Internal orientations and elastic properties of non-Gaussian nematic polymer network

2012

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The theory presented starts from the model of gas of statistical segments with potential interactions between them. The fact that the system considered is an elastomer is incorporated into the model by constraints imposed on orientations of segments. Constraints are caused by the elastomer structure. The structure is determined by a connection of segments in linear chains, while chains are connected in the network structure. The statistical and thermodynamic description of the system is obtained by use of the conditional optimization of its free energy (Helmholtz function). The Lagrange multipliers for that optimization are calculated by use of cumulants and the multivariate method. In general, results of the theory presented are formulated for any type of potential interactions.

Gas‐Like Theory of Polymer Networks

2012

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Stress–Strain Relation for Polymer Networks Near the Isotropic–Nematic Transition

Jedynak

2013

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A network of polymer chains, which is undergoing an external deformation, is considered. Each of the network chains is linear and consists of segments interacting by nematic potential orienting interactions between segments within a chain and segments of other chains. Interactions are considered in calculations within the limit of the Maier and Saupe molecular mean‐field model. Chains of the network are connected at junctions with arbitrary functionality; this is the number of chains issuing from a junction. This parameter is included in calculations. The network free energy is calculated. Then, formulas for the work of the system elongation and the stress‐strain relation are obtained. This is done for the network, which is elongated uniaxially and in an arbitrary direction to the nematic axis. Parameters used in these formulas are as follows: the network junction functionality, the system thermodynamic temperature, the strength of interactions between segments and the average orientation of the segments within the network. Calculations are performed for the limit of long chains. In the isotropic phase, the elongation work is given by the neo‐Hookean constitutive equation and is an invariant of orientation of the elongation axis. In the nematic phase, that work depends strongly on the relative orientation of the system elongation and the nematic field direction. A formula for the stress of the elongated network is obtained. This formula is described by the following parameters: the network topological structure, the relative orientation of the elongation direction and the nematic field, and the intensity of the nematic molecular mean field.

Stress–Strain Relations for Nematic Polymer Networks with Various Concentrations of Flexible and Stiff Parts

Jedynak

2014

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A polymer network consists of linear chains. Each chain is an alternant sequence of flexible and stiff parts. The stiff parts of all the networked chains interact via nematic potential interactions. The flexible parts do not interact with other parts (flexible or stiff) of the network system. Various concentrations of flexible and stiff parts lend various elastic properties to the network. The influence of these molecular mechanisms on the stress–strain relations of the polymer network near the isotropic–nematic transition is calculated and discussed.