Jian Qin is an Assistant Professor in the Department of Chemical Engineering at the Stanford University. His research focuses on development of microscopic understanding of structural and physical properties of soft matters by using a combination of analytical theory, scaling argument, numerical computation, and molecular simulation. He worked as a postdoctoral scholar with Juan de Pablo in the Institute for Molecular Engineering at the University of Chicago and with Scott Milner in the Department of Chemical Engineering at the Pennsylvania State University. He received his Ph.D. in the Department of Chemical Engineering and Materials Science at the University of Minnesota under the supervision of David Morse and Frank Bates. His research covers self-assembly of multi-component polymeric systems, molecular origin of entanglement and polymer melt rheology, coacervation of polyelectrolytes, Coulomb interactions in dielectrically heterogeneous electrolytes, and surface charge polarizations in particulate aggregates in the absence or presence of flow.

Academic Appointments

Honors & Awards

  • Hellman Faculty Fellow, Hellman Faculty Scholar Fund (2017-2018)
  • 3M Nontenured Faculty Award, 3M Company (2017)
  • Terman Faculty Fellowship, Stanford University (2016-2018)
  • Kadanoff-Rice Fellowship, University of Chicago (2013)
  • Doctor Dissertation Fellowship, University of Minnesota (2008)

Boards, Advisory Committees, Professional Organizations

  • Member, APS (2004 - Present)
  • Member, ACS (2016 - Present)
  • Member, AIChE (2012 - Present)

Professional Education

  • PhD, University of Minnesota (2009)

2017-18 Courses

Stanford Advisees

All Publications

  • Polarization energy of two charged dielectric spheres in close contact Molecular Systems Design & Engineering Lian, H., Qin, J. 2018
  • Field-theoretic simulations of random copolymers with structural rigidity Soft Matter Mao, S., MacPherson, Q., Qin, J., Spakowitz, A. J. 2017; 13: 2760
  • Image method for electrostatic energy of polarizable dipolar spheres J. Chem. Phys. Gustafson, K., Xu, G., Freed, K., Qin, J. 2017; 147 (064908)
  • High-temperature crystallization of nanocrystals into three-dimensional superlattices Nature Wu, L., Willis, J. J., McKay, I. S., Diroll, B. T., Qin, J., Cargnello, M., Tassone, C. J. 2017; 548 (197)
  • Criticality and connectivity in macromolecular charge complexation Macromolecules Qin, J., de Pablo, J. 2016; 49 (8789)
  • Image method for induced surface charge from many-body system of dielectric spheres Journal of Chemical Physics Qin, J., de Pablo, J. J., Freed, K. F. 2016; 145 (124903)
  • An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles Journal of Chemical Physics Jiang, X., Li, J., Zhao, X., Qin, J., Karpeev, D., Hernandez-Ortiz, J., de Pablo, J. J., Hernonen, O. 2016; 145 (064307)
  • Ordering transition in salt-doped diblock copolymers Macromolecules Qin, J., de Pablo, J. J. 2016; 49: 3630-3638
  • Tube dynamics works for randomly entangled rings PHYSICAL REVIEW LETTERS Qin, J., Milner, S. T. 2016; 116: 068307
  • Singular electrostatic energy of nanoparticle clusters PHYSICAL REVIEW E Qin, J., Krapf, N. W., Witten, T. A. 2016; 93: 022603
  • A theory of interactions between polarizable dielectric spheres JOURNAL OF COLLOID & INTERFACE SCIENCE Qin, J., Li, J., Lee, V., Jaeger, H., de Pablo, J. J., Freed, K. F. 2016; 469: 237
  • A Hybrid Human-computer Approach to the Extraction of Scientific Facts from the Literature Procedia Computer Science Tchoua, R. B., Chard, K., Audus, D., Qin, J., de Pablo, J. J., Foster, I. 2016; 80: 386
  • Blending education and polymer science: semiautomated creation of a thermodynamic property database Journal of Chemical Education Tchoua, R. B., Qin, J., Audus, D. J., Chard, K., Foster, I. T., de Pablo, J. J. 2016; 93 (1561)
  • Broadly accessible self-consistent field theory for block polymer materials discovery Macromolecules Arora, A., Qin, J., Morse, D. C., Delaney, K. T., Fredrickson, G. H., Bates, F. S., Dorfman, K. D. 2016
  • Sculpting bespoke mountains: Determining free energies with basis expansions JOURNAL OF CHEMICAL PHYSICS Whitmer, J. K., Fluitt, A. M., Antony, L., Qin, J., McGovern, M., de Pablo, J. J. 2015; 143 (4)


    The intriguing behavior of a wide variety of physical systems, ranging from amorphous solids or glasses to proteins, is a direct manifestation of underlying free energy landscapes riddled with local minima separated by large barriers. Exploring such landscapes has arguably become one of statistical physics's great challenges. A new method is proposed here for uniform sampling of rugged free energy surfaces. The method, which relies on special Green's functions to approximate the Dirac delta function, improves significantly on existing simulation techniques by providing a boundary-agnostic approach that is capable of mapping complex features in multidimensional free energy surfaces. The usefulness of the proposed approach is established in the context of a simple model glass former and model proteins, demonstrating improved convergence and accuracy over existing methods.

