Configurational free energy chains

The configurational free energy of the chain, G, is simply equal to -kT In n. The mean number of segments bound to the confining surfaces can be obtained by differentiating the free energy with respect to 0... 

As noted above, the first study of the problem of partial chain flexibility has been done by Flory (1) - one more problem in polymer science which he was the first to tackle. Flory has assumed the existence of a favorable arrangement of a number of consecutive base units. The configurational free energy of this arrangement differs by an amount e from other possible sequences. Apparently, these other arrangements do not have to be all identical thus e represents an average value. Flory points out that the stiffness of the chain is involved. He places the chains and solvent molecules on a lattice, a convenient although not a necessary step. 

The configurational free energy resulting from the loss in conformational degrees of freedom was evaluated by means of the mean-field single-chain statistical mechanical approach. 

Clark and Lai (1981), however, have simulated a polymer molecule on a tetrahedral latice using a Monte Carlo procedure. Three rotational conformational states were assumed to be accessible to each bond. The excluded volume condition was incorporated into the model by assuming that two or more segments cannot occupy the same position in space. These calculations permitted the evaluation of the change in configurational free energy of the polymer chains as a function of the interplane separation. 

The fluid is modeled as an assembly of lattice sites occupied by chain segments in contact with a fraction h of empty sites or holes. The h-function is to account for the temperature, pressure (and stress) dependent structural disorder in the system. What is required is the configurational free energy F (1)... 

Finally, an alchemical free energy simulation is needed to obtain the free energy difference between any one substate of system A and any one substate of system B, e.g., Ai- In practice, one chooses two substates that resemble each other as much as possible. In the alchemical simulation, it is necessary to restrain appropriate parts of the system to remain in the chosen substate. Thus, for the present hybrid Asp/Asn molecule, the Asp side chain should be confined to the Asp substate I and the Asn side chain confined to its substate I. Flat-bottomed dihedral restraints can achieve this very conveniently [38], in such a way that the most populated configurations (near the energy minimum) are hardly perturbed by the restraints. Note that if the substates AI and BI differ substantially, the transfomnation will be difficult to perform with a single-topology approach. 

The Alexander model and its descendants impose strong restrictions on the allowed chain configurations within the tethered assembly. The equilibrium state thus found is subject to constraints and may not attain the true minimum free energy of the constraint-free system. In particular, the Alexander model constrains the segment density to be uniform and all the chain ends to be at the same distance from the grafting surface. Related treatments of curved systems retain only the second... 

In the intermediate stages of the expulsion, the chain comprises a segment which is embedded in the layer to a depth of a g x g L, and an expelled segment. The configuration of the expelled chain segment is similar to that of a free coil of comparable size. The excess free energy of the partly expelled chain is thus primarily due to the embedded segment ... 

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