Elasticity single chain

Abstract Atomic force spectroscopy (AFM)-based single-molecule force spectroscopy (SMFS) was invented in the 1990s. Since then, SMFS has been developed into a powerful tool to study the inter- and intra-molecular interactions of macro-molecules. Using SMFS, a number of problems in the field of supramolecular chemistry and mechanochemistry have been studied at the single-molecule level, which are not accessible by traditional ensemble characterization methods. In this review, the principles of SMFS are introduced, followed by the discussion of several problems of contemporary interest at the interface of supramolecular chemistry and mechanochemistry of macromolecules, including single-chain elasticity of macromolecules, interactions between water and macromolecules, interactions between macromolecules and solid surface, and the interactions in supramolecular polymers. 

However, there are still some challenges in this field. Here are two examples. (1) The database of single-chain elasticity of macromolecules is not yet complete. As with the periodic table of elements, a complete database of macromolecules would certainly be helpful for the development of science and engineering. (2) The noise level of SMFS is still too high. A typical noise of 5-10 pN conceals some important data. However, it is greatly anticipated that, in the future, SMFS can contribute further to the development of supramolecular chemistiy and mechano-chemistry of macromolecules. 

As mentioned previously, by using relation 6, the single chain elastic modulus within a crystalline lamella for various polymers can be calculated from the slope of the line fitted to the plot of v versus 1/L. This estimation requires the single chain density generally obtained from luiit cell parameters. For example, the modulus for polyethylene is foimd to be 300 GPa (124). The fact that the upper limit of the modulus along the chain direction can be measured is particularly valuable when an estimation of processing efficiency is required. 

Hie total elastic free energy, or the Helmholtz free energy, of a network consists of the sum of the free energies of the individual chains and the contributions coming from intermolecular correlations. Hie elementary theories of rubber elasticity ignore contributions from intermolecular effects. Improvements in the elementary models have been made by different researchers in different ways. In this section most of the models will be covered. Since the single-chain elasticity forms the basis of rubber elasticity, it will be discussed first in some detail. 

In the case that the chain is able to retain its equilibrimn structure, the single chain elasticity can be derived from the first and second law of thenno-dynamics. Assuming pdV/fdl 10 , the retractive force can be expressed as [10] ... 

The value should be that of single polymer chain elasticity caused by entropic contribution. At first glance, the force data fluctuated a great deal. However, this fluctuation was due to the thermal noise imposed on the cantilever. A simple estimation told us that the root-mean-square (RMS) noise in the force signal (AF-lS-b pN) for an extension length from 300 to 350 nm was almost comparable with the thermal noise, AF= -21.6 pN. 

The basic postulate of elementary molecular theories of rubber elasticity states that the elastic free energy of a network is equal to the sum of the elastic free energies of the individual chains. In this section, the elasticity of the single chain is discussed first, followed by the elementary theory of elasticity of a network. Corrections to the theory coming from intermolecular correlations, which are not accounted for in the elementary theory, are discussed separately. 

It will be obvious that the treatment of the present section can also be applied to the subchain model (77). As is well-known, this model where every junction point of subchains is assumed to interact with the surroundings, seems to provide a more realistic description of the dynamic behaviour of chain molecules than the simple model used in the proceeding paragraphs, viz. the elastic dumb-bell model where only the end-points of the chain are assumed to interact with the surrounding. One of the important assumptions of the subchain model is that every subchain should contain enough random links for a statistical treatment. From this it becomes evident that the derivations given above for a single chain, can immediately be applied to any individual subchain. In particular, those tensor components which were characterized by an asterisk, will hold for the individual subchains as well. 

As for the elastic Helmholtz energy of a single chain, applying Equation (48) to A block gives... 

Transfersomes are vesicles prepared from lipids and an edge activator that might be a single-chain lipid or surfactant. The edge activator renders the vesicles elastic. As a result of the hydration force in the skin, elastic vesicles can squeeze through SC lipid lamellar regions [47], Transfersomes were much more effective than conventional liposomes when applied nonocclusively with respect to mass flow of lipid across the skin. After 8 h of transfersome application... 

This section seeks to make a quantitative evaluation of the relation between the elastic force and elongation. The calculation requires determining the total entropy of the elastomer network as a function of strain. The procedure is divided into two stages first, the calculation of the entropy of a single chain, and second, the change in entropy of a network as a function of strain. 

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