Flory parameter, repulsion between

One question that these simulations can address is the relation between different estimates of the incompatibility between polymer species, i.e. How can one identify the mutual repulsion between polymer species parameterized by the product of the Flory-Huggins parameter and chain length, xfV, for a specific microscopic polymer model [65,78] ... 

Depending on the Flory parameter x, there is a particular special temperature T = 6 at X = 1/2, which corresponds to an exact cancellation between steric repulsion and van der Waals attraction between monomers, and thus the chains are nearly ideal. This temperature is known as the collapse temperature or theta temperature [15]. Equation (15.10) for the free energy of mixing is an expression that finds wide use in physical chemistry. A quantitative understanding of hydrophobie eollapse is required to understand the initial stage of protein folding, as proteins are often a finite chain consisting of a 50-300 amino acid residue linear chain, which in many aspects resembles a heteropolymer. 

Here, each component species is specified by index a the first term of the integrand describes the repulsion between a and a beads, whose strength is controlled by the Flory-Huggins parameter/ the second term gives the system a compressibility, which is controlled by the compressibility parameter k. In the framework of the MFA, the coiresponding mean-field density-dependent potential can be written as follows " ... 

An important parameter in the theory of diluted polymers, polymer mixtures, and block copolymers is the Flory-Huggins x parameter, as it determines the propensity of the system to mix or de-mix. In DPD, the x parameter is taken into account by systematically varying the conservative interaction parameter between unlike particles, whilst the repulsion between like particles remains unchanged to maintain a homogeneous compressibility. Hence, for a mixture of A and B particles one has aAA = aBB and aAB = (Iaa + Groot and Warren [24] argued on the basis of the DPD... 

The incompatibility between molecules is described by the product of the Flory-Huggins parameter, %, and the number of segments, N, per molecule. X denotes the strength of repulsion between different segments. The product, XN, parameterizes the repulsion between molecules in a polymer blend or the distinct blocks of the diblock copolymer. 

The molecular weight of the constituent polymer and the solvent influences two important phenomena, namely, the phase separation and the film thickness. Incompatibility between copolymers (A and B) results in the repulsion between the constituent polymers and when this repulsion becomes strong enough, phase separation can be observed, that is, rich micro-domains of one type (for example A) is formed [92]. The state of the phase, as inferred by Leibler [92], is dependent on the volume fraction of the dominating component (A), the product of the number of monomers (N) in the polymer and the Flory parameters, x [93]. The relationship can be expressed as ... 

When the concentration of the free polymer is set equal to zero, the situation corresponds to pure steric stabilization. The free energy of interaction due to the interpenetration of the adsorbed polymer chains has a range of 26, where 6 is the thickness of the adsorbed layer. This free energy is proportional to the quantity (0.5 - x), where x is the Flory interaction parameter for the polymer-solvent system. Thus, a repulsive potential is expected between two particles when x < 0.5 and this repulsion is absent when x = 0.5. For this reason, it was suggested [25] that instabilities in sterically stabilized dispersions occur for x > 0.5, hence for theta or worse-than-theta conditions. However, the correlation with the theta point only holds when the molecular weight of the added polymer is sufficiently high... 

It is clear from Equation (12.10) that when the Flory-Hugging interaction parameter, y, is less than 0.5 - that is, the chains are in good solvent conditions - then will be positive and the interaction repulsive, and wiU increase very rapidly with decreasing h, when the latter is lower than 25. This explains the strong repulsion obtained between water droplets surrounded by PHS chains. The latter are highly soluble in the hydrocarbon medium, and any attempt to overlap the chains results in very strong repulsion as a result of the above-mentioned unfavourable mixing. 

In a poor solvent, one parameter is no longer sufficient and now the three-body terms must be taken into account, not only implicitly but also explicitly. The second basic parameter required to study chains in the vicinity of TF is the repulsive three-body interaction c. The comparison made in Chapter 14 between the Flory-Huggins theory and the continuous model suggests calculating c by the formula... 

The natural approach initiated by the classic woikers (Kuhn, Hetmans, Flory, etc.) and formalized later by Edwards —Is based on the idea of a self-consistent field. We describe it for a typical case where I) all monomers are chemically identical, and 2) the interactions are repulsive and local (no long range forces). We write the interaction between monomers (i) and O ) in the form vT8(xy), where v is the excluded volume parameter defined in eq. (III. 10). This form is adequate for uncharged molecules in semi-dilute (or dilute) solutions with good solvents. 

Because of the liquid-crystal-like order, the viscosity of the block copolymer is usually high and is non-Newtonian with reference to dependance on shear rate. As the repulsive interaction energy or the Flory-Huggins interaction parameter increases, the temperature dependence of viscosity decreases. For styrene-diene polymers, the activation energy of flow in the melt state is similar to that of polystyrene. As the interaction gets smaller the distinction between melt state and disordered state disappears. 

---