Polymer Physics

Taking the minimum with respect to the coil sizeR, one calculates @F @R ¼ 0 (4.20) and one can have Rn^3 =ðdþ^2 Þ (4.21) This i ...

monomers consecutively occupying 2D lattice sites in athermal concentrated solutions (De Gennes 1979 ). The bond of the solute m ...

Due to the screening effect in the volume exclusion of polymer chains, single- chain conformation in the concentrated solutions ...

defined as the screening lengthx. Each single chain contains a number of blobsg. Within the length scale ofx(r<x), the volume ...

resulting ina¼3/4. This gives xC^3 =^4 (4.32) and then Rn^1 =^2 x^1 =^6 n^1 =^2 C^1 =^8 (4.33) For polymer solutions with ...

The behavior of the collapse transition of a single chain is also related to the chain length. Figure4.9ademonstrates the collap ...

Dme 1 ¼ @DHemix @N 1 T @DSemix @N 1 (4.37) The excess mixing enthalpy @DHmixe @N 1 ¼kTK 1 f^22 (4.38) The excess mixing entropy ...

which can be obtained from Flory-Krigbaum theory on dilute polymer solutions (see Sect.8.3.3), wherenis the specific volume of p ...

The repulsive energy between the blobs should be comparable with the energy level ofkTfor thermal fluctuations. Accordingly, the ...

The fraction of charged monomerspon the polyelectrolyte backbone is highly sensitive to the environmental factors such as temper ...

wherebis the size of chain units. From the minimum of this free energy with respect toR, i.e. let its first derivative toRequal ...

and the ionic strength for the salts in solution is I¼Sz^2 iri (4.61) in whichirepresents ion species,zirepresents the number de ...

cascading phenomenon can be attributed to theRayleigh instabilityof the charged liquid droplets, which explains the splitting of ...

SubstitutingR~m1/3into the equation above, the critical charge density on the chain to stabilize each bead is thus, pcm^1 =^2 ...

Sincexis a local property of the chain, irrelevant to chain lengthn, thus 1+2a¼0, and we obtaina¼1/2. Substituting again (4.68) ...

Rxð n m Þ^1 =^2 n^1 =^2 ð pc C Þ^1 =^3 (4.79) Since the chain conformation appears as unperturbed in the concentrated solution ...

r R^5 =^2 Rf^3 =^2 (4.81) The total free energy F¼kT n g ¼kTð Rf R Þ^5 =^2 (4.82) and the stretching force f¼ @F @Rf ¼ kT b ð ...

If a single polymer chain is confined between two parallel plates with a distance d, we can assumeN/gblobs, each with the linear ...

and the coils are assumed unperturbed, asR//¼(nb^2 )1/2, then one obtains Cint b d (4.90) which shows no dependence on the chai ...

membrane translocation, and bio-compatibility. When a single polymer coil is forced to form too many contacts with a flat substr ...