This work was supported by a Grant-in-Aid for Scientific Research No. 22750122 (S.H.), No. 26288099 (T.Y.), and No. 23350050 (Y.T.) of the Japan Society for the Promotion of Science. S.H. is grateful for The Kurata Memorial Hitachi Science and Technology Foundation. The research reported in this publication was supported by the King Abdullah University of Science and Technology (S.H.).

1. Synthesis of Monofunctional and Bifunctional Poly(THF)
<ol>
	<li>Monofunctional poly(THF)
	<ol>
		<li>Flame dry a 2-neck 100-ml round-bottom flask. Vacuum and fill the flask with nitrogen (3 cycles).</li>
		<li>Add distilled tetrahydrofuran (THF) (50 ml) to the flask. Put the flask in a water bath at 20 &#176;C and equilibrate the temperature.</li>
		<li>Add methyl triflate (0.5 mmol) to the flask by a syringe. Stir the mixture for 5-10 min at 20 &#176;C.</li>
		<li>Add N-phenyl pyrrolidine (4-6 equiv.) to the flask by a syringe. Stir the mixture for 30-60 min.</li>
		<li>Completely remove the solvent under reduced pressure (ca. 100 Torr). Dissolve the residue in 3-5 ml of acetone. Add the acetone solution into 300-500 ml of n-hexane. Filter the precipitate and dry it under reduced pressure.</li>
	</ol>
	</li>
	<li>Bifunctional poly(THF)
	<ol>
		<li>Flame dry a 2-neck 100-ml round-bottom flask. Vacuum and fill the flask with nitrogen (3 cycles).</li>
		<li>Add distilled THF (50 ml) to the flask. Put the flask in a water bath at 20 &#176;C and equilibrate the temperature.</li>
		<li>Add triflic anhydride (0.3 mmol) to the flask by a syringe. Stir the mixture for 5-10 min at 20 &#176;C.</li>
		<li>Add N-phenyl pyrrolidine (4-6 equiv.) to the flask by a syringe. Stir the mixture for 30-60 min.</li>
		<li>Completely remove the solvent under reduced pressure (ca. 100 Torr). Dissolve the residue in 3-5 ml of acetone. Add the acetone solution to 300-500 ml of n-hexane. Filter the precipitate and dry it under reduced pressure.</li>
	</ol>
	</li>
</ol>
2. Synthesis of Perylene Diimide-incorporated 4-armed Star and 8-shaped Dicyclic Poly(THF)
<ol>
	<li>Armed star poly(THF)
	<ol>
		<li>Ion exchange
		<ol>
			<li>Dissolve perylene diimide tetracarboxylate sodium salt in water (10 mg/ml, 150 ml). Dissolve monofunctional poly(THF) in acetone (160 mg/ml, 4 ml). Add the acetone solution dropwise into the vigorously stirred aqueous solution. Collect the formed precipitate by filtration.</li>
			<li>Repeat the above procedure with the recovered precipitate (2.1.1.1) four times.</li>
		</ol>
		</li>
		<li>Covalent fixation
		<ol>
			<li>Dissolve the obtained precipitate in toluene (5 mg/ml). Reflux the solution for 4 hr.</li>
			<li>Completely remove the solvent under reduced pressure (ca. 100 Torr). Filter the residue through a plug of silica gel with n-hexane/acetone (2/1 vol/vol). Add the solution into ice-cooled water (300-500 ml) to precipitate the product. Collect the precipitate by filtration.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Dicyclic 8-shaped poly(THF)
	<ol>
		<li>Ion exchange
		<ol>
			<li>Dissolve perylene diimide tetracarboxylate sodium salt in water (6 mg/ml, 50 ml). Dissolve bifunctional poly(THF) (0.5 g) in 30-50 ml of acetone. Add the acetone solution dropwise into the vigorously stirred aqueous solution at 0 &#176;C. Collect the formed precipitate by filtration.</li>
			<li>Repeat the above procedure with the recovered precipitate (2.2.1.1).</li>
		</ol>
		</li>
		<li>Covalent fixation
		<ol>
			<li>Dissolve the obtained precipitate in toluene (0.05 g/L). Reflux the solution for 4 hr.</li>
			<li>Completely remove the solvent under reduced pressure (ca. 100 Torr). Add toluene to partially dissolve the residue. Re-precipitate into 300-500 ml of n-hexane.</li>
			<li>Filter the formed precipitate through a plug of silica gel with n-hexane/acetone (2/1 vol/vol). Re-precipitate into 300-500 ml of water.</li>
			<li>Purify the formed precipitate by column chromatography18 using a polystyrene gel. Further purify the crude product by preparative gel permeation chromatography (GPC)19 with an eluent of CHCl3 to remove byproducts by monitoring refractive index (RI) and UV detectors.</li>
		</ol>
		</li>
	</ol>
	</li>
</ol>
3. Single-molecule Fluorescence Imaging Experiment
<ol>
	<li>Sample preparation
	<ol>
		<li>Cleaning of microscope cover slips
		<ol>
			<li>Place No. 1.5 24 x 24 mm microscope cover slips in a staining jar.</li>
			<li>Add 1 M potassium hydride solution (100 ml) into the jar and sonicate for 15 min. Pour off the potassium hydroxide solution by decantation and rinse the cover slips with ultra-pure water for several times. Add spectroscopic grade ethanol (100 ml) into the jar and sonicate for 15 min.</li>
			<li>Pour off the ethanol by decantation and rinse the cover slips with ultra-pure water for several times. After pouring off the ultra-pure water by decantation, repeat the step 3.1.1.2.</li>
			<li>Add ultra-pure water to the jar and sonicate for 15 min. Rinse the cover slips with ultra-pure water for several times. Take out the cover slips from the jar by a plastic tweezers and dry them by either dry air or dry nitrogen.</li>
		</ol>
		</li>
		<li>Preparation of polymer melt samples14,15
		<ol>
			<li>Add 100 &#181;l of non-labeled linear poly(THF) in a glass bottle and heat it to a temperature above the melting point (approximately 25 &#176;C) using a hair dryer.</li>
			<li>Dissolve the fluorophore-incorporated polymer (linear, 4-armed star, cyclic, or 8-shaped dicyclic synthesized in 2.1 and 2.2) in chloroform (1 ml, 10-6 M). Add 1 &#181;l of the solution to the 100 &#181;l of the melt of the non-labeled linear poly(THF).</li>
			<li>After thoroughly mixing the sample with a pipette tip, evaporate chloroform by heating the sample using a dryer. 
			NOTE: This provides a melt of the non-labeled linear poly(THF) containing 10-8 M of the fluorophore incorporated polymers.</li>
