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1
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0003879578
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Addison-Wesley, Reading, MA
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S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, Reading, MA, 1994).
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(1994)
Statistical Thermodynamics of Surfaces, Interfaces, and Membranes
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Safran, S.A.1
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3
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0345197550
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unpublished results
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L. Ramos, T. C. Lubensky, N. Dan, P. Nelson, D. A. Weitz, unpublished results.
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Ramos, L.1
Lubensky, T.C.2
Dan, N.3
Nelson, P.4
Weitz, D.A.5
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4
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0345629601
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note
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Changes in the materials used had little effect on the experimental results in (3). We used colloidal spheres of diameters 0.98, 0.83, and 1.00 μm, with sulfate groups, sulfate and carboxylate groups, and carboxylate and amine groups, respectively. Electrophoretic velocity measurements confirmed that all types of particles were negatively charged in our experimental conditions. All three samples behaved similarly in the experiments. We also varied the bilayer characteristics through the addition of octanol. Although this co-surfactant is known to alter the curvature-elasticity properties of bilayers, we could not see any qualitative effect on our results at alcohol-to-Triton-X weight ratios ranging from 0 to 0.7. In Fig. 1, the weight ratio DDAB (didodecyl dimethyl ammonium bromide):Triton:octanol was 1:0.37:0.13. The buffer solution contained NaCl at concentrations from 1 to 10 mM, as discussed below.
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5
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0004165558
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Springer-Verlag, New York
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R. B. Gennis, Biomembranes (Springer-Verlag, New York, 1989).
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(1989)
Biomembranes
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Gennis, R.B.1
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9
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0345197548
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note
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0r, and so forth.
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10
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0345629599
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note
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We need not assume the membrane to be impermeable to water; because the bulk salt concentration is assumed the same on both sides, there will be no net osmotic flow.
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11
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0345197547
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note
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+/e). The numbers of individual counterions of each species are not, however, conserved. because neutral +/-pairs can be exchanged with large reservoirs (the bulk solution inside and outside the vesicle) without macroscopic charge separation.
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12
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0344767084
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note
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Poisson-Boltzmann theory is a mean-field approximation. It is well known that correlated fluctuations can cause surprising effects if the counterions are multivalent For example, like-charged parallel plates can have attractive regimes (15, 16), although we are not aware of a similar prediction of repulsion for opposite charges. Correlation effects are generally small if the ions are univalent, as in the experiment of (3). The physical mechanism we present, in contrast, arises already in mean-field theory; it does not rely on any fluctuation effects (nor on finite ion-size effects). Including such effects does not materially change our conclusions (7). Other colloidal forces not included in our analysis (for example solvation forces) are short-ranged; our effect relies on the physics of surfaces when they are separated by more than a nanometer.
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13
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0345197546
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note
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The extent of coverage is not directly measurable, since the degree to which each colloidal sphere is engulfed by membrane is not observed. In addition, the actual situation in Fig. 1 may not be in equilibrium. Our point is simply that our theory explains why the vesicle in Fig. 1 has stopped attracting further colloidal particles.
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15
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36549103137
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L. Guldbrand, B. Jönnson, H. Wennerström, P. Linse, J. Chem. Phys. 80, 2221 (1984).
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(1984)
J. Chem. Phys.
, vol.80
, pp. 2221
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Guldbrand, L.1
Jönnson, B.2
Wennerström, H.3
Linse, P.4
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17
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0344335049
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We thank R. Bruinsma and S. Safran for discussions; J. Crocker, K. Krishana, and E. Weeks for experimental assistance; and J. Nardi for communicating results to us before publication. N.D. was supported in part by NSF grant CTS-9814398; T.C.L, L.R., and D.A.W. were supported in part by NSF Materials Research and Engineering Center Program under award number DMR96-32598 and equipment grants DMR97-04300 and DMR97-24486; P.N. was supported in part by NSF grant DMR98-07156; L.R. was supported in part by a Bourse Lavoisier from the Ministère des Affaires Etrangères de France
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We thank R. Bruinsma and S. Safran for discussions; J. Crocker, K. Krishana, and E. Weeks for experimental assistance; and J. Nardi for communicating results to us before publication. N.D. was supported in part by NSF grant CTS-9814398; T.C.L, L.R., and D.A.W. were supported in part by NSF Materials Research and Engineering Center Program under award number DMR96-32598 and equipment grants DMR97-04300 and DMR97-24486; P.N. was supported in part by NSF grant DMR98-07156; L.R. was supported in part by a Bourse Lavoisier from the Ministère des Affaires Etrangères de France.
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