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85033819661
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An example of the effect of fluctuations is the appearance of an exponential tail in the monomer density profile of a brush of polymers of finite chain length. This exponential tail is particularly important to the study of the forces between two brushes of short chains.
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85033830528
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By using the averaged local monomer density, we implicitly make the assumption that the time scale at which the monomer density fluctuates is much shorter than the time scales typical for the macroscopic flow of the solvent.
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28
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85033823147
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note
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z=h, eliminates the "kink" that appeared in the velocity profile calculated in ref 11. This condition is correct, since a "kink", or the discontinuity, in the first derivative of the velocity would imply a singular viscous force acting upon the fluid elements at the interface.
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30
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85033809846
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note
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The picture that leads to this scaling for the brushes is the following: Each chain is described as a sequence of subunits, called "blobs", and each blob is characterized by the swelling exponent v = 3/5. Of course, it should be kept in mind that a brush formed from polymer molecules of finite chain length deviates to some extent from this picture. It should also be noted that, when chains are stretched by very strong forces, as may be the case when the shear flow is strong, the blob size is determined by the stretching force.
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32
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85033830579
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note
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shear, is linear in γ.
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34
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85033827931
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note
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In this approximation, the effect of the excluded-volume interaction is being neglected.
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35
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85033811171
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note
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Barrat discussed a mechanism in ref 27 for swelling of a brush under shear. However, it can be shown that the "brush swelling" predicted there is an artifact due to an underestimate of the brush thickness in the limiting case of zero shear (Ling Miao, unpublished results).
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36
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36549094371
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