			<li>Take 10 &#181;l of the sample using a micro-pipette and drop it on a cleaned cover slip. Put another cleaned cover slip on the sample and sandwich the sample between the two cover slips.</li>
			<li>Press the sample gently using a plastic tweezers.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Wide-field fluorescence imaging setup15
	<ol>
		<li>Introduction of an excitation laser (488 nm) into the back port of the inverted microscope
		<ol>
			<li>Insert an excitation bandpass filter and polarizer into the beam path.</li>
			<li>Expand the beam to approximately 1 cm in diameter by a beam expander.</li>
			<li>Insert a quarter wave plate into the beam path. Set the optical axis of the wave plate at 45 degree with respect to that of the polarizer. Alternatively, insert a Berek compensator and set the optical delay to &#955;/4.</li>
			<li>Insert a diaphragm in the excitation beam path to adjust the beam size.</li>
			<li>Before introducing the laser beam into the back port of the inverted optical microscope, insert a focusing lens (plan-convex lens, focal length &#8776; 300 mm) at a position where the laser beam out of the objective lens is collimated.</li>
		</ol>
		</li>
		<li>After reflecting the laser beam using a dichroic mirror mounted on a filter cube, introduce the laser beam to the sample through a high numerical aperture (NA) objective lens (e.g., NA 1.3, 100X magnification, oil immersion).</li>
		<li>Attach an objective heater to the objective lens and set the temperature to 30 &#176;C.</li>
		<li>Mounting the sample on the stage of the inverted microscope
		<ol>
			<li>Drop one drop of immersion oil on the objective lens and mount the sample on the microscope state.</li>
			<li>Ensure that the sample thickness of approximately 10 &#181;m is obtained by checking the axial position of the bottom and top surface of the sample.</li>
			<li>Adjust the focus of the microscope to a few micrometers above the bottom surface of the sample.</li>
		</ol>
		</li>
		<li>Obtain circularly polarized excitation light under the objective lens
		<ol>
			<li>Insert a polarizer into the collimated laser beam out of the objective lens.</li>
			<li>Record the intensity of the laser transmitted through the polarizer by inserting a power meter after the polarizer. Record the transmitted laser power at different polarization angles by rotating the polarizer.</li>
			<li>If the transmitted laser power is not constant at all polarization angles, slightly rotate the quarter wave plate or Berek compensator inserted in the excitation beam path.</li>
			<li>Repeat step 3.2.5.2 and 3.2.5.3 until the constant transmitted laser power is obtained at all polarization angles. Ensure that the circularly polarized light is obtained at the sample.</li>
		</ol>
		</li>
		<li>Setup the EM (electron multiplying)-charge coupled device (CCD) camera
		<ol>
			<li>Attach the EM-CCD camera to the side port of the microscope and connect it to the image acquisition software.</li>
			<li>If necessary, synchronize the camera exposure to a mechanical shutter or acousto-optical tunable filter inserted in the excitation beam path by sending the transistor-transistor logic (TTL) signals generated by the EM-CCD camera to the devices. Alternatively, synchronize the camera exposure to the laser output by sending the TTL signals generated by the EM-CCD camera to the laser. 
			NOTE: The latter option is applicable only when a solid-state laser whose output power can be modulated by input transistor-transistor logic (TTL) signals is used for the experiment.</li>
			<li>Apply an EM gain (typically approximately 300) to the CCD camera using software controlling the camera in order to obtain a high quality fluorescence image of the single fluorophore.</li>
			<li>Set a region of interest (ROI) (typically 128 x 128 pixels at the center of the field of view) using software controlling the camera. 
			NOTE: This allows for the imaging experiments at the frame rates of 100 - 200 Hz in the frame transfer mode, which is required for visualizing the motion of the fluorophore-incorporated polymer chains in the melt sample.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Running the experiment
	<ol>
		<li>Optimizing the experimental conditions
		<ol>
			<li>Adjust the illumination area of the sample to approximately 20 &#181;m in diameter using the diaphragm inserted in the excitation beam path.</li>
			<li>Set the excitation laser power at the sample to 4 - 8 mW by manually selecting an appropriate neutral density (ND) filter inserted in the excitation beam path. 
			NOTE: This provides the mean laser power of 1 - 2 kW cm-2 at the sample.</li>
			<li>Record fluorescence images of the sample at the frame rates of 100 - 200 Hz. If the fluorescence intensity obtained from the individual fluorophore-incorporated polymers is too low, gradually increase the excitation power using the ND filter until reaching approximately 100 mW at the sample.</li>
			<li>If the quality of the single-molecule fluorescence image is still not satisfactory, check the fluorescence impurities in the sample by recording fluorescence images of a pure melt of the non-labeled poly(THF). In case a high fluorescence background is observed, use different non-labeled poly(THF).</li>
			<li>If the density of the fluorescence spot obtained from the fluorophore-incorporated polymers in the melt is too high to spatially isolate them (this causes errors in the analysis of the diffusive motion), decrease the concentration of the fluorophore-incorporated polymers in the sample until spatially isolated spots are observed.</li>
			<li>If the density of the fluorescence spot obtained from the fluorophore-incorporated polymers in the melt is too low (this causes a low throughput of the imaging experiment), increase the concentration of the fluorophore-incorporated polymers in the sample until an appropriate density of the fluorescence spot is reached.</li>
