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cr becomes lower; however, the contraction at small voltages also becomes more extensive, so that its critical value stays approximately the same.
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* their mean dielectric constant. Such a modification alters estimated voltages negligibly, by ∼2%.
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note
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These estimates are based on direct measurements of membrane capacitance under applied voltage (Refs. 2 73 74 75 76 77). The following argument is also illuminating. Since the lipid is incompressible the elastic capacitor model would require significant stretching of the membrane prior to breakdown (a fractional area increase ΔA/A∼2/3) in order to maintain constant volume. However, experimental studies of mechanical rupture indicate that the stretching preceding breakdown does not exceed 2%-5% (Refs. 2, 44, 76 77 78 79) consistent with 1%-3% thinning.
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52
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22244468487
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note
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As has been shown (Ref. 80), the stretching modulus that Crowley used was significantly underestimated (by almost two orders of magnitude). As a result the critical voltages that he found were well below 1 V.
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53
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0, estimates which are difficult to verify.
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It is more consistent to treat σ as an applied stress, because real bilayers typically attain a tensionless state (Refs. 67 68 81 82 83 84 85). This stress can be created either by mechanical means (e.g., osmotic stress), or by contact between the bilayer and a bulk lipid phase, due to a difference between the chemical potential of lipid in bulk and in the bilayer.
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22244439019
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Similar problems have been considered for various approximations and geometries for both fixed and variable membrane surface charge (Refs. 81, 86 87 88 89 90 91 92).
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