Hairy Gels: A Computational Study

Abstract

We present results of MD and MC simulations of the equilibrium properties of swelling gels with comb-like or bottlebrush subchains and compare them to scaling-theory predictions. In accordance with theory, the simulation results demonstrate that swelling coefficient of the gel increases as a function of the polymerization degree of the main chains and exhibits a very weak maximum (or is virtually constant) as a function of the polymerization degree and grafting density of side chains. The bulk osmotic modulus passes through a shallow minimum as the polymerization degree of the side chains increases. This minimum is attributed to the onset of overlap of side chains belonging to different bottlebrush strands in the swollen gel.

Polyelectrolyte Cylindrical Brushes in Hairy Gels

“…The scaling model of PE cylindrical brush could be also used to compare the equilibrium swelling ratios of hairy gels with ionized and neutral side chains with similar architectures of the strands, i.e., with same DP M of the backbone and DP n of the side chains, separated by spacers with DP m (n/m 1). In the hollow mesh regime, the swelling coefficient Q gel is specified by the average end-to-end distance R backbone of the backbone, and the total DP of the strand, N = M(1 + n/m) as Q gel = R 3 backbone /a 3 N. At fixed N, ionization of the bottlebrush side chains in salt-free solution (osmotic regime O with β > (nm) −2/3 ) led to stretching of the backbone up to its contour length, h ma, L aM, and R backbone (β) L. In contrast, neutral side chains with β = 0 exhibited self-avoiding statistics on length scales larger than the brush thickness D, and hairy gels with such strands had R backbone (β = 0) ∼ aM 3/5 , supplemented with weakly increasing dependence on n (specified by the degree of local stretching of spacers) [26]. Therefore, ratio of the swelling coefficients of the osmotic and neutral hairy gels in hollow mesh regime, Q gel (β)/Q gel (β = 0) ∼ M 3 /M 9/5 ∼ M 6/5 , strongly increased with DP M of the backbone and exhibited weakly decreasing dependence on DP n of the side chains.…”

“…At fixed N , ionization of the bottlebrush side chains in salt-free solution (osmotic regime O with ) led to stretching of the backbone up to its contour length, , , and . In contrast, neutral side chains with exhibited self-avoiding statistics on length scales larger than the brush thickness D , and hairy gels with such strands had , supplemented with weakly increasing dependence on n (specified by the degree of local stretching of spacers) [ 26 ]. Therefore, ratio of the swelling coefficients of the osmotic and neutral hairy gels in hollow mesh regime, , strongly increased with DP M of the backbone and exhibited weakly decreasing dependence on DP n of the side chains.…”

“…In contrast to conventional gels with linear (undecorated) strands, hairy gels composed of physically or chemically cross-linked bottlebrushes [ 23 , 24 , 25 ] exhibit two distinct regimes of behavior: (i) a hollow mesh regime in which the side chains from neighboring strands do not considerably overlap, and solvent in the mesh is distributed unevenly, and (ii) a filled mesh regime in which side chains overlap and form semi-dilute solution with an almost uniform solvent distribution. The hairy gels with extended backbones are predicted to attain maximal swelling ratios at the boundary between hollow and filled mesh regimes [ 26 ]. Ionization of the side chains would lead to extra stretching of the backbones compared to neutral counterparts, and the corresponding modification of the hairy gel behavior in both regimes.…”

Cylindrical brushes with ionized side chains: Scaling theory revisited

“…In particular, charged cylindrical brushes could model aggrecans -essential components of cartilage in synovial joints, 12 neurofilaments -building blocks of the cytoskeleton in axons of neurons, 13 and cylinder-like cilium decorated with polymeric mucins. 14 Analytical 15 and self-consistent field numerical 16,17 theories as well as coarse-grained computer simulations [18][19][20][21][22][23][24][25] of branched macromolecules have established the relationships between macromolecular topology and experimentally accessible properties of materials comprising elastomers and hairy gels [26][27][28][29] composed of physically or chemically cross-linked bottlebrushes. However, a vast majority of the theoretical studies on bottlebrushes deal with neutral systems, while computational studies of molecular brushes with ionized grafts are relatively sparse.…”

“…Analytical 15 and self-consistent field numerical 16,17 theories as well as coarse-grained computer simulations 18–25 of branched macromolecules have established the relationships between macromolecular topology and experimentally accessible properties of materials comprising elastomers and hairy gels 26–29 composed of physically or chemically cross-linked bottlebrushes. However, a vast majority of the theoretical studies on bottlebrushes deal with neutral systems, while computational studies of molecular brushes with ionized grafts are relatively sparse.…”