Direct Measurement of the Critical Pore Size in a Model Membrane

Abstract

We study pore nucleation in a model membrane system, a freestanding polymer film. Nucleated pores smaller than a critical size close, while pores larger than the critical size grow. Holes of varying size were purposefully prepared in liquid polymer films, and their evolution in time was monitored using optical and atomic force microscopy to extract a critical radius. The critical radius scales linearly with film thickness for a homopolymer film. The results agree with a simple model which takes into account the energy cost due to surface area at the edge of the pore. The energy cost at the edge of the pore is experimentally varied by using a lamellar-forming diblock copolymer membrane. The underlying molecular architecture causes increased frustration at the pore edge resulting in an enhanced cost of pore formation.Nucleation and growth occurs in a variety of physical systems where there is a phase transition. Crystallization of ice, the formation of micelles in solution, and the growth of diamonds from vitreous carbon are all systems where a nucleus can form and then either grow or shrink depending on its size [1]. In crystallization, for example, there is a trade-off between the volumetric free energy contribution which favors the crystalline phase, and the surface area dependent cost of the interfacial tension between the two phases which favors a single liquid phase [2]. By examining the free energy cost of creating a nucleated phase with radius r, the critical radius r c can be derived from classical nucleation theory. For a nucleus with r < r c , the nucleated phase is unstable to fluctuations, while for r > r c the nucleated phase is energetically favorable and the nucleus can grow. The same physics governs diverse phenomena including bubble nucleation of false vacuum states in inflationary cosmology [3], as well as many biologically important processes such as amyloid-beta protein aggregation [4,5], microtubule growth [6], and pore formation in cell membranes [7]. Membrane pores can be created by pathogenic bacteria to invade target cells [8], and play an important role in many biological processes such as mechanical force transduction [9] and water permeability of biological membranes [10]. In this letter we focus on pore formation in a membrane.For the nucleation of a pore in a membrane, there is a balance between two competing effects. First, there is an energy cost of having an interface between the membrane and its surrounding phase. Because the presence of a pore removes interface, this reduces the interfacial energy cost. Opposing this effect is the energetic cost of creating an edge around the perimeter of the pore. The stability and growth of pores depends on the relative contribution of interface reduction compared to the edge cost. The free energy cost of creating a pore in a membrane which has two surfaces with interfacial tension γ is given by [11] ∆G(r) = 2πrΓ − 2πr 2 γ,where Γ is the edge tension (or line tension) of the pore: the free energy cost per unit length of creating interface at t...

Dissipative particle dynamics simulation of critical pore size in a lipid bilayer membrane

“…The growth of supercritical pores proceeds in a roughly exponential fashion, in agreement with the findings for homopolymer films in [1]. For very large times ( t > 1000), the pore approaches the order of the simulation box, and so begins interacting with itself across the periodic boundary, resulting in slower growth.…”

“…The subcritical pore, which closed around t = 400, yielded a stable membrane for the remainder of the simulation. The observed critical ratio 1.34 < r c / h < 1.47 is larger than the ratio r c / h = π /4 derived by Ilton et al [1] for a homopolymer film, suggesting an additional free energy cost for pore formation due to the lipid structure. Note that we define the ratio in terms of the initial size r 0 , meaning it is possible a pore which evolves to be smaller than the critical radius may still expand as t → ∞.…”

“…The curvature of the membrane around the lip of the pore decreases with the membrane width h ; increasing the thickness should decrease the energy cost of pore formation, thereby increasing the critical radius r c . It was shown in [1] that for a homogeneous film, where the free energy cost of pore formation is derived entirely from edge tension, the scaling should be linear as r c = hπ /4. To examine this scaling for the simulated lipid membrane, we changed the membrane thickness by altering the number of particles per lipid tail.…”

“…The liquid polymer films of [1] are easily observable via traditional microscopy techniques due to their large size (the thinnest homopolymer film studied was approximately 100 nm thick, with most films of the order of 1 μm). By contrast, a typical lipid membrane, as might be found in a biological cell, is much smaller (approx.…”

Thermocapillary approaches to the deliberate patterning of polymers

“…As it stands, however, the ability to generate subwavelength 1 or 2D patterns without the need for pulsed laser systems or immersion optics is highly attractive. Further, the CNT dewetting has already been applied to the device‐level fabrication of all‐semiconductor CNT transistor architectures, and the laser‐induced FLaSk approach has recently been employed in single dot exposures by Dalnoki‐Veress and coworkers as a means to generate controlled disturbances on polymer thin films to establish initial conditions for the study of smoothing/dewetting behavior …”