    View details for DOI 10.1063/1.4927147

    View details for Web of Science ID 000358929100007

    View details for PubMedID 26233101

  • Finding Entanglement Points in Simulated Polymer Melts MACROMOLECULES Cao, J., Qin, J., Milner, S. T. 2015; 48 (1): 99-110

    View details for DOI 10.1021/ma5010315

    View details for Web of Science ID 000348085600012

  • Chirality-selected phase behaviour in ionic polypeptide complexes NATURE COMMUNICATIONS Perry, S. L., Leon, L., Hoffmann, K. Q., Kade, M. J., Priftis, D., Black, K. A., Wong, D., Klein, R. A., Pierce, C. F., Margossian, K. O., Whitmer, J. K., Qin, J., de Pablo, J. J., Tirrell, M. 2015; 6


    Polyelectrolyte complexes present new opportunities for self-assembled soft matter. Factors determining whether the phase of the complex is solid or liquid remain unclear. Ionic polypeptides enable examination of the effects of stereochemistry on complex formation. Here we demonstrate that chirality determines the state of polyelectrolyte complexes, formed from mixing dilute solutions of oppositely charged polypeptides, via a combination of electrostatic and hydrogen-bonding interactions. Fluid complexes occur when at least one of the polypeptides in the mixture is racemic, which disrupts backbone hydrogen-bonding networks. Pairs of purely chiral polypeptides, of any sense, form compact, fibrillar solids with a β-sheet structure. Analogous behaviour occurs in micelles formed from polypeptide block copolymers with polyethylene oxide, where assembly into aggregates with either solid or fluid cores, and eventually into ordered phases at high concentrations, is possible. Chirality is an exploitable tool for manipulating material properties in polyelectrolyte complexation.

    View details for DOI 10.1038/ncomms7052

    View details for Web of Science ID 000348830100006

    View details for PubMedID 25586861

  • Tubes, Topology, and Polymer Entanglement MACROMOLECULES Qin, J., Milner, S. T. 2014; 47 (17): 6077-6085

    View details for DOI 10.1021/ma500755p

    View details for Web of Science ID 000341542900023

  • Evolutionary Optimization of Directed Self-Assembly of Triblock Copolymers on Chemically Patterned Substrates ACS MACRO LETTERS Khaira, G. S., Qin, J., Garner, G. P., Xiong, S., Wan, L., Ruiz, R., Jaeger, H. M., Nealey, P. F., de Pablo, J. J. 2014; 3 (8): 747-752

    View details for DOI 10.1021/mz5002349

    View details for Web of Science ID 000340701900011

  • Interfacial Tension of Polyelectrolyte Complex Coacervate Phases ACS MACRO LETTERS Qin, J., Priftis, D., Farina, R., Perry, S. L., Leon, L., Whitmer, J., Hoffmann, K., Tirrell, M., de Pablo, J. J. 2014; 3 (6): 565-568

    View details for DOI 10.1021/mz500190w

    View details for Web of Science ID 000337644500015

  • Simulating Constraint Release by Watching a Ring Cross Itself MACROMOLECULES Cao, J., Qin, J., Milner, S. T. 2014; 47 (7): 2479-2486

    View details for DOI 10.1021/ma500325z

    View details for Web of Science ID 000338807300034

  • Ternary, tunable polyelectrolyte complexes driven by complex coacervation 247th National Spring Meeting of the American-Chemical-Society (ACS) Priftis, D., Xia, X., Margossian, K., Perry, S. L., Leon, L., Qin, J., de Pablo, J., Tirrell, M. AMER CHEMICAL SOC. 2014
  • Collective and Single-Chain Correlations in Disordered Melts of Symmetric Diblock Copolymers: Quantitative Comparison of Simulations and Theory MACROMOLECULES Glaser, J., Qin, J., Medapuram, P., Morse, D. C. 2014; 47 (2): 851-869

    View details for DOI 10.1021/ma401694u

    View details for Web of Science ID 000330543500043

  • Tube Diameter of Oriented and Stretched Polymer Melts MACROMOLECULES Qin, J., Milner, S. T. 2013; 46 (4): 1659-1672

