Journal of Polymer and Biopolymer Physics Chemistry
ISSN (Print): 2373-3403 ISSN (Online): 2373-3411 Website: Editor-in-chief: Martin Alberto Masuelli
Open Access
Journal Browser
Journal of Polymer and Biopolymer Physics Chemistry. 2018, 6(1), 26-30
DOI: 10.12691/jpbpc-6-1-3
Open AccessArticle

PFG-NMR Studies of Linear and Dendritic Polymers

James E. Hanson1, , Sibel Alkan1, Hershel Lackey2, 3 and Judith B. Cain2

1Department of Chemistry and Biochemistry, Seton Hall University, South Orange, NJ, USA

2Chemistry Department, Virginia Military Institute, Lexington, VA, USA

3Department of Chemistry, University of Utah, Salt Lake City UT, USA

Pub. Date: October 10, 2018

Cite this paper:
James E. Hanson, Sibel Alkan, Hershel Lackey and Judith B. Cain. PFG-NMR Studies of Linear and Dendritic Polymers. Journal of Polymer and Biopolymer Physics Chemistry. 2018; 6(1):26-30. doi: 10.12691/jpbpc-6-1-3


Diffusion coefficients were measured by pulsed-field gradient NMR for low molecular weight linear polystyrenes in THF and for a broader molecular weight range of linear polystyrenes in chloroform and for PAMAM dendrimers up to generation methanol. Radii were calculated from the measured diffusion coefficients using the Stokes-Einstein relationship. The linear polystyrenes displayed a relationship between radius and molecular weight that followed the expected power law. From simple theoretical considerations, the dendritic polymers were expected to follow a logarithmic relationship between radius and molecular weight. The PAMAM dendrimers gave reasonable fits to both a power law and a logarithmic relationship from generation 0 to generation 3 (the power law gave a slightly better fit), but displayed a turnover with generation 4, which gave a smaller Stokes radius than generation 3. These results were compared with earlier results from poly (aryl ether) monodendrons, where the relationship was ambiguous between a power law and a logarithmic relationship.

dendrimers pulsed field gradient NMR diffusion coefficients scaling law hydrodynamic radii

