While chain branching generally promotes swelling of polymer networks, it also leads to nonlinear modulus increase with network expansion. To understand the effect of branched architecture on swelling, we study comb-like and bottlebrush networks using a combination of theoretical analysis, computer simulations, and experiments. The equilibrium swelling ratio of such networks is shown to be larger than that of conventional linear chain networks as a result of two effects: architectural disentanglement of network strands and amplification of polymer–solvent interactions by side chains. For networks of brush-like strands with poly­(dimethylsiloxane) side chains in toluene, we achieve a swelling ratio of Q = 30, which is larger than that of linear chain networks with the same strand length. All of the studied systems, including linear chain, comb, and bottlebrush networks, follow a universal scaling relation, G(Q) ∝ Q –δ, between the deformation-dependent shear modulus G(Q) and swelling ratio Q with scaling exponents δ = 2.6 ± 0.08 (simulations) and δ = 2.6 ± 0.12 (experiments). These values agree with the theoretically predicted exponent δ = 8/3, confirming dominant contribution of three-body interactions to the osmotic pressure which drives network swelling. The established correlations between network strand architecture, nonlinear elastic modulus, and equilibrium swelling ratio provide a general framework for architectural control of swelling capacity and the design of superabsorbent materials.

Entanglements in polyelectrolyte solutions are a controversial issue in polymer science. Experimental studies during the last 20 years have raised doubts about the applicability of the concept of entanglements developed for neutral polymers to polyelectrolytes. To address this issue, we develop an approach based on the scaling relationship between the solution correlation length ξ = lg ν/B and the number of monomers per correlation blob g for polymers with the monomer projection length l. The numerical coefficient B and exponent ν are determined by the solvent quality for the polymer backbone, chain Kuhn length, and type and strength of monomer–monomer interactions at different length scales starting from the solution correlation length down to electrostatic and thermal blob length scales. Values of the B parameters are obtained from plateaus of normalized specific viscosity ηsp(c)­(cl 3)α/N w as a function of the monomer concentration c in different solution regimes of charged and neutral polymers with the weight average degree of polymerization N w. The exponent α = 1/(1 – 3ν) describes the concentration dependence of the number of monomers per correlation blob, g ∼ c α. Knowledge of the B parameters allows calculations of crossover concentrations c D, c th, and c** into solutions of overlapping electrostatic and thermal blobs and concentrated polymer solutions, respectively. It is used for the universal representation of specific viscosity and relaxation time data in terms of the number of blobs per chain, N w/g, which can be viewed as an effective chain degree of polymerization in polymer solutions. By applying this approach to viscosity data in the entangled solution regime, we obtain a packing number P̃ e and a concentration dependence of the degree of polymerization between entanglements Ñ e = P̃ e 2 g, which include system dispersity information. This analysis shows that, in salt-free solutions of chains with degrees of polymerization of up to 104, polyelectrolytes only entangle in the solution regimes where the entanglement concentration c e > c D and solution properties are similar to those of neutral polymers. A similar conclusion is reached from analysis of viscosity data of polyelectrolytes in salt solutions. Therefore, in order to observe entanglements in polyelectrolyte solutions in a concentration range where their properties are controlled by electrostatic interactions, one has to study polyelectrolyte chains with degrees of polymerization of at least an order in magnitude longer than studied so far.

Knowledge of interaction parameters and Kuhn length for a polymer/solvent pair is a foundation of polymer physics of synthetic and biological macromolecules. Here, we demonstrate how to obtain these parameters from the concentration dependence of solution viscosity. The centerpiece of this approach is the scaling relationship between solution correlation length (blob size) ξ = lgν /B and the number of monomers per correlation blob g for polymers with monomer projection length l. The values of parameter B and exponent v are determined by solvent quality for the polymer backbone, chain Kuhn length, and types and strength of monomer–monomer and monomer–solvent interactions. Parameter B assumes values B g, Bth , and 1 for exponent v = 0.588, 0.5, and 1, respectively. In particular, we take advantage of the linear relationship between specific viscosity ηsp in the unentangled (Rouse) regime and the number of correlation blobs Nw /g per chain with the weight average degree of polymerization, Nw , and g = B 3/(3ν – 1)(cl 3)1/(1 – 3ν) as a function of monomer concentration, c, and the corresponding B parameter. The values of the B parameters are extracted from the plateaus of normalized specific viscosity ηsp(c)/Nw (cl 3)1/(3ν – 1) or their locations as a function of the monomer concentration c in different solution regimes. The extension of the approach to entangled polymer solutions provides a means to obtain the chain packing number, Pe , and to complete the set of parameters {B g, Bth , Pe } (a system “fingerprint”) uniquely describing static and dynamic solution properties of a polymer/solvent pair. This approach is illustrated for solutions of poly­(ethylene oxide) in water, poly­(styrene) in tetrahydrofuran and toluene, poly­(methyl methacrylate) in ionic liquids, and sodium carboxymethylcellulose in water at high salt concentrations.

