Adsorption of Single Chains

1 Copolymer Localization on Selective Liquid-Liquid Interfaces 

N (the number of repeating units in the chain) and the block size M (the number of consecutive monomers of the same kind) as well as the selectivity parameter/, that is, the energy gained by a monomer when in the more favorable solvent. 

For / smaller than a critical value/c, the interface is too weak to affect the polymer so that the macromolecule conformation is identical to that in the absence of an interface 

For/ /c, the copolymer is captured by the interface yet is not strongly deformed (weak localization) 

For X — Xoo /c. the interface is strong enough to induce a perfect flattening of the copolymer so that all the monomers are in their preferred environment (strong localization) (cf. Fig. 7b) 

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While the static aspects of the adsorption of single chains at walls have been studied for a long time [2], the dynamic properties of adsorbed polymers have received much less attention [30-32]. Most work considers the kinetics of either adsorption or desorption of polymers at a solid surface [31], or the... 

It should be also mentioned that a lot of insight and information regarding the adsorption of single chains on a solid substrate can be gained from the PDFs of the various building units, trains, loops, and tails that an adsorbed chain is formed of. In the literature [53] one may verify that the theoretically derived and predicted exponential expression for the PDF of trains appears to comply very well with simulation data. 

Both theories of single-chain adsorption, described above, ignore a very important effect—the loss of conformational entropy of a trand due to its proximity to the impenetrable surface. Each adsorption blob has jb contacts with the surface and each strand of the chain near these contacts loses conformational entropy due to the proximity effect. In order to overcome this entropic penalty, the chain must gain finite energy E er per contact between a monomer and the surface. This critical energy Ecr corresponds to the adsorption transition. For ideal chains Ecr A E. The small additional free energy gain per contact kT6 should be considered in excess of the critical value Ecr,... 

Using this C picture, the elastic force produced by the stretching of a single chain is /ei — FvTb/, the total number of chains per unit area is wo = and among these chains, only a fraction Tb/( tb + ff) are in an adsorbing state. The frictional stress due to the adsorption of polymer chains is given as [48, 65] ... 

Escher and Oliveros systematically studied the effect of various parameters on fragrance adsorption onto fabrics [113], They found that the affinity of fragrance for fabrics is mainly determined by the type of fiber (cotton > polyacrylonitrile) and, to a lesser extent, by the type of single-chain surfactant (cationic > anionic and nonionic). These factors are interdependent (the effect of the type of surfactant on the affinity for polyacrylonitrile is weak). The effect of temperature and of surfactant concentration is less. 

The studies on single-chain adsorption on flat substrates were based on the same models used for the studies of single chains in the bulk, as described above. One issue that was addressed is the competition between adsorptimi, coUapse, and crystallization of tethered single chains [5]. 

Equilibria Competitive adsorption Extent of spatial entanglement Number of bound segments Adsorbed layer thickness Patchiness and bare spots Diffusion of single chains Evolution of structural rearrangements Segment-surface contact Ufe Lateral diffusion Diffusion through adsorbed layers Replacement of one species by another Effect of dynamic entanglement... 

It is of interest to compare the adsorption of long-chain polymers with the adsorption of small molecular solutes. Small molecules adsorb on to a surface only if there is a bulk reservoir with nonzero concentration in equilibrium with the surface. An infinite polymer chain N —> co behaves differently as it remains adsorbed also in the limit of zero bulk concentration. This corresponds to a tme thermodynamic phase transition in the limit N —> co [21 ]. For a finite polymer length, however, the equilibrium behavior is, in some sense, similar to the adsorption of small molecules, and a nonzero bulk polymer concentration is needed for the adsorption of polymer chains on the substrate. For fairly long polymers, the desorption of a single polymer is almost a true phase transition, and corrections due to finite (but long) polymer length are often below experimental resolution. 

Kiillrot, N., Linse, P. Dynamic Study of single-chain adsorption and desorption. Macromolecules 40(13), 4669-4679 (2007)... 

Single chains confined between two parallel purely repulsive walls with = 0 show in the simulations the crossover from three- to two-dimensional behavior more clearly than in the case of adsorption (Sec. Ill), where we saw that the scaling exponents for the diffusion constant and the relaxation time slightly exceeded their theoretical values of 1 and 2.5, respectively. In sufficiently narrow slits, D density profile in the perpendicular direction (z) across the film that the monomers are localized in the mid-plane z = Djl so that a two-dimensional SAW, cf. Eq. (24), is easily established [15] i.e., the scaling of the longitudinal component of the mean gyration radius and also the relaxation times exhibit nicely the 2 /-exponent = 3/4 (Fig. 13). 

At low concentrations, adsorption is a single-chain phenomenon. The adsorption takes place when the enthalpy gain by the monomer-surface contact with respect to the monomer-solvent contact surpasses the loss of the conformational entropy. In a good solvent the adsorption is not likely unless there is a specific interaction between monomers and the surface. At high concentrations, however, interactions between monomers dominate the free energy of the solution. The adsorption takes place when the enthalpy gain by the mono-... 

Real polymer processes involved in polymer crystallization are those at the crystal-melt or crystal-solution interfaces and inevitably 3D in nature. Before attacking our final target, the simulation of polymer crystallization from the melt, we studied crystallization of a single chain in a vacuum adsorption and folding at the growth front. The polymer molecule we considered was the same as described above a completely flexible chain composed of 500 or 1000 CH2 beads. We consider crystallization in a vacuum or in an extremely poor solvent condition. Here we took the detailed interaction between the chain molecule and the substrate atoms through Eqs. 8-10. 

This chapter is concerned with the application of liquid state methods to the behavior of polymers at surfaces. The focus is on computer simulation and liquid state theories for the structure of continuous-space or off-lattice models of polymers near surfaces. The first computer simulations of off-lattice models of polymers at surfaces appeared in the late 1980s, and the first theory was reported in 1991. Since then there have been many theoretical and simulation studies on a number of polymer models using a variety of techniques. This chapter does not address or discuss the considerable body of literature on the adsorption of a single chain to a surface, the scaling behavior of polymers confined to narrow spaces, or self-consistent field theories and simulations of lattice models of polymers. The interested reader is instead guided to review articles [9-11] and books [12-15] that cover these topics. 

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