Distance Dependence of Angular Correlations in Dense Polymer Solutions

Wittmer, J. P.; Johner, A.; Obukhov, Sergei; Meyer, H.; Cavallo, A.; Baschnagel, J.

doi:10.1021/ma902299h

Cited by 7 publications

(47 citation statements)

References 20 publications

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“…Summarizing recent theoretical and computational results we have argued in the present contribution that due to the incompressibility constraint both static [80,81,82,83,84,85,86,87,88,89] and dynamical [90,91] correlations of the composition fluctuations, i.e. of the density and displacement fields of marked chains and subchains, must arise for distances r ≫ ξ and for corresponding arc-lengths s ≫ g.…”

Section: Discussionsupporting

confidence: 77%

“…Accordingly, the bond-bond correlation function should reveal a δ (r)-correlation if sampled as a function of the distance r = |r| between bond pairs. This interpretation turns out to be incorrect, however, and we will show that the power law in s simply translates as [87]…”

Section: Distance Dependence Of Angular Correlationsmentioning

confidence: 75%

“…This can be seen by minimizing the Flory-Huggins free energy functional [9,17,107] 15 The only case where the small local chain rigidity qualitatively matters is presented in Sec. 5.4.2 for the bond-bond correlation function P 1 (r) for large distances r ≫ r * between bonds [87]. with respect to the density ρ N ≡ ρ p N / N of chains of length N. The first term on the right is the usual translational entropy.…”

Section: Polydispersitymentioning

confidence: 99%

“…B.5. 39 The complete formula for systems of general rigidity can be recovered by multiplying the final perturbation calculation result with c ∞ as may be seen by scaling considerations [87,89] or by simply comparing the result with the bond-bond correlations obtained using R 2 s . 40 For a general bond vector distribution one may expand B(q) at low momentum as indicated in Sec.…”

Section: Bond-bond Correlation Functionmentioning

confidence: 99%

“…27 numerical results obtained for systems containing Flory-distributed EP. As indicated in the sketch, P 1 (r) is obtained by averaging of all intrachain bond pairs of same distance r. To avoid trivial correlations the second bond l m is outside the subchain between the monomer n and m defining the vector r [87,89]. Model-depending physics not taken into account by theory obviously becomes relevant for short distances corresponding to subchains of a couple of monomers.…”

Section: Distance Dependence Of Angular Correlationsmentioning

confidence: 99%

See 4 more Smart Citations

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

Wittmer

Cavallo

Xu³

et al. 2011

J Stat Phys

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It has been assumed untill very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ξ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances r ≫ ξ . These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.

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Section: Discussionsupporting

confidence: 77%

Section: Distance Dependence Of Angular Correlationsmentioning

confidence: 75%

Section: Polydispersitymentioning

confidence: 99%

Section: Bond-bond Correlation Functionmentioning

confidence: 99%

Section: Distance Dependence Of Angular Correlationsmentioning

confidence: 99%

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Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

Wittmer

Cavallo

Xu³

et al. 2011

J Stat Phys

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Bond−Vector Correlation Functions in Dense Polymer Systems

Semenov

2010

Macromolecules

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It is well-known that homopolymer chains do not exactly follow the Gaussian statistics even in the melt state. In particular, orientations of two bonds l 1 and l 2 of the same chain in a concentrated polymer system are always correlated even when they are separated by a long segment of s . 1 units: AEl 1 3 l 2 ae s = C(s) ∼ 1/s 3/2 . It is important to know how these orientational correlations are distributed in space, i.e. how AEl 1 3 l 2 ae depends on the distance r between the bonds. 1 An unexpected feature is revealed in the present paper: it is shown that the distancedependent bond-vector correlation function K(r) = AEl 1 3 l 2 ae r is extremely sensitive to the definition of r. Depending on the definition, K(r) for r . b (b is the monomer size) can be either significantly lower, or significantly higher than the position-averaged correlator C(s) with s ∼ r 2 /b 2 corresponding to a given distance r. We propose an "invariant" definition of the intrachain orientational correlation function and show that it is related to the formfactor of a single chain. A quantitative link between the orientational and positional correlations in polymer melts is thus discovered. We also have found a quantitative relationship between the intrachain and interchain correlation functions. It is shown that the inter-chain orientational correlation function (for bonds of different chains) is long-range and follows the 1/r 4 scaling law in the case of infinite chains.

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Kinetics of Free-Radical Cross-Linking Polymerization: Comparative Experimental and Numerical Study

et al. 2013

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Modeling free radical polymerization processes in the presence of cross-linkers is a challenging problem that has been addressed using numerous techniques for over more than half a century. However, a model providing a comprehensive description of the phenomenon has not been proposed yet. In this work, we implement a simple free-radical polymerization scheme of a monovinyl (difunctional) monomer and a divinyl (tetrafunctional) cross-linker in a Monte Carlo (MC) scheme, which describes polymer dynamics using a bond-fluctuation model. MC simulations allow us to follow the entire polymerization kinetics and the formation of a percolating network (gel phase) by realistically taking into account diffusion limitations, to extract scaling information at the percolation threshold and to recover the distribution of number of monomer units between two successive fully cross-linked units, from which the extent of swelling can be computed. The predictions of MC simulations are also successfully compared to a kinetic model based on numerical fractionation, with kinetic constants used as fitting parameters. MC data and kinetic simulations are compared to some experimental data on the swelling behavior of polyacrylamide hydrogels and of poly(methyl methacrylate) (PMMA) gels, exhibiting good agreement. We conclude that the proposed MC simulation scheme represents a powerful tool from which precious and experimentally inaccessible information on polymerization processes in the presence of cross-linkers can be extracted.

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Distance Dependence of Angular Correlations in Dense Polymer Solutions

Cited by 7 publications

References 20 publications

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

Bond−Vector Correlation Functions in Dense Polymer Systems

Kinetics of Free-Radical Cross-Linking Polymerization: Comparative Experimental and Numerical Study

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