Flexible polymers, interactions with

Fukunaga H, Takimoto J, Doi M A coarse-graining procedure for flexible polymer chains with bonded and nonbonded interactions, / Chem Phys 116 8183—8190, 2002. 

Polymer adsorption fi om solution onto solid particles is often accompanied by particle aggregation or flocculation. In this case, the particle surface and amount of the adsorbed polymer deerease. Evidently, polymer adsorption proceeds by the following mechanism [80] Macromolecules pass from solution to the tmcovered surface and block some surface area of particle. Adsorbed macromolecules can stretch over the free surface if they are flexible. Simultaneously, flocculation proceeds by biparticle coUision when a surface of one particle eovered by polymer interacts with the uncovered surface of another particle. When the particle aggregate is formed, the part of the particle surface between two or more initial particles in aggregate eannot be attacked by macromolecules from solution. It is the inside surface of the... 

L. C. Shanes and B. G. Nickel, Calculation of the radius of gyration for a linear flexible polymer chain with excluded volume interaction, J. Chem. Phys. (to appear). 

Procedure for Flexible Polymer Chains with Bonded and Nonbonded Interactions. 

The Zimm model predicts correctly the experimental scaling exponent xx ss M3/2 determined in dilute solutions under 0-conditions. In concentrated solution and melts, the hydrodynamic interaction between the polymer segments of the same chain is screened by the host molecules (Eq. 28) and a flexible polymer coil behaves much like a free-draining chain with a Rouse spectrum in the relaxation times. 

It should also be noted that ternary and higher order polymer-polymer interactions persist in the theta condition. In fact, the three-parameter theoretical treatment of flexible chains in the theta state shows that in real polymers with finite units, the theta point corresponds to the cancellation of effective binary interactions which include both two body and fundamentally repulsive three body terms [26]. This causes a shift of the theta point and an increase of the chain mean size, with respect to Eq. (2). However, the power-law dependence, Eq. (3), is still valid. The RG calculations in the theta (tricritical) state [26] show that size effect deviations from this law are only manifested in linear chains through logarithmic corrections, in agreement with the previous arguments sketched by de Gennes [16]. The presence of these corrections in the macroscopic properties of experimental samples of linear chains is very difficult to detect. 

To determine A we need to implement the path integration as a numerical path summation. The path integral in Eqs. 23-24 is in fact isomorphic to the configuration integral of a flexible polymer which interacts with the external potential V(r(P)). This analogy can be made more explicit by considering a discrete approximation to the path integral [71]. If the path is cut up into P... 

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