from below room temperature to 190°C, which results from the conformational disordering of the aliphatic side chains (5). Pressure will suppress this thermal disorder, which we predict will provide a negative linear compressibility over a broad temperature range. This mechanically robust polymer conveniently self-assembles (from solution or melt) as oriented films with the desired film-perpendicular side-chain orientation (5), so application prospects exist for both the observed negative thermal expansion and the predicted negative compressibility.

Kornblatt's comment on the reported effect (6) ofP on increasing the hydrodynamic volume of human butyrylcholinesterase (BuChE) is also interesting. This effect appears to be a non-equilibrium transformation that occurs above a critical P for a particular time-scale experiment. Also, the measured hydrodynamic volume of BuChE is a shape-dependent parameter that need not correspond to the conventionally defined volume. Thus, it is not strictly correct to think of this expansion process as resulting from a negative volumetric compressibility. Moreover, it is thermodynamically impossible for a closed system to have a negative volumetric compressibility. This issue of a closed system is important, because there are numerous instances where a material's volume will increase with increasing P because of the intercalation of a component of the P medium. In addition, if one is willing to generalize the concept of compressibility to molecular systems that interact with the P medium, various examples of negative linear compressibilities should be identifiable. One is a polymer-solvent system in which the distance between chain ends increases with increasing P because of a coil-to-rod transformation.

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