Transition coil-globule

Most protein molecules are globular. Strong interactions due to hydrogen bonding and S-S linkage force the protein to take a specific structure close to a globule. 

In addition to the two terms in Equation 2.69, we take the three-body contribution into account when w 0. The energy per chain due to three-body interactions is proportional to the product of the triple-contact energy (W3, in units of ksT), probability of finding three monomers in a volume of (proportional to the cube of monomer density, (N/R ) ) and the volume of the coil ( R ). Adding this term to Equation 2.69 and ignoring the numerical factors, we get 

By minimizing the free energy with respect to R and writing w as - w, we obtain 

the numerical coefficients are ignored. When the chain collapses such that R [NI (the Gaussian chain value), we expect that the free energy contribution arising from the conformational entropy to be weaker in comparison with the two-body and three-body interaction terms. Therefore, by ignoring the first term in the above equation, we get 

Substitution of Equation 2.86 into Equation 2.85 for/ self-consistently justifies the omission of the first (entropic) term in arriving at Equation 2.86. 

The main conclusion is that when w becomes negative, for temperatures below the Elory temperature, the chain attains the globular state in the asymptotic regime of large N, 

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In contrast to PNIPAM, direct observation of the coil-globule transition of a single PVME chain has not been reported. However, a number of reports... 

Taken together, the experimental observations reported in the previous sections suggest that the formation of colloidally stable particles heated above their phase-transition temperature may be a universal phenomenon, taking place not only in aqueous polymer solutions, but also in solutions of polymers that can undergo a coil-globule transition in organic solvents. 

Partial vitrification may affect kinetic processes during the coil-globule transition. Thus, at very high dilution, macroscopic phase separation well above the LCST might be stopped by partial vitrification of the polymer-rich phase. At this point we can only speculate whether vitrification interferes with the coil-globule transition or not. This problem is open for discussion and needs experimental confirmation. 

Random distribution of a significant number of hydrophilic NVIAz units along the polymer chain could result in uniform hydrophilization. This, in turn, could lead to a loss of ability for the coil-globule transition, which is caused by the hydrophobic interactions. As a result, such copolymers should be water-soluble over a wide temperature range. 

P.-G. de Gennes later also considered the multisegment attraction regime. He suggested the so-called p-cluster model [11] in order to explain certain anomalies in behavior observed in many polymer species such as polyethyle-neoxide (PEO) see also [12]. The scenario of coil-globule transition with dominating multisegment interaction first considered by I.M. Lifshitz has been recently studied in [13]. The authors used a computer simulation of chains in a cubic spatial lattice to show that collapse of the polymer can be due to crystallization within the random coil. 

Note that the paper [ 1 ] by I.M. Lifshitz forestalled the corresponding experiments by at least 10 or rather 20 years. Experimental observation of such transitions is even now far from a routine procedure. Here we shall limit the discussion to mentioning several studies, which are in our opinion the most important achievements in this field [31-34]. We shall also refer to very informative reports on computer simulation of the coil-globule transition, namely, recent paper [35], and a very good reference list therein. 

As we mentioned earlier, I.M. Lifshitz was the first to realize that the coil-globule transition is not just a decrease of the chain size, but a phase transition to a condensed phase. Considering the multiplicity of known and possible condensed states, such a bro ad view on the coil-globule transition opened a perspective for unified understanding of a great number of physical phenomena in a variety of polymer systems. This gave rise to the concept of coil-globule-type transitions. Below we discuss several examples of such transitions. 

If network chains carry charged units, the coil-globule transition becomes sharper the amplitude of the jump increases, the critical value of pcr decreases down to unity pcr 1 (see Fig. 10). 

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