Swelling and Residual Bond Orientations of Polymer Model Gels: The Entanglement-Free Limit

Abstract

We investigate the swelling of polymer model networks prepared at different polymer volume fractions and in solvents of different quality. We extend the existing theory to describe residual bond orientations (the vector and the tensor order parameters) for theta, good, and athermal solvents and put these relations in context with modulus at preparation conditions and the equilibrium degree of swelling. We find good agreement with the assumption of affine swelling for the weakly entangled networks of our study. The same scaling relations (up to numerical coefficients) are obtained for the vector order parameter, m, and the tensor order parameter, S, as a function of the preparation conditions, network structure, the equilibrium degree of swelling, Q, and the modulus at swelling equilibrium, G. We obtain m ∝ Q –2 and G ∝ m 3/2 for swelling in theta solvents and m ∝ Q –1.08 with G ∝ m 2.14 in the good-solvent regime, in both cases independent of preparation conditions. Modulus and residual bond orientation are related by G ∝ ϕ0 m and G ∝ ϕ0 1.23 m as a function of the preparation polymer volume fraction ϕ0 for theta solvents and good solvents, respectively. Computer simulations and experimental data for the good-solvent regime show good agreement with the predictions.

Amphiphilic Model Networks Based on PEG and PCL Tetra-arm Star Polymers with Complementary Reactivity

“…A simulation study reported exponents increasing from −0.25 to −0.55 with increasing length of still quite short chains . In contrast to this, we found only a very weak increase of the exponent for increasing N . Altogether, the dependence on ϕ 0 has not been settled yet, but this open question could be advanced by using network architectures as ours that are less susceptible to network defects.…”

“…In a subsequent simulation, a series of gels prepared at a broader range of concentrations were swollen to equilibrium, and the equilibrium degree of swelling was determined from the average polymer volume fraction inside the swollen gel. More details on the simulations with a particular focus on equilibrium swelling properties and the residual bond orientations are available in ref .…”

“…The equilibrium swelling degrees show a power law dependence on the polymer volume fraction at preparation, ϕ 0 –0.40 ± 0.01 . This dependence is in between the scaling limits of entanglement-free networks and entanglement dominated systems and is only coincidentally close to the classical prediction …”

Reversible Networks made of Star Polymers: Mean Field Treatment with Consideration of Finite Loops

“…But since c i decays quickly as a function of Z, see equation ( 1), we expect that the shortest path still dominates the true return probability. Besides these corrections, there is an effective repulsion between f -functional star polymers in a melt of the same star polymers that affects the average strand size in a network 45 . Altogether, we expect that equation ( 1…”

Amphiphilic tetra-PCL-b-PEG star block copolymers using benzoxazinone-based linking groups

“…Our interest in tetra-PCL-b-PEG micelles stems from investigations on model amphiphilic co-networks based on tetra-arm PEG and PCL star polymers. [23][24][25] Here, soluble amphiphilic star block copolymers containing the same building blocks are needed to structure the material prior to network formation.…”