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


Figure of 3


[1]  Boss, B.D.; Stejskal, E.O.; Ferry, J.D. "Self-Diffusion in High Molecular Weight Polyisobutylene-Benzene Mixtures Determined by the Pulsed-Gradient, Spin-Echo Method" J. Phys. Chem. 71 (5). 1501-1506. 1967.
[2]  Stejskal, E.O.; Tanner, J.E., "Spin Diffusion Measurements: Spin Echoes in the Presence of a Time Dependent Field Gradient" J. Chem. Phys. 42 (1). 288-292. 1965.
[3]  Balcom, B.J.; Fischer, A.E.; Carpenter, T.A.; Hall, L.D. "Diffusion in Aqueous Gels: Mutual Diffusion Coefficients Measured by One-Dimensional Nuclear Magnetic Resonance Imaging" J. Am. Chem. Soc. 115 (8). 3300-3305. 1993.
[4]  Chen, A.; Wu, D. Johnson, C.S. Jr. "Determination of Molecular Weight Distributions for Polymers by Diffusion Ordered NMR" J. Am. Chem. Soc. 117 (30). 7965-7970. 1995.
[5]  Cain, J.B.; Zhang, K.; Betts, D.E.; DeSimone, J.M; Johnson, C.S. Jr. "Diffusion of Block Copolymers in Liquid CO2: Evidence of Self-Assembly from Pulsed-Field Gradient NMR" J. Am. Chem. Soc. 120 (36). 9390-9391. 1998.
[6]  Chen, A.; Shapiro, M.J. "NOE Pumping. 2. A High-Throughput Method to Determine Compounds with Binding Affinity to Macromolecules by NMR" J.Am.Chem. Soc. 122 (2). 414-415. 2000.
[7]  Karger, J.; Fleischer, G. "NMR Diffusion Studies in Heterogeneous Systems" Trends in Analyt. Chem., 13 (4), 145-157, 1994.
[8]  Callaghan, P.T.; Pinder, D.N. "Influence of Polydispersity on Polymer Self-Diffusion Measurements by Pulsed-Field-Gradient Nuclear Magnetic Resonance" Macromolecules, 18, 373-379. 1985.
[9]  Tyrrell, H.J.V. Diffusion and Heat Flow in Liquids, Butterworths: London, 1961.
[10]  Ricka, J.; Gysel, H.; Schneider, J.; Nyffenegger, R.; Binkert, T. "Mobility of Fluorescent Polyacrylamide Derivatives in Water-Acetone Mixtures" Macromolecules 20 (6). 1407-1411. 1987.
[11]  Edward, J.T. "Molecular Volumes and the Stokes-Einstein Equation" J. Chem. Ed. 47 (4). 261. 1970.
[12]  Riley, J.M.; Alkan, S.; Chen, A.; Shapiro, M.; Khan, W.A.; Murphy, W.R., Jr.; Hanson, J.E. "Pyrene-Labeled Poly(aryl ether) Monodendrons: Synthesis, Characterization, Diffusion Coefficients, and Photophysical Studies" Macromolecules 34 (6). 1797-1809. 2001.
[13]  Rietveld, I.B.; Bedeaux, D. "Self-Diffusion of Poly(Propylene Imine) Dendrimers in Methanol" Macromolecules, 33, 7912-7917. 2000.
[14]  Goldsmith, J.I.; Takada, K.; Abruna, H.D. "Probing Diffusional Transport in Redox Active Dendrimers" J. Phys. Chem. B. 106, 8504-8513. 2002.
[15]  Krykin, M.A.; Volkov, V.I.; Volkov, E.V.; Surin, N.M.; Ozerina, L.A; Muzafarov, A.M.; Ozerin, A.N. "Structure and Dynamics of Carbosilane Dendrimers as Revealed by Pulsed Field Gradient NMR Technique" Appl. Magn. Res. 29, 459-469. 2005.
[16]  Ghoneim, A.; Karger, J.; Sangoro, J.R.; Turky, G. Abdel Rahim, M.; Iacob, C.; Naumov, S.; Kremer, F. "Charge Transport and Dipolar Relaxation in Hyperbranched Polyamide Amines" Macromolecules, 42, 1648-1651, 2009.
[17]  Wu, D.; Chen, A.; Johnson, C.S. Jr. "An Improved Diffusion-Ordered Spectroscopy Experiment Incorporating Bipolar-Gradient Pulses" J. Magn. Res. Ser. A 115 (2). 260-264. 1995.
[18]  Jerschow, A.; Muller, N. "Convection Compensation in Gradient Enhanced Nuclear Magnetic Resonance Spectroscopy" J. Magn. Res. 132 (1). 13-18. 1998.
[19]  CRC Handbook of Chemistry and Physics 78th Edition, Lide, D.R. Ed. CRC Press: Boca Raton FL, 1997.
[20]  Rabinovich, L.B. The Influence of Isotopy on the Physico-Chemical Properties of Liquids, Consultants Bureau: New York, 1970.
[21]  Cataliotti, R.S.; Sassi, P.; Morresi, A.; Paliani, G. "Mandalstam-Brillouin Spectra and Hyperacoustic Velocities Dispersion of Trideuteroacetonitrile in the Liquid State" Chem. Phys. 255(1). 85-93. 2000.
[22]  De Backer, S.; Prinzie, Y.; Verheijen, W.; Smet, M.; Desmedt, K.; Dehaen, W.; DeSchryver, F.C. "Solvent Dependence of the Hydrodynamical Volume of Dendrimers with a Rubicene Core" J. Phys. Chem. A 102 (28). 5451-5455. 1998.
[23]  Flory, P.J. "The Configuration of Real Polymer Chains" J. Chem. Phys. 17 (3). 303-310 1949.
[24]  Flory, P.J. Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1971.
[25]  Flory, P.J. Polymer Science: Achievements and Prospects, Markovitz H. and Casassa, E.F. eds., Wiley Interscience, New York, 1976.
[26]  de Gennes, P.G. Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.
[27]  Gedde, U.W. Polymer Physics, Chapman and Hall, New York, 1995.
[28]  Schafer, L. Excluded Volume Effects in Polymer Solutions, Springer-Verlag, Berlin, 1999.
[29]  deGennes, P.G.; Hervet, H. "Statistics of Starburst Polymers" J. Physique Lett. 44 (9). L351-360. 1983.
[30]  Dubin, P.L.; Edwards, S.L.; Kaplan, J.I.; Mehta, M.S.; Tomalia, D.A.; Xia, J. "Carboxylated Starburst Dendrimers as Calibration Standards for Aqueous Size Exclusion Chromatography" Anal. Chem. 64 (20) 2344-2347. 1992.
[31]  Gibbs, S.J.; Johnson, C.S. Jr. "A PFG NMR Experiment for Accurate Diffusion and Flow Studies in the Presence of Eddy Currents" J. Magn. Res. 1991; 93 (2) 395-402. 1991.