Thermal blob

For the tensile blob, thermal blob, and concentration blob we find that the coil accommodates external stress (thermal, concentration, or force) through a scaling transition that leads to two regimes of chain scaling. This directly impacts the free energy of the chain, the mechanical response, and the coil size. 

In this section, we will consider the excluded volume interaction follow-ing a similar scaling approach, rhe main idea is that of a thermal length scale (the thermal blob). On length scales smaller than the thermal blob size the excluded volume interactions are weaker than the thermal energy kT and the conformations of these small sections of the chain are nearly ideal. The thermal blob contains gr monomers in a random walk conformation ... 

The thermal blob size can be estimated by equating the Flory excluded volume interaction energy [Eq. (3.17)] for a single thermal blob and the thermal energy kT. 

In this section, we discuss both good (v > 0) and poor (v < 0) solvents and therefore, use v in the definition of the thermal blob. The above two equations are combined to estimate the number of monomers in a thermal blob... 

The thennal blob size is the length scale at which excluded volume becomes important. For v the thermal blob is the size of a monomer Ht b) and the chain is fully swollen in an athermal solvent [Eq. (3.12)]. For V —b, the thermal blob is again the size of a monomer ( 7- Ri b) and... 

On length scales larger than the thermal blob size in athermal and good solvents, the excluded volume repulsion energy is larger than the thermal energy kT and the polymer is a swollen chain of Njgj- thermal blobs (Fig. 3.14). The end-to-end distance of this chain is determined as a self-... 

The conformation of a single chain in a good solvent (left side) is a self-avoiding walk of thermal blobs while the conformation in a poor solvent (right side) is a collapsed globule of thermal blobs. 

Thermal blobs in a poor solvent attract each other like molecules in a liquid droplet. The shape of the globule is roughly spherical to reduce the area of the unfavourable interface between it and the pure solvent. The volume fraction inside the globule is independent of the number of monomers N and is the same as inside a thermal blob ... 

End-to-end distance of dilute polymers in various types of solvents, sketched on logarithmic scales. In a 0-solvent the thermal blob size is infinite. For athermal solvent and non-solvent the thermal blob is the size of a single monomer. Good and poor solvents have intermediate thermal blob size (shown here for the specific example of equivalent thermal blobs in good and poor solvent. 

Note that the square of the chain interaction parameter z is equal to the number of thermal blobs in a chain z Njgr. 

In solvents near the -temperature, the thermal blob is larger than the chain gr>N meaning z < 1 or T—9 jTexcluded volume interactions are weak. The interaction energy of two overlapping chains is less than the thermal energy kT, so chains can easily inter-... 

Examples of excluded volume and numbers of Kuhn monomers per thermal blob are given in Table 3.1. 

Table 3.1 Number of Kuhn monomers per thermal blob and excluded volume of a Kuhn monomer for polystyrene in various solvents...

Measurement of the temperature dependence of second virial coefficient A2 for polymers with known molar mass M and Kuhn length b allows estimation of the number of thermal blobs per chain A /gj using Eq. (3.109). 

The chain conformation is a self-avoiding walk of thermal blobs, whose size decreases as temperature is raised. 

If the attraction between monomers is stronger than the hard-core repulsion, the excluded volume is negative and the chain collapses. This occurs below the -temperature, and corresponds to a poor solvent. In a poor solvent, the polymer is in a collapsed globular conformation corresponding to a dense packing of thermal blobs. The size of a globule is smaller than the ideal size ... 

What is the size of a thermal blob and the number of monomers in a... 

What is the number of monomers in a compression blob Note Be careful with respect to relative sizes of compression and thermal blobs. What is the free energy of confinement of the chain in a slit ... 

Hint. Recall that the cumulative energy of all excluded volume interactions inside a thermal blob is equal to kT. 

Determine the relation between the chain interaction parameter z [defined in Eq. (3.22)] and the number of thermal blobs per chain N/gr-... 

The effect of this interaction on the conformations of an A chain can be analysed using the scaling approach described in detail in Chapter 3. On small length scales (smaller than the thermal blob size < 7), the excluded olume interactions barely affect the Gaussian statistics of the chain where gj- is the number of monomers in a thermal blob. The thermal blob is defined as the section of the chain with excluded volume interactions of order of the thermal energy ... 

The number of monomers in a thermal blob is very large when the excluded volume is small ... 

If an A chain is smaller than the thermal blob (TVa < A g), its conformation is almost ideal. In a monodisperse melt with Aa = Ab, or in a weakly polydisperse melt, all chains have ideal statistics. On the other hand, strongly asymmetric binary blends of dilute long chains in a melt of short chains with have swollen long chains. The size of these swollen... 

Two-dimensional melts are quite different. The thermal blob for a dilute A polymer in a two-dimensional melt of chemically identical B polymers with excluded area a h /N can be estimated in a similar way. The... 

The number of monomers in a two-dimensional thermal blob is smaller than in the three-dimensional thermal blob. 

The chains in a monodisperse two-dimensional melt are roughly the size of a thermal blob and are therefore barely ideal. The number of the other chains in a pervaded area of a given chain is the product of this area Nb and the two-dimensional number density of chains 1 jNb and is of the order of unity (Pss 1). Thus, chains do not significantly interpenetrate each other in two dimensions. This is the expected result whenever the fractal dimension of the object and the dimension of space are the same. 

Chains are nearly ideal not only at the 0-temperature, but also at temperatures sufficiently close to 9. Recall that for real chains with T 9, the conformations deviate from ideal statistics only on length scales larger than the thermal blob size [Eq. (3.76)]. 

The entire chain is nearly ideal if its size R bN is smaller than the thermal blob size This condition defines the two temperature bound-aries of the dilute 0-regime. 

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