The concentration dependent cooperative friction coefficient of dilute polymer solutions at the theta point

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Rheological, thermodynamic, and structural studies of linear and branched alkanes under shearMolecular dynamics ͑MD͒ simulations of united atom models for alkane melts are compared with a recently developed theory for calculating the memory functions of flexible polymers. The theory is based upon an approximate solution of the diffusion equation without hydrodynamic interactions. The polymer dynamics are described by using time correlation functions which are expressed in terms of a set of equilibrium averages and the approximate eigenvalues and eigenfunctions of the diffusion operator. For flexible enough chains with sufficiently high molecular weight, the hydrodynamic interactions are screened, and the simplified solvent model used by the theory is expected to be adequate. The only parameter not defined by the MD simulations is the bead friction coefficient . In the limit of weak hydrodynamic interactions ͑Rouse dynamics͒, can be determined from the molecular diffusion coefficient by applying the Rouse relation DϭkT/N R . Given this choice of R , the time correlation functions computed from the theory are compared with those obtained directly from the MD simulations. Excellent agreement with the simulations is found for all correlation functions and all times for the decane dynamics, provided the theory employs one scale factor to increase R and, hence, to compensate for the inadequacy of the Rouse relation. The same picture holds for hexadecane and triacontane (C 30 H 62 ͒ but with smaller scale factors. Scaling becomes unnecessary for C 44 H 90 which is long enough for the crossover to Rouse dynamics for D to be almost complete. Very good agreement ͑after appropriate scaling of R ͒ also emerges between theory and simulations for several branched alkanes with carbon numbers C 25 -C 30 . Computations for hexadecane at different temperatures show that the scale factors may be weakly temperature dependent.

Section: Discussionmentioning

confidence: 99%

“…This trend is expected based on the theory of hydrodynamic screening. 22,[37][38][39] Indeed, the bead friction coefficient used in Fig. 5, which displays the calculations for the C 44 melt, is unscaled from the Rouse value.…”

Section: ͑45͒mentioning

confidence: 99%

Dynamics of linear and branched alkane melts: Molecular dynamics test of theory for long time dynamics

Kostov

Freed

Webb

et al. 1998

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“…This finding is natural given the common utilization of c͓͔ϭc/c* as a reducing variable for the viscosity of polymer solutions. Recent RG calculations by Cherayil and Freed 46 Although there is no fully acceptable theory of the concentration dependence of D c at nonvanishing concentration, we can develop a reasonable phenomenological description based on the observations of Wiltzius et al 12 mentioned above and on the preliminary RG calculations by Shiwa et al 43 We take as the scaling variable X D ϭr D (k D c), where r D is a proportionality factor to be determined from the data. We use the very simple scaling equation following Nystrom and Roots 41 in adapting the scaling form from Shiwa 44 to give the approximant:…”

Section: Master Curve Describing the Concentration Dependence Of Smentioning

confidence: 99%

Thermal and mass diffusion in a semidilute good solvent-polymer solution

Zhang

Briggs

Gammon

et al. 1999

124

The Soret coefficient S T and collective ͑mass͒ diffusion coefficient D c of polystyrene dissolved in the good-solvent toluene has been measured over a range of concentrations and molecular masses with an optical beam-deflection method. Our measurements indicate that S T scales inversely with the polymer translational diffusion coefficient in dilute solutions, exhibits a power-law scaling with polymer concentration, and an independence of polymer molecular mass in semidilute solutions. These findings are consistent with the known scaling of 1/D c in dilute and semidilute polymer solutions, the relative insensitivity of the thermal-diffusion coefficient D th of polystyrene in toluene to polymer concentration, and the relation S T ϭD th /D c from irreversible thermodynamics. We are able to represent our S T and D c data by theoretically motivated reduced-concentration master curves, but the concentration-molecular mass scaling variables are found to be different for each transport property, a result contrary to theoretical expectations. However, the asymptotic concentration scaling exponents deduced from these data fits are compatible with de Gennes' scaling arguments for D c and with modern estimates of the chain-size exponent for swollen polymers in good solvents.

“…A recent multiple scatteringrenormalization group calculation of the friction coefficient of Gaussian chains at the theta point illustrates the kind of approach that would be required to go beyond the present zeroth order approximation. 14 At time tϩs, then, the position of the monomer segment at is given by…”

Section: ͑9͒mentioning

confidence: 99%

Chain dynamics in steady shear flow

Dua

Cherayil

2000

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Recent experimental measurements of the static and dynamic properties of single fluorescently labeled molecules of DNA in steady shear flow are compared with the predictions of a theoretical model of chain dynamics. The model is based on a set of coupled kinetic equations for the evolution of chain conformations and solvent fluctuations. The polymer is represented as a continuous curve with no excluded volume or hydrodynamic interactions, while the solvent is described by a time and space-varying velocity field. In the absence of constraints that enforce the finite extensibility of the chain at large shear rates, the calculated curves of the normalized dynamic autocorrelation function of the mean extension reproduce the qualitative features of the measured curves, but otherwise deviate significantly from them. We develop an analytically tractable finitely extensible model of the Gaussian chain that is more successful in reproducing the experimental data.