Macromolecule size

Another kind of situation arises when it is necessary to take into account the long-range effects. Here, as a rule, attempts to obtain analytical results have not met with success. Unlike the case of the ideal model the equations for statistical moments of distribution of polymers for size and composition as well as for the fractions of the fragments of macromolecules turn out normally to be unclosed. Consequently, to determine the above statistical characteristics, the necessity arises for a numerical solution to the material balance equations for the concentration of molecules with a fixed number of monomeric units and reactive centers. The difficulties in solving the infinite set of ordinary differential equations emerging here can be obviated by switching from discrete variables, characterizing macromolecule size and composition, to continuous ones. In this case the mathematical problem may be reduced to the solution of one or several partial differential equations. 

We have tried to explain the general principles of the chromatography at critical conditions applicable not only to functionality determination. In order to analyse the herterogeneities in macromolecules, it is necessary to take into account not only the relationships between the macromolecule size and the pore size of the stationary phase, but also the energy of the interaction of the molecule with the adsorbent. 

The equilibrium values of the parameter /3 and of the macromolecule size R are determined by minimizing the free energy F over these variables. The obtained system of two equations is solved numerically. 

The time of polymer solutions free relaxation (xdetermined experimentally, is the parameter, sensitive to macromolecules sizes and conformation change. It characterizes the rate, with which the optically anisotropic molecules primary orientation disappears, having established under... 

In a more general sense, the size exclusion mode of liquid chromatography relates to a separation regime, where entropic interactions are predominant and TAS > AH. In the reverse case, AH > TAS, separation is mainly directed by enthalpic interactions. As both separation modes in the general case are affected by the macromolecule size and the pore size, a certain energy of interaction may be introduced, characterizing the specific interactions of the monomer unit of the macromolecule and the stationary phase, e is a function of the chemical composition of the monomer unit, the composition of the mobile phase of the chromatographic system, and the temperature. 

Both the theoretical and experimental studies have shown the macromolecule sizes near the critical point to be comparable with the size of an unperturbed coil at the tf-state, and /M. 

Both convective and capillary assemblies have been shown to be compatible with macromolecule-sized nanoparticles with diameters <10 nm. Unfortunately such small particles do not form well-ordered structures as compared to larger ones, t)q>ically above 50 nm. These results bring up important questions for further studies, in particular how solvent fluctuations, substrate interactions, and thermod5mamic states affect drying patterns in a confined geometry. 

Seksek O, Biwersi J,Verkman AS (1997) Translational diffusion of macromolecule-sized solutes in cytoplasm andnucleus.J Cell Biol 138 131-142... 

The topology in actual gels is more complicated, but gel strands are uncrossable to macromolecular solutes, and they play the role of the walls pictured above. The coefficient depends on the macromolecule size and varies from 0 for a very high molecular weight polymer unable to penetrate the gel to 1 for a very small macromolecule capable of entering the total gel volume. Consequently, the elution volume of a macromolecule through a orc column takes the following form ... 

The value of A describes the macromolecule size change before and after cluster formation and is determined according to the relationship [82] ... 

The conformation plot is the scaling law between macromolecule size and molecular weight (i.e., the chain length) and it is very useful in studying the stiffness (flexible, stiff, or compact conformation) of polymers. Also branching, degree of functionalization, or derivatization could be studied using the conformation plot of the polymer. Therefore, it is very useful in the molecular characterization of polymers. 

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