Counting loops in sidechain-crosslinked polymers from elastic solids to single-chain nanoparticles† †Electronic supplementary information (ESI) available: Synthetic procedures, methods and materials, and characterization data; Monte Carlo simulation algorithm for obtaining φλ for side-chain crosslinked polymer networks. See DOI: 10.1039/c9sc01297d

The vast differences in material properties accessible via crosslinking of sidechain-functionalized polymers are driven by topology.

Liquid chromatography-mass spectrometry (LC-MS) was performed on an Agilent 1260 LC system equipped with a Zorbax SB-C18 rapid resolution HT column and a Zorbax SB-C18 semi-preparative column. Solvent gradients consisted of mixtures of nano-pure H 2 O with 0.1% acetic acid (AcOH) and HPLC-grade acetonitrile (MeCN). Mass spectra were obtained using an Agilent 6130 single quadrupole mass spectrometer. 1 H nuclear magnetic resonance ( 1 H NMR) spectra were recorded on Bruker AVANCE-400 NMR spectrometers in the Department of Chemistry Instrumentation Facility at MIT. Chemical shifts are expressed in parts per million (ppm); splitting patterns are designated as s (singlet), d (doublet), t (triplet), m (multiplet) and br (broad). Coupling constants J are reported in Hertz (Hz).
Gel permeation chromatography (GPC) was performed on an Agilent 1260 Infinity system equipped with three PL gel columns (103 Å, 104 Å, 105 Å) in series. Tetrahydrofuran (THF) was used as the mobile Electronic Supplementary Material (ESI) for Chemical Science. This journal is © The Royal Society of Chemistry 2019 phase. The system was calibrated using narrowly dispersed polystyrene standards. A sample concentration of 0.5 mg/mL was used.
Details of the rheology instrumentation and experiments are provided in the relevant section below.

Synthesis of B 20H and B 20D .
Synthesis of polymer 1.
Styrene (3.0 g, 28.8 mmol), 4-vinyl benzyl acetate (0.92 g, 5.2 mmol), TEMPO (0.045 g, 0.288 mmol) and benzoyl peroxide (0.049 g, 0.202 mmol) were added to a 10 mL microwave reaction vial. The mixture was degassed with three freeze-pump-thaw cycles. The mixture was then heated to 95 °C and heated for 4 h under N 2 followed by additional stirring at 130 °C for 12 h under N 2 . The polymerization was quenched in a liquid nitrogen bath. After warming, the crude reaction mixture was dissolved in 10 mL THF and added dropwise into methanol. The precipitated polymer was re-dissolved in 10 mL THF and re-precipitated via dropwise addition into methanol. The product was dried on a Schlenk line under vacuum at room temperature to provide a white powder

Synthesis of polymer 2.
To a 10 mL THF solution of polymer 1 (3.0 g) was added 10 mL 0.  Synthesis of B 20H .

Quantifying the azide content in B 20H and B 20D .
The azide (-N 3 ) content in B 20H and B 20D was quantified by reacting the polymers with a known but excess amount of propargyl 4-bromobenzamide by copper-catalyzed azide-alkyne cycloaddition (CuAAC). The detailed procedure is described as follows: For B 20H : B 20H (4.67 mg) and propargyl 4-bromobenzamide (3.53 mg, 0.0148 mmol) were weighed and added into a vial (vial I). The mixture was dissolved in 250 µL of THF-d 8 . In another vial, CuBr (1.4 mg, 0.01 mmol) and Me 6 TREN (2.5 mg, 0.011 mmol) were dissolved in 250 µL of THF-d 8 , and the resulting solution was added to vial I. The reaction was allowed to proceed overnight. After this time, the reaction mixture was characterized by 1 H NMR.
The content of -N 3 in B 20H was determined according to: 0.00116 mmol/mg.

Network degradation.
The samples were removed from the glovebox and were exposed to 0.

Analysis of degradation products.
The degradation products were analyzed by LC-MS using the Single Ion Mode (SIM) feature. The principal isotope peak for each degradation product was extracted in the "Extract Ion" feature of ChemStation, and quantified using the integration feature for each extracted ion.

Rheology.
Gel samples (300 µL in total) for rheology were prepared in NMP in 4 mL vials. The vials were broken with a hammer to remove the gels, which were subsequently cut with an 8 mm hole puncher (purchased where the summations are taken over all unreacted A-B pairs. is the square end-to-end adjacent functionalized B monomers belonging to the same B f macromolecule has a distribution, which will change the probability of loop formation as shown in Eq. S1. The distances between any two adjacent functionalized B monomers belonging to the same B f are recorded, and the distances between two nonadjacent B groups can be straightforwardly calculated.
In the simulation of loop formation, 10000 A 2 bifunctional polymers and 1000 B 20 macromolecules are initially placed in the system at various concentrations. The number of molecules is chosen to be large enough so that the loop fractions are not sensitive to the system size. Ten parallel simulations were run for each set of parameters to obtain the average fraction of 1° loops. In the simulation, intrinsic parameters of