			<li>If the fluorescence images obtained from the fluorophore-incorporated polymers in the melt are blurred, increase the frame rates of the imaging acquisition. 
			NOTE: This often requires a smaller ROI, typically 64 x 64 pixels.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Image acquisition
	<ol>
		<li>Once the experimental conditions are optimized, leave the mounted sample on the microscope stage for an hour so that the sample reaches equilibrium conditions.</li>
		<li>Record 500 - 1,000 fluorescence image sequences of the fluorophore-incorporated polymers in the melt state at a 100 - 200 Hz frame rate. If the default file format is not TIFF, convert all the image sequences to the TIFF format.</li>
	</ol>
	</li>
</ol>
4. Analysis of the Diffusive Motion
<ol>
	<li>Mean-squared displacement (MSD) analysis
	<ol>
		<li>Crop the fluorescence image sequences in such a way that each image sequence contains a single and well-focused diffusing fluorophore-incorporated polymer using image processing software, such as ImageJ.</li>
		<li>When the cropped image sequences contain more than 10 frames, split the image sequences into multiple sequences such that each sequence consists of 10 frames.</li>
		<li>Determine the positions of the molecules in each image sequences accurately by two-dimensional Gaussian fitting of the images.</li>
		<li>Determine the diffusion coefficient (D) of individual molecules by mean-squared displacement (MSD) analysis of the diffusion trajectories (i.e., time-dependent positions of the molecule) using an equation20 
		<img alt="Equation1" src="/files/ftp_upload/54503/54503equation1.jpg" /> 
		where xi and yi are the positions of the molecule in the image frame i, and n denotes the frame number with the time lapse &#916;t from frame i.</li>
		<li>Plot the diffusion coefficients in a frequency histogram. 
		NOTE: Typically, the histogram is constructed from more than 100 molecules.</li>
	</ol>
	</li>
	<li>Cumulative distribution function (CDF) analysis 
	NOTE: A CDF, P(r2, i&#916;t) corresponds to the cumulative probability of finding the diffusing molecules within a radius r from the origin after a certain time lag i&#916;t.
	<ol>
		<li>Calculate the squared-displacement occurring during time lags of 1&#916;t, 2&#916;t, &#183;&#183;&#183;&#183;, i&#916;t for all the diffusion trajectories obtained in 4.1.3. 
		NOTE: These calculations give total mi squared-displacements for the time lags of i&#916;t.</li>
		<li>Calculate numbers of the squared-displacements (li) within total mi data set that are smaller than r2 at different r2 values (0 &#60; r2 &#60; &#8734;). Normalized li vs r2 plots correspond to the CDF, P(r2, i&#916;t).</li>
	</ol>
	</li>
	<li>Analysis of CDFs with distinct diffusion models 
	Note: The obtained CDFs are fitted by distinct diffusion models; homogeneous diffusion model, multiple diffusion modes in which the D distribution is described by a Gaussian (single Gaussian model), and multiple diffusion modes in which the D distribution is described by multiple Gaussian (multiple Gaussian model).
	<ol>
		<li>In the homogeneous diffusion model, determine a mean D by fitting the CDF using an equation21 
		<img alt="Equation2" src="/files/ftp_upload/54503/54503equation2.jpg" /> 
		NOTE: Any deviation from the equation suggests the heterogeneous diffusion of the molecule.</li>
		<li>In the single Gaussian model, determine the probability distribution of D described by a Gaussian (f(D)) by fitting the CDF using15 
		<img alt="Equation3" src="/files/ftp_upload/54503/54503equation3.jpg" /> 
		<img alt="Equation4" src="/files/ftp_upload/54503/54503equation4.jpg" /> 
		where A, w, and D0 are the amplitude, width, and center of the Gaussian.</li>
		<li>In the double Gaussian model, determine the probability distribution of jth component of D described by a Gaussian (f(D)) by fitting the CDF using14 
		<img alt="Equation5" src="/files/ftp_upload/54503/54503equation5.jpg" /> 
		<img alt="Equation6" src="/files/ftp_upload/54503/54503equation6.jpg" /> 
		where Aj is the fraction of each diffusion component, and &#945;j, wj, and D0j are the amplitude, width, and center of the jth component of the Gaussian.</li>
	</ol>
	</li>
	<li>Calculation of the theoretical probability distribution of diffusion coefficient 
	NOTE: The probability distributions of D occurring due to the statistical errors (p(D)dD) are calculated for the different diffusion models; homogeneous diffusion model, multiple diffusion modes in which the D distribution is described by a Gaussian (single Gaussian model), and multiple diffusion modes in which the D distribution is described by multiple Gaussian (multiple Gaussian model).
	<ol>
		<li>In the homogeneous diffusion model, calculate the statistical probability distribution of D using an equation22 
		<img alt="Equation7" src="/files/ftp_upload/54503/54503equation7.jpg" /> 
		where N is the number of the data points in a diffusion trajectory (N = 10, see 4.1.2), D0 is the mean diffusion coefficient (determined by the CDF analysis, see 4.2.3.1), and D is the experimentally obtained diffusion coefficient for an individual trajectory.</li>
		<li>In the single Gaussian diffusion model, calculate the statistical probability distribution of D using an equation15 
		<img alt="Equation8" src="/files/ftp_upload/54503/54503equation8.jpg" /> 
		where f(D) denotes probability distribution of D determined by the CDF analysis (see 4.2.3.2), and D0 is the mean diffusion coefficient (determined by the CDF analysis, see 4.2.3.2).</li>
		<li>In the double Gaussian diffusion model, calculate the statistical probability distribution of D using an equation14 
		<img alt="Equation9" src="/files/ftp_upload/54503/54503equation9.jpg" /> 
		where f(Dj) denotes probability distribution of the jth component of D (Dj) determined by the CDF analysis (see 4.2.3.3), and D0j is the mean diffusion coefficient of the jth component (determined by the CDF analysis, see 4.2.3.3).</li>
	</ol>
	</li>
</ol>

