Conformation of a single polyelectrolyte in poor solvents

Abstract

Understanding the conformation of a polyelectrolyte (PE) is not only a fundamental challenge in polymer science but also critical for understanding the folding and aggregation of proteins. Here, we develop a theory by systematically including the electrostatic interactions into the self-consistent field theory for polymers to study the conformational behaviors of a single PE in poor solvents. As the backbone charge fraction of the PE increases, our theory predicts that the spherical globule (Sph) can either be elongated to a series of pearl-necklace (PN) structures or be flattened to two novel structures that have not been reported before: biconcave red cell and toroid. While the PN structures are stable conformations, the two fattened structures are metastable. We find that the cylindrical globule, the stability of which is under debate, is an unstable structure. The signature of the PN structures obtained by our calculation is less pronounced than that reported by other theoretical works due to the continuous change in the curvature from the pearl to the necklace, which, however, is in good agreement with the results from molecular simulations and neutron scattering experiments. In addition, our theory reveals different characteristics of the globule to PN transition: the transition from the Sph to the PN with double pearls is discontinuous, whereas those from adjacent PN structures are continuous at finite salt concentrations. Furthermore, we observe different scaling behaviors: the string width is not a constant as a thermal blob but decays as the backbone charge fraction increases.

Association of two polyelectrolytes in salt solutions

“…The asymptotic behaviour of the length ratio can be explained by the linear scaling L – N for the length of the PN structure of a single PE. 25,27 In poor solvents, the associate formed by two PEs with a chain length N is equivalent to the morphology of a single PE with a chain length 2 N if the end effect is neglected. The two PN unimers hence associate in a ‘head-to-head’ manner.…”

“…Mobile ions are taken as point charges with a valency z ± . Following the standard procedure of field theory, the set of self-consistent equations for the polymer density ϕ p ( r ), conjugate fields ω p ( r ) and ω s ( r ), electrostatic potential ψ ( r ) and ion concentration c ± ( r ) can be obtained: 25 1 − ϕ p ( r ) = e μ s exp [− ω s ( r )] c ± ( r ) = λ ± exp [ z ± ψ ( r ) − u ± ( r )]where χ is the Flory–Huggins parameter, ε ( r ) = kTε 0 ε r ( r )/ e 2 is the scaled permittivity with ε 0 being the vacuum permittivity and e the elementary charge. ε r ( r ) is the local dielectric constant, which can be determined based on the local composition of species by adopting some mixing models, such as the volume fraction weighted average 51–54 or the Clausius–Mossotti relation, 54,55 and ν 0 is the volume of the chain segment.…”

“…15 Great efforts have been made to study the conformation of a single PE, particularly in poor solvents because of the hydrophobic nature of the chain backbone. [16][17][18][19][20][21][22][23][24][25][26] Most of our fundamental understanding of this problem relies on the framework of the globule-to-pearl-necklace transition, as discussed extensively by Dobrynin, Rubinstein, and Obukhov using scaling theory. [27][28][29] By systematically incorporating the electrostatics into the self-consistent field theory (SCFT) of polymers, Duan et al recently predicted that a homogeneous PE with a uniform charge distribution can adopt a stable vesicle structure in the presence of salt ions, which is an important complement to the well-known spherical globule (Sph), pearl-necklace (PN) and coil conformations.…”

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

“…In the vicinity of a charged electrode, electrolyte solution forms an electric double layer (EDL) that reflects the competition between electrostatic attraction of the counter-ions to the electrode surface and the translational entropy of the ions. The EDL is a problem of fundamental importance to subjects as diverse as colloid science [ 1 , 2 ], macromolecular conformation [ 3 , 4 ], and biological membranes [ 5 ], and has been a subject of much research interest over the past several decades [ 6 , 7 , 8 , 9 , 10 , 11 ]. It is well known that charged colloids (i.e., macroions) have typically a low relative dielectric constant ( ≈ 2−5) which is much smaller than that of the surrounding solvent (e.g., for water ≈ 80).…”

Hybrid polarizable simulations of a conventional hydrophobic polyelectrolyte. Toward a theoretical tool for green science innovation

“…Small Angle Neutron and X-ray Scattering, SANS/SAXS, techniques are also commonly used to investigate polymer-based solutions [8][9][10][11] even if the interpretation of their data may be controversial. 12 To tackle out the lack of experimental data, molecular simulations are a 3 lar simulation approach a priori well suited for accelerating innovation with digital strategies for Green Sciences. That approach relies on modeling interactions among non-solvent atoms using the all atoms polarizable force field TCPEp, which is based on a polarizable induced dipole moment approach 31 , like the one of Fig.…”