Phenomenological formulation of the principle of corresponding states for liquids consisting of chain molecules

Carbohydrate Polymers in Amorphous States: An Integrated Thermodynamic and Nanostructural Investigation

The effect of water on the structure and physical properties of amorphous polysaccharide matrices is investigated by combining a thermodynamic approach including pressure- and temperature-dependent dilatometry with a nanoscale analysis of the size of intermolecular voids using positron annihilation lifetime spectroscopy. Amorphous polysaccharides are of interest because of a number of unusual properties which are likely to be related to the extensive hydrogen bonding between the carbohydrate chains. Uptake of water by the carbohydrate matrices leads to a strong increase in the size of the holes between the polymer chains in both the glassy and rubbery states while at the same time leading to an increase in matrix free volume. Thermodynamic clustering theory indicates that, in low-moisture carbohydrate matrices, water molecules are closely associated with the carbohydrate chains. Based on these observations, we propose a novel model of plasticization of carbohydrate polymers by water in which the water dynamically disrupts chains the hydrogen bonding between the carbohydrates, leading to an expansion of the matrix originating at the nanolevel and increasing the number of degrees of freedom of the carbohydrate chains. Consequently, even in the glassy state, the uptake of water leads to increased rates of matrix relaxation and mobility of small permeants. In contrast, low-molecular weight sugars plasticize the carbohydrate matrix without appreciably changing the structure and density of the rubbery state, and their role as plasticizer is most likely related to a reduction of the number of molecular entanglements. The improved molecular packing in glassy matrices containing low molecular weight sugars leads to a higher matrix density, explaining, despite the lower glass transition temperature, the reduced mobility of small permeants in such matrices.

A new cell model for equation of state of polyethylene melt and n-alkane

The connectivity of successive carbon atoms in polymer decreases the degrees of freedom, and hence, the external degrees of freedom should correspond only to translational motion. We therefore, introduce a coarse-grained particle of a few successive monomers. A cell model (or the hard core model with attractive potential) for the particles can accordingly be used for the derivation of the equation of state of polymers. Modifying the classical cell model by Lennard-Jones and Devonshire, we construct a new equation of state for polyethylene melt and for liquid n-alkane; the free volume term is modified by using the Sutherland potential instead of the Lennard-Jones potential. The characteristic quantities P*, V*0, and T* in the equation of state are almost independent of temperature; the principle of corresponding state holds well. Since our equation of state contains the external degrees of freedom explicitly, we can evaluate the external degrees of freedom, c, for CH2. The value of c for the coarse-grained particle is equal to 1, and hence the particle is composed of 1/c repeating units. The linear length of the particle evaluated, 4.09 A at 0 K, is consistent with that obtained by neutron and x-ray scatterings.