Interplay Between Long-Range And Short-Range Interactions In Polymer Self-Assembly And Cell Adhesion
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...Recently it has been pointed out that there are natural parallels between reversible gelation and glass transition [63] and there is considerable interest in unifying these two classes of disordered materials [64]....
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References
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"Interplay Between Long-Range And Sh..." refers background in this paper
..., 2006; Moore and Kuhl, 2006; Moreira and Marques, 2004; Sain and Wortis, 2004), and suggests a new route to controlling the interactions between surfaces typically achieved by generic physical interactions (Israelachvili, 1992; Hiddessen et al., 2000; Carignano and Szleifer, 2003; Nap and Szleifer, 2005)....
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...The interplay between specific and other generic physical interactions, such as electrostatic, hydrophobic and steric interactions (Israelachvili, 1992), is crucial to the adhesion and signalling between cells and the extracellular matrix, and has been extensively studied by researchers in physiology, biochemistry, biophysics, and bioengineering (Alberts et al....
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16,827 citations
"Interplay Between Long-Range And Sh..." refers background or methods in this paper
...Near the mean-field spinodal γ2(q,−q) can be approximated as γ2(q,−q) = c2 4 ( q2Nb2 − q2mNb2 )2 + 2 (χN)S − 2χN, where χN is the Flory-Huggins interaction parameter between A and B blocks, (χN)S is its value at the spinodal, and c is a parameter independent of N ....
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...It was Flory (1953) who first calculated the amount of crosslinkers that are necessary to generate a macroscopic network (Flory-Stockmayer model) and studied the elasticity of this network (“rubber elasticity” theory)....
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...In the classical model by Flory and Stockmayer (see Flory, 1953), the crosslinked network (e.g., vulcanized rubber) is assumed to be an infinitely large branched tree (without cycles), which is the mean-field limit of the percolation model (i.e., percolation on a Cayley tree)....
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...The polymer solution is treated following the mean-field theory of Flory and Huggins (Flory, 1953) and the reversible gelation is treated as a micellation....
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10,942 citations
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...Such polyfunctional units are interconnected 1An exception is the network generated by topological entanglements, such as in melts of very long polymer chains, or a series of interconnected rings (de Gennes, 1979)....
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...Furthermore, as each crosslinker (multi-functional unit) is surrounded by many monomers, cycle structures are rare, therefore the Flory-Stockmayer model is accurate even near the critical threshold (de Gennes, 1979)....
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10,225 citations
"Interplay Between Long-Range And Sh..." refers background in this paper
...Second, we construct the mean-field phase diagram through a quadratic expansion of the free energy (effective potential) from the Edwards Hamiltonian....
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...A continuum Gaussian chain with length N in an external field V (r) is described by the Edwards Hamiltonian (Doi and Edwards, 1986) h0[R(t)] = 3kBT 2Nb2 ∫ 1 0 [( ∂R(t) ∂t )2 + V (R(t)) ] dt (2.1) where R(t) maps the configuration of the polymer (0 ≤ t ≤ 1 is a parametrization of the polymer chain), and Nb2 is mean square end-to-end distance....
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...A continuum Gaussian chain with length N in an external field V (r) is described by the Edwards Hamiltonian (Doi and Edwards, 1986) h0[R(t)] = 3kBT 2Nb2 ∫ 1 0 [( ∂R(t) ∂t )2 + V (R(t)) ] dt (2.1) where R(t) maps the configuration of the polymer (0 ≤ t ≤ 1 is a parametrization of the polymer chain),…...
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...Using the Green’s function for Gaussian chains (Doi and Edwards, 1986) we can express the partition function qp as qp = ∫ G(r, r′;N), where G(r, r′;N) satisfies [ ∂ ∂N − b 2 6 ∇2r +W (r) ] G(r, r′;N) = δ(r− r′)....
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7,128 citations