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Ed. 49 (8), 1418-1421 (2010).</li><li>Habuchi, S., Tezuka, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Topological Polymer Chemistry: Progress of Cyclic Polymers in Syntheses, Properties and Functions. , 265-290 (2013).</li><li>Fernandez, P., Bayona, J. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Use+of+off-line+gel-remeation+chromatography+normal-phase+liquid-chromatography+fro+the+determination+of+polycyclic+aromatic-compounds+in+environmental-samples+and+standard+reference+materials+(air+particulate+matter+and+marine+sediment).">Use of off-line gel-remeation chromatography normal-phase liquid-chromatography fro the determination of polycyclic aromatic-compounds in environmental-samples and standard reference materials (air particulate matter and marine sediment).</a> J. 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J. 65 (5), 2021-2040 (1993).</li><li>Schutz, G. J., Schindler, H., Schmidt, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Single-molecule+microscopy+on+model+membranes+reveals+anomalous+diffusion.">Single-molecule microscopy on model membranes reveals anomalous diffusion.</a> Biophys. J. 73 (2), 1073-1080 (1997).</li><li>Vrljic, M., Nishimura, S. Y., Brasselet, S., Moerner, W. E., McConnell, H. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Translational+diffusion+of+individual+class+II+MHC+membrane+proteins+in+cells.">Translational diffusion of individual class II MHC membrane proteins in cells.</a> Biophys. J. 83 (5), 2681-2692 (2002).</li><li>Margineanu, A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photophysics+of+a+water-soluble+rylene+dye:+Comparison+with+other+fluorescent+molecules+for+biological+applications.">Photophysics of a water-soluble rylene dye: Comparison with other fluorescent molecules for biological applications.</a> J. Phys. Chem. B. 108 (32), 12242-12251 (2004).</li><li>Tezuka, Y., Oike, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Self-assembly+and+covalent+fixation+for+topological+polymer+chemistry.">Self-assembly and covalent fixation for topological polymer chemistry.</a> Macromol. Rapid Commun. 22 (13), 1017-1029 (2001).</li><li>Deres, A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Origin+of+Heterogeneity+of+Polymer+Dynamics+near+the+Glass+Temperature+As+Probed+by+Defocused+Imaging.">The Origin of Heterogeneity of Polymer Dynamics near the Glass Temperature As Probed by Defocused Imaging.</a> Macromolecules. 44 (24), 9703-9709 (2011).</li><li>Flier, B. M. I., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Heterogeneous+Diffusion+in+Thin+Polymer+Films+As+Observed+by+High-Temperature+Single-Molecule+Fluorescence+Microscopy.">Heterogeneous Diffusion in Thin Polymer Films As Observed by High-Temperature Single-Molecule Fluorescence Microscopy.</a> J. Am. Chem. Soc. 134 (1), 480-488 (2012).</li><li>Habuchi, S., Oba, T., Vacha, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Multi-beam+single-molecule+defocused+fluorescence+imaging+reveals+local+anisotropic+nature+of+polymer+thin+films.">Multi-beam single-molecule defocused fluorescence imaging reveals local anisotropic nature of polymer thin films.</a> Phys. Chem. Chem. Phys. 13 (15), 6970-6976 (2011).</li><li>Zettl, U., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Self-Diffusion+and+Cooperative+Diffusion+in+Semidilute+Polymer+Solutions+As+Measured+by+Fluorescence+Correlation+Spectroscopy.">Self-Diffusion and Cooperative Diffusion in Semidilute Polymer Solutions As Measured by Fluorescence Correlation Spectroscopy.</a> Macromolecules. 42 (24), 9537-9547 (2009).</li><li>Kirstein, J., Platschek, B., Jung, C., Brown, R., Bein, T., Brauchle, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Exploration+of+nanostructured+channel+systems+with+single-molecule+probes.">Exploration of nanostructured channel systems with single-molecule probes.</a> Nat. Mater. 6 (4), 303-310 (2007).</li></ol>

