Surface attraction strength

Structural phase diagram of an off-lattice homopolymer with 20 monomers interacting with a continuous attractive substrate. The diagram, which is parametrized by the surface attraction strength Cj and the temperature T, was constructed by means of the information gained from the guantities discussed previously. Stripes separate the individual conformational phases. The thickness reflects the (principle ) uncertainty in the canonical estimation of the location of the transition points and arises from the input of the different quantities investigated for a small system. The conformational phases are discussed in the text. 

Pseudophase diagram of a lattice polymer with 179 monomers as in Fig. Z2, but here parametrized by the surface attraction strength e and the temperature 7. The color encodes the specific-heat profile the darker the color, the larger Its value. From [304]. 

We will now take a closer look at the adsorption transition in the phase diagram (Fig. 13.12) and we do this by a microcanonical analysis [307, 308]. As we have discussed in detail in Section 2,7, the microcanonical approach allows for a unique identification of transition points and a precise description of the energetic and entropic properties of structural transitions in finite systems. The transition bands in canonical pseudophase diagrams are replaced by transition lines. Figure 13.15 shows the microcanonical entropy per monomer s e)=N lng e) as a function of the energy per monomer e=EfN for a polymer with N=, 20 monomers and a surface attraction strength = 5, as obtained from multicanonical simulations of the model described in Section 13.6. 

Table 1. Attractive strength between cationic and ionic surfaces (N/cm2)... 

In general, interaction between particles is regulated by the relationship between the strength of the attractive (or repulsive) forces and gravitational forces. Thus, surface attraction forces can have a negligible effect on larger particles (e.g., granular sucrose). Such effects are evident not only in the powder microstructure and appearance of particles, but also in properties like bulk density, compressibility, and flowability, which can be totally altered. 

When two (or more) adsorbed atoms bond to the same surface atom(s), they experience a repulsive interaction. When two adsorbed atoms bond to two different neighboring metal atoms that share a metal-metal bond, they tend to experience attractive interactions. These two rules can readily be deduced from the Bond Order Conservation principle which indicates that the atom-surface bond strength decreases with an increase in the number of adatoms bonded to the same surface metal atom. This change does not occur linearly with the number of neighboring atoms or molecules, but instead tends to vary exponentially. 

As the force is negative the two surfaces attract each other. The strength as well as the range of the attraction increase with increasing correlation length. 

For example, for g > 3.4, (R ) vanishes at low temperatures, while attains small values at lower attraction strengths g. The vanishing of R ) corresponds to conformations, where the polymer is spread out flat on the surface without any extension into the third dimension. The associated pseudophases are the adsorbed compact (ACl) and adsorbed expanded (AEl) phases. The phases ACl and AEl are separated by a freezing transition. Polymer sfructures in AC 1 are maximally compact at lower temperatures, while AEl conformations are less compact and more flexible but still he rather planar at the surface. 

To parameterize the coarse-grained model to a specific physical realization, one has to tune the interactions, Vwaii, between solid and polymer to reproduce the experimental value of the surface free energy difference. Ay. Once Ay has been obtained via the method described above for a particular strength, Ewaii, of Vwaii, the dependence on the attractive strength of the wall can be obtained via thermodynamic integration [120, 124] ... 

The analysis of the adhesion data thus resolves to that of two curved elastic bodies in contact. The strength of the adhesive junction will be determined By a balance between the surface attractive forces and the bulk elastic forces opposing deformation. Two theories have been proposed to describe such a contact. The first is due to Derjaguin, Muller and Toporov (DMT theory) which was developed for hard materials (E > 10 Nm 2) On the assumption that the deformation is Hertzian and that separation occurs when the contact area is reduced to zero, they derived the following expression for the force of detachment... 

---