Interpenetration depth

From the modelling results for bilayers composed of unsaturated lipids one can begin to speculate about the various roles unsaturated lipids play in biomembranes. One very well-known effect is that unsaturated bonds suppress the gel-to-liquid phase transition temperature. Unsaturated lipids also modulate the lateral mobility of molecules in the membrane matrix. The results discussed above suggest that in biomembranes the average interpenetration depth of lipid tails into opposite monolayers can be tuned by using unsaturated lipids. Rabinovich and co-workers have shown that the end-to-end distance of multiple unsaturated acyl chains was significantly less sensitive to the temperature than that of saturated acyls. They suggested from this that unsaturated... 

The average monomer interpenetration depth of segments on the interdiffusing chains, jc(0, is obtained from an integration over the Gaussian segment density profiles of the inter-diffused minor chain population,(2i) such that... 

Usually, in numerically simulated dynamic systems, such as multistory buildings under earthquake excitations, structural impact is considered using force-based methods, also known as penalty methods. These methods allow relatively small interpenetration between the colliding strucmres, which can be justified by the local deformability at the point of impact. The interpenetration depth is used together with an impact stiffness coefficient, which represents an impact spring, to calculate the impact forces that act on the colliding structures and push them apart. 

Based on the mathematical relation between the impact force and the interpenetration depth, the impact models can be classified as linear and non linear models. Moreover, some models assume that an impact dashpot acts in parallel to the contact spring in order to take into account the energy that is dissipated during an impact (Polycarpou and Komodromos 2010). 

Intuitively the toughness of an interface would be expected to be related to the depth of interpenetration of the chains. Wool [32] argues that the fracture energy, r, for chain disentanglement at least, is proportional to the square of the interface thickness, which, via Eqs. 36 and 37, gives ... 

Total interpenetration of chains (X approaches Rg) is not necessary to achieve complete strength when M > M and x < 7). However, a word of caution while complete strength may be obtained in terms of critical fracture measures such as G c and A lc, the durability, measured in sub-critical fracture terms, such as the fatigue crack propagation rate da/AN, may be very far from its fully healed state at r. We have shown that while the weld toughness A lc increases linearly with interdiffusion depth X as K f. X, the fatigue crack propagation behavior of partially healed welds behaves as [1]... 

The diffusion theory states that interpenetration and entanglement of polymer chains are additionally responsible for bioadhesion. The intimate contact of the two substrates is essential for diffusion to occur, that is, the driving force for the interdiffusion is the concentration gradient across the interface. The penetration of polymer chains into the mucus network, and vice versa, is dependent on concentration gradients and diffusion coefficients. It is believed that for an effective adhesion bond the interpenetration of the polymer chain should be in the range of 0.2-0.5 pm. It is possible to estimate the penetration depth (/) by Eq. (5),... 

There are several methods available to probe the actual interphase to demonstrate the existence of interpenetrating networks directly. Among these techniques are depth profiling by SIMS (secondary ion mass spectrometry) or SNMS (sputtered neutral mass spectrometry), and the use of X-ray photoelectron spectroscopy (XPS) depth profiling or Auger electron spectroscopy (AES) depth profiling. 

Over the last 10 years there have been a large number of experimental, theoretical and numerical simulations on the properties of polymer brushes. The static properties of polymer brushes are now very well understood and have been reviewed extensively elsewhere [26-29]. In this article I will concentrate on more recent results for polymer brushes in a shear flow. Accordingly, the next section on the static properties will be brief. In Section III, the hydrodynamic penetration depth for the solvent into the brush will be discussed for shear flow past the brush and for two surfaces approaching each other. In Section IV, the normal and shear forces between two surfaces bearing end-grafted chains will be discussed. Two processes, interpenetration and compression, are found to occur concurrently. The origin of the reduced friction observed in recent SFA ex-... 

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