The authors have nothing to disclose.

The 4-armed and 8-shaped polymers were prepared via the ESA-CF protocol (Figure 1), which is a critical step for the synthesis.12,24 Monofunctional and bifunctional linear poly(THF)s with N-phenylpiperidinium end groups were synthesized according to the previous procedure.11 The ion exchange was carried out by reprecipitation of an acetone solution of a polymer precursor with triflate counteranions into an aqueous solution containing an excess amount of carboxylate.
<p ...

Cyclic polymers are unique in that they do not have chain ends. They often exhibit unusual behaviors which is distinct from their linear counterpart, including increased thermal stability of polymer micelles by a linear-to-cyclic conversion,1,2 and spatial organization of DNA in bacterial cells by a loop formation.3 Topological interactions between the cyclic chains are believed to be the critical factor for such unusual behaviors.4,5 Therefore, characterizing the motion and relaxation of cyclic polymers under entangled conditions has been an important research topic in polymer science for decades.6
Cyclic polymer dynamics has been investigated using both synthetic and naturally occurring molecules by means of ensemble averaged experimental methods such as nuclear magnetic resonance (NMR), light scattering, and viscosity measurements.7-9 However, these studies often suffer from impurity molecules in the samples.10 Furthermore, spatiotemporal heterogeneities of the motion of individual molecules caused by inherent structural heterogeneity of entangled polymers are often hidden behind the ensemble averaging in these studies. In order to characterize molecular level dynamics of cyclic polymers, a synthesis method that provides high purity cyclic polymers and an experimental and analysis methods that allow for quantitative characterization of molecular motion at the single molecule level have to be developed. Here, we will show a method to synthesize high-purity cyclic and dicyclic poly(THF)s that incorporate a fluorophore unit using an electrostatic self-assembly and covalent fixation (ESA-CF) process11-13 and a method to analyze the motion of the individual fluorophore-incorporated polymer chains using a combination of mean-squared displacement (MSD) and cumulative distribution function (CDF) analyses.
A proper data processing has been shown to be essential for the accurate characterization of the diffusive motion. With an adequate MSD and CDF analyses, a multiple-mode diffusion of the cyclic and dicyclic polymers in the melt and semi-dilute solution of the linear polymer chains has been revealed,14-16 suggesting the significant effects of the topological states of the polymers on the diffusive motion of the chains under entangled conditions.17 While the experimental and analytical approaches to characterize the motion of the cyclic polymers are described in this protocol, the same method can be used to quantitatively characterize the diffusive motion in many other heterogeneous systems. The approach would be especially suitable when multiple diffusion components existing in the samples are to be analyzed.

<table><tbody><tr><td>&lt;strong&gt;Materials&lt;/strong&gt;</td><td></td><td></td><td></td></tr><tr><td>THF</td><td>Godo</td><td></td><td></td></tr><tr><td>Wakosil C-300</td><td>Wako Pure Chemical Industries</td><td></td><td></td></tr><tr><td>Acetone</td><td>Godo</td><td></td><td></td></tr><tr><td>Toluene</td><td>Godo</td><td></td><td></td></tr><tr><td>&lt;em&gt;n&lt;/em&gt;-Hexane</td><td>Godo</td><td></td><td></td></tr><tr><td>CHCl&lt;sub&gt;3&lt;/sub&gt;</td><td>Kanto Chemical</td><td></td><td></td></tr><tr><td>Bio-Beads S-X1</td><td>Bio-Rad</td><td></td><td></td></tr><tr><td>Methyl triflate</td><td>Nacalai Tesque</td><td></td><td></td></tr><tr><td>Triflic anhydride</td><td>Nacalai Tesque</td><td></td><td></td></tr><tr><td>Potassium Hydroxide</td><td>Wako Pure Chemical Industries</td><td></td><td></td></tr><tr><td>Ethanol</td><td>Wako Pure Chemical Industries</td><td></td><td></td></tr><tr><td>Poly(tetrahydrofuran)</td><td>Aldrich</td><td></td><td></td></tr><tr><td>Chloroform</td><td>Wako Pure Chemical Industries</td><td></td><td></td></tr><tr><td>Immersion oil</td><td>Cargille</td><td>Type 37 / Type A</td><td></td></tr><tr><td>&lt;strong&gt;Equipment&lt;/strong&gt;</td><td></td><td></td><td></td></tr><tr><td>2-Neck 100-ml round-bottom flask</td><td></td><td></td><td></td></tr><tr><td>Flask</td><td></td><td></td><td></td></tr><tr><td>Beaker</td><td></td><td></td><td></td></tr><tr><td>Funnel</td><td></td><td></td><td></td></tr><tr><td>Filter paper</td><td>Whatman</td><td></td><td></td></tr><tr><td>Reflux condenser</td><td></td><td></td><td></td></tr><tr><td>Syringe</td><td></td><td></td><td></td></tr><tr><td>Water bath</td><td></td><td></td><td></td></tr><tr><td>Magnetic stirrer</td><td></td><td></td><td></td></tr><tr><td>Rotary evaporator</td><td></td><td></td><td></td></tr><tr><td>Microscope cover slips (24 x 24 mm, No. 1)</td><td>Matsunami Glass</td><td>CO22241</td><td></td></tr><tr><td>Staining jar</td><td>AS ONE Corporation</td><td>1-7934-01</td><td></td></tr><tr><td>Ultrasonic cleaner</td><td>VWR International&amp;nbsp;</td><td>142-0047</td><td></td></tr><tr><td>Inverted microscope</td><td>Olympus</td><td>IX71</td><td></td></tr><tr><td>Ar-Kr ion laser</td><td>Coherent</td><td>Innova 70C</td><td></td></tr><tr><td>Berek compensator</td><td>Newport</td><td>5540</td><td></td></tr><tr><td>Excitation filter</td><td>Semrock</td><td>LL01-488-12.5</td><td></td></tr><tr><td>Dichloric mirror</td><td>Omega optical</td><td>500DRLP</td><td></td></tr><tr><td>Emission filter</td><td>Semrock</td><td>BLP01-488R-25</td><td></td></tr><tr><td>Lens and mirror</td><td>Thorlabs</td><td></td><td></td></tr><tr><td>EM-CCD camera</td><td>Andor Technology</td><td>iXon</td><td></td></tr><tr><td>Objective lens (100X, N.A. = 1.3)</td><td>Olympus</td><td>UPLFLN 100XOP</td><td></td></tr><tr><td>Objective heater</td><td>Bioptechs</td><td></td><td></td></tr><tr><td>Preparative GPC</td><td>Japan Analytical Industry</td><td>LC-908</td><td></td></tr></tbody></table>