We apply a scaling theory of semidilute polymer solutions to quantify solution properties of polysaccharides such as galactomannan, chitosan, sodium carboxymethyl cellulose, hydroxypropyl methyl cellulose, methyl cellulose, xanthan, apple pectin, cellulose tris(phenyl carbamate), hydroxyethyl cellulose, hydroxypropyl cellulose, sodium hyaluronate, sodium alginate, and sodium κ-carrageenan. In particular, we obtain the molar mass of the chain segment inside a correlation blobas a function of concentration c, interaction parameter B ̂, and exponent ν. Parameter B ̂assumes values B ̂g, B ̂th and M 0 /N A 1/3 l for exponents v = 0.588, 0.5 and 1, respectively, where M 0 is the molar mass of a repeat unit, l is the projection length of a repeat unit, and N A is the Avogadro number. In the different solution regimes, the values of the B ̂-parameters are extracted from the plateaus of the normalized specific viscosity η sp (c)/M w c 1/(3ν−1) , where M w is the weight-average molecular weight of the polymer chain. The values of the B ̂-parameters are used in calculations of the excluded volume v, Kuhn length b, and crossover concentrations c*, c th , and c** into a semidilute polymer solution, a solution of overlapping thermal blobs and a concentrated polymer solution, respectively. This information is summarized as a diagram of states of different polysaccharide solution regimes by implementing a v/bl 2 and c/ c** representation. The scaling approach is extended to the entangled solution regime, allowing us to obtain the chain packing number, P ̃e. This completes the set of parameters {B ̂g, B ̂th , P ̃e} which uniquely describes the static and dynamic properties of a polysaccharide solution.

We implemented a scaling approach, based on the relationship between the solution correlation length ξ = lg ν /B and the number of repeat units per correlation blob g for polymers with repeat unit projection length l, to quantify properties of solutions of carboxymethylcellulose and polystyrene sulfonate with monovalent and divalent counterions. The parameter B is equal to B pe , B g , B th , and 1, and the exponent v = 1, 0.588, 0.5, and 1 in semidilute polyelectrolyte solutions, solutions of overlapping electrostatic and thermal blobs, and concentrated polymer solutions, which are separated by crossover concentrations c D , c th , and c**, respectively. The values of the B-parameters are obtained using the linear relationship between the specific viscosity η sp (c) in the unentangled solution regime and the number of correlation blobs N w /g per chain, with the weight-average degree of polymerization, N w , and g = B 3/(3ν−1) (cl 3 ) 1/(1−3ν) as a function of the repeat unit concentration, c, and the B-parameters in different solution regimes. This analysis shows that (i) there is only a small fraction of free counterions, f * < 12%; (ii) divalent ions have a strong effect on the renormalization of the excluded volume, reducing it by a factor of 2; and (iii) the effect of divalent counterions is much weaker on the renormalization of the Kuhn length, accounting for an increase of up to 10%. In combination, these effects significantly reduce chain stretching, increase the number of repeat units per solution correlation length, and promote chain disentanglement in polyelectrolyte solutions with divalent ions in comparison with that in solutions with monovalent counterions. There is an indication of chain bridging by Ca 2+ ions in concentrated solutions of carboxymethylcellulose, manifested as an increase in solution viscosity. The concentration dependence of the solution correlation length ξ calculated using the set of B-parameters is in good agreement with that obtained from the peak position of the scattering function for concentrations c < c D .