The interpenetration of two chain polymers in a good solvent

Witten, Thomas A.; Prentis, Jeffrey J.

doi:10.1063/1.444336

Cited by 36 publications

(23 citation statements)

References 27 publications

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“…implying that G(r 9 0,t)/P eq (r) is independent of r for r<£x t ', i.e., the asymptotic behavior must match that of the equilibrium distribution, P eq (r)-r 8 , where [18,21,22] g is the correlation hole exponent quantifying the reduced contact probability between chain units due to excluded-volume repulsions (# vanishes for melts). Finally, let us assume that the only scales in G are r and x t .…”

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confidence: 94%

From mean field to diffusion-controlled kinetics: Concentration-induced transition in reacting polymer solutions

O’Shaughnessy

1993

Phys. Rev. Lett.

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We study irreversible interpolymeric reaction rates k in polymer solutions as a function of concentration 0. At high dilution, kinetics obey mean field theory, and screening of excluded-volume repulsions as 0 increases results in a growth, &~0 3g/4 , where g is the monomer contact exponent. Screening effects cause a transition to diffusion-controlled kinetics at a value 0**, beyond which (for entangled solutions) k decreases as /c~0 _(5/8+r) , y being the entanglement exponent. Thus k is peaked at 0** which, in agreement with experiment, is distinct from the overlap threshold.

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confidence: 94%

From mean field to diffusion-controlled kinetics: Concentration-induced transition in reacting polymer solutions

O’Shaughnessy

1993

Phys. Rev. Lett.

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“…Equation 8 should be compared to the analogous coefficient between a short and a long chain discussed by Witten and Prentis. 6 The same reasoning applied to a small sphere interacting with an ideal Gaussian coil of radius…”

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confidence: 99%

Protein−Macromolecule Interactions

Odijk

1996

Macromolecules

117

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Although the interactions between proteins and various types of macromolecules are of considerable technological interest, 1 little theoretical work has been done that makes use of the fact that proteins are often comparatively small particles. Thus, our interest is in a regime opposite to that focused on in the usual depletion theories. 2 Here, a protein will be viewed, perhaps naively, as a small hard sphere whose dielectric permittivity is negligible compared to that of water. Its interaction otherwise with some macromolecular segment will be inert. Some time ago, de Gennes already presented several, not so widely known, preliminary calculations of a spherical particle interacting with a semidilute solution of polymers. 3 One supposition he made concerning the irrelevance of a certain scale, will be proved here. My aim is to present a scaling analysis of the interaction between a small sphere and a macromolecule, particularly in dilute solution. Though obviously of restricted validity, the expressions derived may prove helpful in qualitatively understanding phase separation phenomena occurring in nondilute suspensions.We first consider a protein sphere of radius a immersed in an aqueous solution containing a semidilute polymer which is well soluble. Its Kuhn length is A K , and the excluded volume between two segments is ) A K 3 . In a self-consistent field approximation, the polymer segment density ψ 2 (r b) at position r b is given by 2 where the origin is at the center of the sphere, is an eigenvalue, and ψ must tend to zero at the protein surface (r ) a). Without solving eq 1, I wish to investigate the nature of the depletion layer surrounding the protein. Far from the sphere, the concentration ψ 2 asymptotes toward a constant c o , the bulk concentration of Kuhn segments, so we conveniently introduce ψ ≡ c o 1/2 f and eq 1 becomes Here, the correlation length ≡ A K (3 c o ) -1/2 is supposed to be larger than the radius a, a condition easily realizable in practice. Assuming spherical symmetry and setting r ≡ aR, one is faced with finding the solution f ) f(R,a/ ) to with boundary conditions f ) 0 at R ) 1 and f ) 1 at R ) ∞. For an infinitesimally small sphere, we have simply which implies the depletion layer around the sphere is approximately of size a. Moreover, the second and third terms in eq 3 are straightforward regular perturbations for a , . Hence, eq 4 remains valid within a zero-order approximation, even when a > 0 provided a , . We conclude that the scale of the depletion layer for a small sphere is given solely by its radius a and does not involve at all, at least to the leading order. The irrelevancy of (assumed earlier 3 ) is nontrivial for it is circumstantial. Note that an improved theorysa hybrid approach combining scaling and self-consistent arguments as in the theory of polymer adsorption 4 swould not alter this conclusion. One would require a correlation length ∼ c o -3/4 from scaling theory instead of ∼ c o -1/2 and hence replace f 3 in eq 3 by f 4 .We now rederive a previous result 3...

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“…In recent years increasing attention has been paid to the second virial coefficient of a solution of two different polymers [1][2][3][4][5][6][7][8][9][10]. A number of authors applied the renormalization group (RG) methods to this problem [2][3][4][6][7][8][9][10]. Most of these authors used the massless renormalization schemes which are successful by the study of the monodisperse polymer solutions.…”

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confidence: 99%

Renormalization group evaluation of the second virial coefficient of polydisperse polymer solutions

Stepanow

Straube

1985

J. Phyique Lett.

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2014 A l'aide du groupe de renormalisation on a évalué le deuxième coefficient du viriel d'une solution composée de deux polymères monodispersés. On a montré que le terme croisé A12 atteint sa valeur limite lorsque le poids moléculaire de l'un des deux polymères tend vers l'infini. Un tel comportement donne le maximum de A2 avec le changement en teneur relative des polymères. Le maximum calculé au premier ordre du groupe de renormalisation est situé en dehors du domaine expérimental. Abstract. 2014 The second virial coefficient A2 for a mixture of two monodisperse polymers is studied by means of the renormalization group. It is found that the cross-term A12 has a finite limit if the segment number of one of the polymers tends to infinity. Such behaviour predicts a maximum of A2 in dependence on the relative composition of the polymers. The maximum resulting from our firstorder RG-calculation lies outside the molecular weight ratio investigated so far experimentally.

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The interpenetration of two chain polymers in a good solvent

Cited by 36 publications

References 27 publications

From mean field to diffusion-controlled kinetics: Concentration-induced transition in reacting polymer solutions

From mean field to diffusion-controlled kinetics: Concentration-induced transition in reacting polymer solutions

Protein−Macromolecule Interactions

Renormalization group evaluation of the second virial coefficient of polydisperse polymer solutions

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