synthesis of cyclic polymers and characterization of their diffusive motion in the melt state at the single molecule level

We demonstrate a method for the synthesis of cyclic polymers and a protocol for characterizing their diffusive motion in a melt state at the single molecule level. An electrostatic self-assembly and covalent fixation (ESA-CF) process is used for the synthesis of the cyclic poly(tetrahydrofuran) (poly(THF)). The diffusive motion of individual cyclic polymer chains in a melt state is visualized using single molecule fluorescence imaging by incorporating a fluorophore unit in the cyclic chains. The diffusive motion of the chains is quantitatively characterized by means of a combination of mean-squared displacement (MSD) analysis and a cumulative distribution function (CDF) analysis. The cyclic polymer exhibits multiple-mode diffusion which is distinct from its linear counterpart. The results demonstrate that the diffusional heterogeneity of polymers that is often hidden behind ensemble averaging can be revealed by the efficient synthesis of the cyclic polymers using the ESA-CF process and the quantitative analysis of the diffusive motion at the single molecule level using the MSD and CDF analyses.

The perylene diimide-incorporated 4-armed star and 8-shaped dicyclic poly(THF)s were synthesized using the electrostatic self-assembly and covalent fixation (ESA-CF) process (Figure 1, Figure 2). Time-lapse single-molecule fluorescence images were measured for the 4-armed (Figure 3a) and 8-shaped (Figure 3b) polymers. The time-lapse fluorescence images (Figure 3) show spatially isolated bright and sharp s...

Watch this Scientific Journal Video about Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level at JoVE.com

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

A protocol for the synthesis and characterization of diffusive motion of cyclic polymers at the single molecule level is presented.

We demonstrate a method for the synthesis of cyclic polymers and a protocol for characterizing their diffusive motion in a melt state at the single ...

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7.8K Views.  King Abdullah University of Science and Technology (KAUST). A protocol for the synthesis and characterization of diffusive motion of cyclic polymers at the single molecule level is presented.

Video: Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this work, we use single particle tracking of fluorescently labeled PNIPAM microgels as a showcase for tuning microgel size by a rapid non-stirred precipitation polymerization procedure. This approach is well suited for prototyping new reaction compositions and conditions or for applications that do not require large amounts of product. Microgel synthesis, particle size and structure determination by dynamic and static light scattering are detailed in the protocol. It is shown that the addition of functional comonomers can have a large influence on the particle nucleation and structure. Single particle tracking by wide-field fluorescence microscopy allows for an investigation of the diffusion of labeled tracer microgels in a concentrated matrix of non-labeled microgels, a system not easily investigated by other methods such as dynamic light scattering.

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Non-stirred precipitation polymerization provides a rapid, reproducible prototyping approach to the synthesis of stimuli-sensitive poly(N-isopropylacrylamide) microgels of narrow size distribution. In this protocol synthesis, light scattering characterization and single particle fluorescence tracking of these microgels in a wide-field microscopy setup are demonstrated.

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this ...

Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives

A facile method for the preparation of polycarbodiimide-based secondary structures (e.g., nano-rings, &#34;craters,&#34; fibers, looped fibers, fibrous networks, ribbons, worm-like aggregates, toroidal structures, and spherical particles) is described. These aggregates are morphologically influenced by extensive hydrophobic side chain-side chain interactions of the singular polycarbodiimide strands, as inferred by atomic force microscopy (AFM) and scanning electron microscopy (SEM) techniques. Polycarbodiimide-g-polystyrene copolymers (PS-PCDs) were prepared by a combination of synthetic methods, including coordination-insertion polymerization, copper(I)-catalyzed azide alkyne cycloaddition (CuAAC) &#34;click&#34; chemistry, and atom transfer radical polymerization (ATRP). PS-PCDs were found to form specific toroidal architectures at low concentrations in CHCl3. To determine the influence of a more polar solvent medium (i.e., THF and THF/EtOH) on polymer aggregation behavior, a number of representative PS-PCD composites have been tested to show discrete concentration-dependent spherical particles. These fundamental studies are of practical interest to the development of experimental procedures for desirable architectures by directed self-assembly in thin film. These architectures may be exploited as drug carriers, whereas other morphological findings represent certain interest in the area of novel functional materials.

