We develop a model to describe the effect of cell wall ageing on the local expansion rate of tip growing cells. Starting from an exact equation for the stationary age-distribution of the wall material, we propose a generic measure for the local expansion propensity of the wall if the ageing process is described by a constant rate Poissonian decay process. This ageing process may be either interpreted as biochemical in nature describing the finite lifetime of regulatory proteins, or as mechanical in nature describing the gradual "hardening" of the wall through cross-linking or gelation of the wall polymers. In this way we can construct models for tip-growth in which material deposition, evolving wall properties and surface expansion are selfconsistently intertwined. As a proof of principle, we implement our ageing approach in two different idealized models of tip-growth, obtaining the stationary tip shapes as a function of the ageing parameter. In the first, the spatial distribution of delivery of growth material is determined by the local curvature of the cell and the growth mode is orthogonal. In the second, the growth material originates from a Vesicle Supply Center, a point-like representation of the Spitzenkörper as found in fungal hyphae, and the growth mode is isometric.

We explicitly calculate the orientation-dependent second virial coefficient of short charged rods in an electrolytic solvent, assuming the rod-rod interactions to be a pairwise sum of hard-core and segmental screened-Coulomb repulsions. From the parallel and isotropically averaged second virial coefficient, we calculate the effective length and diameter of the rods, for charges and screening lengths that vary over several orders of magnitude. Using these effective dimensions, we determine the phase diagram, where we distinguish a low-charge and strong-screening regime with a liquid crystalline nematic and smectic phase, and a high-charge and weak-screening regime with a plastic crystal phase in the phase diagram.

Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.

We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquidlike with respect to translational degrees of freedom are also isotropic with respect to particle orientation.