Smectic phases of semiflexible manifolds: Constant-pressure ensemble

We pursue the constant-pressure ensemble approach to elucidate the statistical mechanics of the smectic phases of semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. We use this approach to consider in detail sterically stabilized phases of semiflexible polymers in two-dimensional (2D) smectic systems. For these 2D systems, we obtain the universal constants characterizing the entropic repulsion between semiflexible polymers, such as those in the osmotic pressure $P=\alpha {(k}_B{T)}^{4/3}/{\kappa }^{1/3}(a-a_{\min }{)}^{5/3}$ with $\alpha$ found here to be $\cong 0.432$ (here, a is the smectic phase period, and $a_{\min }$ and $\kappa$ are the polymer cross-sectional diameter and bending rigidity constant, respectively). We address, by numerical simulations and analytic arguments, finite stacks of N semiflexible manifolds, and discuss in detail the practically interesting thermodynamic limit $\overrightarrow{N}\infty .$ We show that the thermodynamic limit is quickly approached within the constant-pressure ensemble: Already from numerical simulations involving just few semiflexible polymers under constant isotropic pressure, one can obtain the infinite 2D smectic equation of state within a few percent accuracy. We use our results to discuss the competition of electrostatic and entropic effects in quasi-2D smectic phases of DNA-cationic-lipid complexes. We use our quantitative results to discuss in detail the elasticity, topological defects, anomalous elasticity, and the effects of externally applied tension in sterically stabilized 2D smectic phases of long semiflexible polymers.