Here, we present a protocol to prepare and visualize secondary structures (e.g., fibers, toroidal architectures, and nano-spheres) derived from helical polycarbodiimides. The morphology characterized by both atomic force microscopy (AFM) and scanning electron microscopy (SEM) was shown to depend on molecular structure, concentration, and the solvent of choice.

A facile method for the preparation of polycarbodiimide-based secondary structures (e.g., nano-rings, &#34;craters,&#34; fibers, looped fibers, fibrous ...

Synthesis of Terpolymers at Mild Temperatures Using Dynamic Sulfur Bonds in Poly(S-Divinylbenzene)

Elemental sulfur (S8) is a byproduct of the petroleum industry with millions of tons produced annually. Such abundant production and limited applications lead to sulfur as a cost-efficient reagent for polymer synthesis. Inverse vulcanization combines elemental sulfur with a variety of monomers to form functional polysulfides without the need for solvents. Short reaction times and straight forward synthetic methods have led to rapid expansion of inverse vulcanization. However, high reaction temperatures (&#62;160 &#176;C) limit the types of monomers that can be used. Here, the dynamic sulfur bonds in poly(S-divinylbenzene) are used to initiate polymerization at much lower temperatures. The S-S bonds in the prepolymer are less stable than S-S bonds in S8, allowing radical formation at 90 &#176;C rather than 159 &#176;C. A variety of allyl and vinyl ethers have been incorporated to form terpolymers. The resulting materials were characterized by 1H NMR, gel permeation chromatography, and differential scanning calorimetry, as well as examining changes in solubility. This method expands on the solvent-free, thiyl radical chemistry utilized by inverse vulcanization to create polysulfides at mild temperatures. This development broadens the range of monomers that can be incorporated thus expanding the accessible material properties and possible applications.

Synthesis of Terpolymers at Mild Temperatures Using Dynamic Sulfur Bonds in PolyS-Divinylbenzene

The goal of this protocol is to initiate polymerization using dynamic sulfur bonds in poly(S-divinylbenzene) at mild temperatures (90 &#176;C) without using solvents. Terpolymers are characterized by GPC, DSC and 1H NMR, and tested for changes in solubility.

Elemental sulfur (S8) is a byproduct of the petroleum industry with millions of tons produced annually. Such abundant production and limited applications ...

Synthesis of Monodisperse Cylindrical Nanoparticles via Crystallization-driven Self-assembly of Biodegradable Block Copolymers

The production of monodisperse cylindrical micelles is a significant challenge in polymer chemistry. Most cylindrical constructs formed from diblock copolymers are produced by one of three techniques: thin film rehydration, solvent switching or polymerization-induced self-assembly, and produce only flexible, polydisperse cylinders. Crystallization-driven self-assembly (CDSA) is a method which can produce cylinders with these properties, by stabilizing structures of a lower curvature due to the formation of a crystalline core. However, the living polymerization techniques by which most core-forming blocks are formed are not trivial processes and the CDSA process may yield unsatisfactory results if carried out incorrectly. Here, the synthesis of cylindrical nanoparticles from simple reagents is shown. The drying and purification of reagents prior to a ring-opening polymerization of &#949;-caprolactone catalyzed by diphenyl phosphate is described. This polymer is then chain extended by methyl methacrylate (MMA) followed by N,N-dimethyl acrylamide (DMA) using reversible addition&#8722;fragmentation chain-transfer (RAFT) polymerization, affording a triblock copolymer that can undergo CDSA in ethanol. The living CDSA process is outlined, the results of which yield cylindrical nanoparticles up to 500 nm in length and a length dispersity as low as 1.05. It is anticipated that these protocols will allow others to produce cylindrical nanostructures and elevate the field of CDSA in the future.

Crystallization-driven self-assembly (CDSA) displays the unique ability to fabricate cylindrical nanostructures of narrow length distributions. The organocatalyzed ring-opening polymerization of &#949;-caprolactone and subsequent chain extensions of methyl methacrylate and N,N-dimethyl acrylamide are demonstrated. A living CDSA protocol that produces monodisperse cylinders up to 500 nm in length is outlined.

The production of monodisperse cylindrical micelles is a significant challenge in polymer chemistry. Most cylindrical constructs formed from diblock ...

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

We have developed a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package is best suited for applications on natural systems, like silicate and oxide melts, water-based fluids, and various supercritical fluids. The package is a collection of Python scripts that include two major libraries dealing with file formats and with crystallography. All the scripts are run at the command line. We propose a simplified format to store the atomic trajectories and relevant thermodynamic information of the simulations, which is saved in UMD files, standing for Universal Molecular Dynamics. The UMD package allows the computation of a series of structural, transport and thermodynamic properties. Starting with the pair-distribution function it defines bond lengths, builds an interatomic connectivity matrix, and eventually determines the chemical speciation. Determining the lifetime of the chemical species allows running a full statistical analysis. Then dedicated scripts compute the mean-square displacements for the atoms as well as for the chemical species. The implemented self-correlation analysis of the atomic velocities yields the diffusion coefficients and the vibrational spectrum. The same analysis applied on the stresses yields the viscosity. The package is available via the GitHub website and via its own dedicated page of the ERC IMPACT project as open-access package.

Melts and fluids are ubiquitous vectors of mass transport in natural systems. We have developed an open-source package to analyze ab initio molecular-dynamics simulations of such systems. We compute structural (bonding, clusterization, chemical speciation), transport (diffusion, viscosity) and thermodynamic properties (vibrational spectrum).

We have developed a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package ...

