Macromolecules conformational entropy

These two examples show that regular patterns can evolve but, by definition, dissipative structures disappear once the thermodynamic equilibrium has been reached. When one wants to use dissipative structures for patterning of materials, the dissipative structure has to be fixed. Then, even though the thermodynamic instability that led to and supported the pattern has ceased, the structure would remain. Here, polymers play an important role. Since many polymers are amorphous, there is the possibility to freeze temporal patterns. Furthermore, polymer solutions are nonlinear with respect to viscosity and thus strong effects are expected to be seen in evaporating polymer solutions. Since a macromolecule is a nanoscale object, conformational entropy will also play a role in nanoscale ordered structures of polymers. 

The effect of exclusion on the retention volumes of macromolecules was qualitatively explained above. The pioneering work of Casassa [54] has shown that the extent of pore exclusion of macromolecules is controlled by the changes in their (conformational) entropy. The principle is explained in a simplified form in Figure 16.4a through c. A zone of polymer solution with a nonzero concentration travels along a column packed with porous particles. Initially, the concentration of macromolecules within pores is zero (Figure 16.4a). The concentration gradient outside of pore (c > 0) and within pore (c = 0) pulls macromolecules into the pores. 

There is a tendency to equalize the chemical potentials in both volumes. Macromolecules entering the pore lose part of their conformational entropy. 

According to the current state of the theory, the deformation of polymeric networks must be accompanied not only by the intrachain conformational entropy changes but intrachain energy changes which depend on the conformational energies of macromolecules. Therefore, reliable experimental determination of these intrachain energy changes and their interpretation by means of isomeric state theory is of fundamental importance for polymer physics. 

W. L. Mattice, G. Nemethy, and H. A. Scheraga, Macromolecules, 21,2811 (1988). Conformational Entropy Associated with the Formation of Internal Loops in Collagen. 

Using the notation introduced, it is possible to formulate the following result which can be proved analogously to the corresponding result for the model of beads (see Refs.23"2 ). If the macromolecules is in the globular state, i.e. if the fluctuations of the generalized density n(g) are weak, the macromolecular conformational entropy is equal to... 

The above simple model of a steric exclusion mechanism was considered by several authors attempting to describe quantitatively the gel chromatographic separation process. Distribution coefficients were expressed on the basis of the model considerations of the dimensions of both the separated molecules and the pores of gel, as well as of the stochastic model approaches (for reviews see e.g.. Refs. 1, 3-6), and also of the thermodynamic reasoning on the changes of conformational entropy of macromolecules due to their transfer from the interstitial volume into the pores in the course of separation [7]. However, besides the steric exclusion from the pores, at least two other size-based mechanisms are operative in the ideal gel chromatography ... 

The conformational entropy of a macromolecule measures its degree of conformational freedom. It is related to the degree of degeneracy at each energy level of the biomacromolecule and can be estimated from the degree of rotational freedom about the freely rotating bonds of the chain. For a biomacromolecule consisting of n monomers, the number of possible conformations, N can be estimated from the number of possible conformations, g for each monomeric imit by... 

Abe, A., Furuya, H., Shimizu, R. N., and Nam, S. Y., Calculation of the conformation entropies of dimer liquid crystals and comparison with the observed transition entropies at constant volume. Macromolecules, 28, 96-103 (1995a). 

Naoki, M., and Tomomatsu, T., Analysis of melting entropy and effect of volume on the conformational entropy of frawi-polyisoprene. Macromolecules, 13, 322—327 (1980). 

The box-like cell model of a PE star can be considered as a generalization of a classical mean-field Flory approach, which was first suggested to describe the swelling of a polymer chain in a good solvent [90], The Flory approach estimates the equilibrium dimensions of a macromolecule, as a function of its parameters, by balancing the free energy of intramolecular (repulsive) interactions with the conformational entropy loss of a swollen chain. Within the box-like approximation, the star is characterized by the radius of its corona, R (end-to-end distanee of the arms), or by the average intramolecular concentration of its monomers ... 

A theoretical analysis of the effect of counterion localization in a dilute solution of weakly charged branched polyions of different topologies [31-33] and ionic microgels [34, 35], was performed on the basis of a cell model, similar to that used here for a star-like PE. The elastic term in the free energy that accounts for the conformational entropy of a uniformly swollen branched macromolecule, has to be specified depending on the polyion topology. The shape of the cell might also be modified. For example, in the case of a molecular PE brush, a cylindrical instead of spherical cell should be used. 

Conformation of macromolecules in solid state and in solution exhibits both many contingencies and restrictions. Coiled conformation of macromolecules is most appropriate for majority of methods employed for molecular characterization of polymers. Statistical coils of macromolecules in equilibrium exhibit large conformational entropy. Any external intervention that leads to a change in the conformation of macromolecules has to surmoimt considerable resistance, which is cormected with the loss of overall conformational entropy. 

Macromolecules in solution may assmne various shapes for example statistical coils, worm-like, rods or globules. The coiled stracture is most suitable for molecular characterization by hquid chromatography. As indicated in section 11.2.1, polymer coils in solution possess large conformational entropy and any forced change of the coil dimension is accompanied with the entropy alteration. 

In conclusion, large differences exist in the behavior of small molecules and large (chain) macromolecules in the chromatographic systems. These mainly result from substantial role of conformational entropy of macromolecules and are augmented by distinctions in the viscosity, flow patterns, as well as in the mobility (diffusibility) of solutes of different sizes. It is necessary to consider these differences in order to devise the appropriate chromatographic system for efficient HPLC separation of particular polymer samples. 

The adsorption process can be well affected by temperature. Rising temperature as a rale decreases extent of adsorption of small molecules. This is not the general case for macromolecules beeause their conformational entropy strongly depends on temperature. The gain in enthalpy due to adsorption may be exceeded by the large loss of conformational entropy. This could result in the infrequently observed rise of polymer adsorption with increasing temperature. 

It can be concluded that the adsorption processes extensively affect retention volumes in coupled methods of polymer HPLC. Eluent nature (composition) and temperature are the most common tools employed in control of adsorption in the particular polymer - colunm packing system. The thermodynamic quality of eluent likely plays less important role. The statement, which can be formd in the literature ... addition of a nonsolvent to eluent increases polymer adsorption... is misleading. The nonsolvent can be either a desorli or an adsorb for the given polymer so that a nonsolvent present in the solvent mixture can correspondingly either decrease or increase the extent of adsorption of macromolecules. Considerations on the role of conformational entropy of macromolecules in the adsorption processes may help explain some unexpected results in coupled methods of polymer HPLC. 

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