Designed for Molecular Recycling: A Lignin-Derived Semi-aromatic Biobased Polymer

The development of chemically recyclable biopolymers offers opportunities within the pursuit of a circular economy. Chemically recyclable biopolymers make a positive effort to solve the issue of polymer materials in the disposal phase after the use phase. In this paper, the production of biobased semi-aromatic polyesters, which can be extracted entirely from biomass such as lignin, is described and visualized. The polymer poly-S described in this paper has thermal properties similar to certain commonly used plastics, such as PET. We developed a Green Knoevenagel reaction, which can efficiently produce monomers from aromatic aldehydes and malonic acid. This reaction has been proven to be scalable and has a remarkably low calculated E-factor. These polyesters with ligno-phytochemicals as a starting point show an efficient molecular recycling with minimal losses. The polyester poly(dihydrosinapinic acid) (poly-S) is presented as an example of these semi-aromatic polyesters, and the polymerization, depolymerization, and re-polymerization are described.

An example of a closed-loop approach towards a circular materials economy is described here. A whole sustainable cycle is presented where biobased semi-aromatic polyesters are designed by polymerization, depolymerization, and then re-polymerized with only slight changes in their yields or final properties.

The development of chemically recyclable biopolymers offers opportunities within the pursuit of a circular economy. Chemically recyclable biopolymers make ...

Methods for the Self-integration of Megamolecular Biopolymers on the Drying Air-LC Interface

Living organisms that use water are always prone to drying in the environment. Their activities are driven by biopolymer-based micro- and macro-structures, as seen in the cases of moving water in vascular bundles and moisturizing water in skin layers. In this study, we developed a method for assessing the effect of aqueous liquid crystalline (LC) solutions composed of biopolymers on drying. As LC biopolymers have megamolecular weight, we chose to study polysaccharides, cytoskeletal proteins, and DNA. The observation of biopolymer solutions during drying under polarized light reveals milliscale self-integration starting from the unstable air-LC interface. The dynamics of the aqueous LC biopolymer solutions can be monitored by evaporating water from a one-side-open cell. By analyzing the images taken using cross-polarized light, it is possible to recognize the spatio-temporal changes in the orientational order parameter. This method can be useful for the characterization of not only artificial materials in various fields, but also natural living tissues. We believe that it will provide an evaluation method for soft materials in the biomedical and environmental fields.

A method for the drying-induced self-integration of megamolecular biopolymers on the air-liquid crystalline interface is provided here. This methodology will be useful not only for understanding the macroscopic potentials of biopolymers, but also as an evaluation method for soft materials in biomedical and environmental fields.

Living organisms that use water are always prone to drying in the environment. Their activities are driven by biopolymer-based micro- and ...

Bioengineering

Depolymerizable Olefinic Polymers Based on Fused-Ring Cyclooctene Monomers

The growing consumption of synthetic polymers and the accumulation of polymer waste have led to a pressing need for new routes to sustainable materials. Achieving a closed-loop polymer economy via chemical recycling to monomer (CRM) is one such promising route. Our group recently reported a new CRM system based on polymers prepared by ring-opening metathesis polymerization (ROMP) of trans-cyclobutane fused cyclooctene (tCBCO) monomers. This system offers several key advantages, including the ease of polymerization at ambient temperatures, quantitative depolymerization to monomers under mild conditions, and a broad range of functionalities and thermomechanical properties. Here, we outline detailed protocols for the preparation of tCBCO-based monomers and their corresponding polymers, including the preparation of elastic polymer networks and compression molding of linear thermoplastic polymers. We also outline the preparation of high ring strain E-alkene tCBCO monomers and their living polymerization. Finally, the procedures for the depolymerization of linear polymers and polymer networks are also demonstrated.

Here, we describe protocols for the preparation of trans-cyclobutane fused cyclooctenes (tCBCO),&#160;their polymerization to prepare depolymerizable olefinic polymers, and the depolymerization of these polymers under mild conditions. Additionally, protocols for the preparation of depolymerizable networks and compression molding of rigid linear plastics based on this system are described.

The growing consumption of synthetic polymers and the accumulation of polymer waste have led to a pressing need for new routes to sustainable materials. ...

Polymerization

Source: Vy M. Dong and Jan Riedel, Department of Chemistry, University of California, Irvine, CA
Polymers are made from macromolecules, which are composed of repeating units (the so called monomeric units). In our modern world, polymers play an important role. One of the first important polymers was nylon, which is a polyamide. It found widespread application in tooth brushes and stockings.

Polymerization: Types of Polymerizations and Applications

Source: Vy M. Dong and Jan Riedel, Department of Chemistry, University of California, Irvine, CA
Polymers are made from macromolecules, which are composed ...

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Kinetics of Addition Polymerization to Polydimethylsiloxane

Source: <a href="https://www.jove.com/author/Kerry+M._Dooley">Kerry M. Dooley</a> and Michael G. Benton, Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA
Polymers are molecules consisting of many repeating monomer units that are chemically bonded into long chains. They exhibit a broad range of physical properties, which are affected by their chemical structure, molecular weight and degree of polymerization. The polymer industry manufactures thousands of raw materials used in a broad variety of commercial products.1,2
The goal of this video is to perform an addition polymerization reaction and then evaluate the resulting product to understand how viscosity can be used to determine polymer molecular weight. Additionally, this experiment will investigate how molecular weight can be related to monomer conversion.

Synthesis of Polydimethylsiloxane via Addition Polymerization

Source: Kerry M. Dooley and Michael G. Benton, Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA
Polymers are molecules ...