    View details for DOI 10.1021/ma302095k

    View details for Web of Science ID 000315618800046

  • Evolutionary pattern design for copolymer directed self-assembly SOFT MATTER Qin, J., Khaira, G. S., Su, Y., Garner, G. P., Miskin, M., Jaeger, H. M., de Pablo, J. J. 2013; 9 (48): 11467-11472

    View details for DOI 10.1039/c3sm51971f

    View details for Web of Science ID 000327500200005

  • Tube Diameter of Stretched and Compressed Permanently Entangled Polymers MACROMOLECULES Qin, J., So, J., Milner, S. T. 2012; 45 (24): 9816-9822

    View details for DOI 10.1021/ma301830w

    View details for Web of Science ID 000312563900028

  • Effects of tube persistence length on dynamics of mildly entangled polymers JOURNAL OF RHEOLOGY Qin, J., Milner, S. T., Stephanou, P. S., Mavrantzas, V. G. 2012; 56 (4): 707-723

    View details for DOI 10.1122/1.4708594

    View details for Web of Science ID 000304305700004

  • Fluctuations in Symmetric Diblock Copolymers: Testing Theories Old and New PHYSICAL REVIEW LETTERS Qin, J., Morse, D. C. 2012; 108 (23)


    Computer simulations are used to study composition fluctuations in disordered diblock copolymer melts over a range of values of the chain length N, and test several theories for the structure factor S(q). Specifically, we test the random-phase approximation (RPA), which is based on a self-consistent field treatment of fluctuations, the Fredrickson-Helfand theory, which was designed to describe fluctuations near the order-disorder transition, and the relatively new renormalized one-loop (ROL) theory. The results confirm claims that the RPA is exact in the limit N→∞ and that the ROL theory yields the dominant corrections to the RPA within a systematic expansion in powers of N(-1/2), and show that the ROL theory is much more accurate than either older theory.

    View details for DOI 10.1103/PhysRevLett.108.238301

    View details for Web of Science ID 000304855900012

    View details for PubMedID 23003999

  • Test of a scaling hypothesis for the structure factor of disordered diblock copolymer melts SOFT MATTER Glaser, J., Qin, J., Medapuram, P., Mueller, M., Morse, D. C. 2012; 8 (44): 11310-11317

    View details for DOI 10.1039/c2sm26536b

    View details for Web of Science ID 000310829600013

  • Finding the Tube with Isoconfigurational Averaging MACROMOLECULES Bisbee, W., Qin, J., Milner, S. T. 2011; 44 (22): 8972-8980

    View details for DOI 10.1021/ma2012333

    View details for Web of Science ID 000296893400032

  • Renormalized one-loop theory of correlations in disordered diblock copolymers JOURNAL OF CHEMICAL PHYSICS Qin, J., Grzywacz, P., Morse, D. C. 2011; 135 (8)


    A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)] is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q∗), peak position q∗, and single-chain statistics for symmetric and asymmetric copolymers as functions of χ(e)N, where χ(e) is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q∗) upon χ(e)N for symmetric diblock copolymers in the limit of strong scattering, or large χ(e)N, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q∗) and a decrease of q∗ for large values of χ(e)N, relative to the RPA predictions, but an enhancement of S(q∗) and an increase in q∗ for small χ(e)N. The decrease in q∗ near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q∗ at small values of χ(e)N is a direct result of non-Gaussian single-chain statistics.

    View details for DOI 10.1063/1.3609758

    View details for Web of Science ID 000294484700072

    View details for PubMedID 21895217

  • Relationships among coarse-grained field theories of fluctuations in polymer liquids JOURNAL OF CHEMICAL PHYSICS Morse, D. C., Qin, J. 2011; 134 (8)


    Two closely related field-theoretic approaches have been used in previous work to construct coarse-grained theories of corrections to the random phase approximation for correlations in block copolymer melts and miscible polymer blends. The "auxiliary field" (AF) approach is based on a rigorous expression for the partition function Z of a coarse-grained model as a functional integral of an auxiliary chemical potential field. The "effective Hamiltonian" (EH) approach is instead based on an expression for Z as a functional integral of an observable order parameter field. The exact effective Hamiltonian H(eff) in the EH approach is defined as the free energy of a system with a constrained order parameter field. In practice, however, H(eff) has often been approximated by a mean-field free energy functional, yielding what we call a mean-field effective Hamiltonian (MFEH) approximation. This approximation was the starting point of both the Fredrickson-Helfand analysis of fluctuation effects in diblock copolymers and earlier work on the Ginzburg criterion in polymer blends. A more rigorous EH approach by Holyst and Vilgis used an auxiliary field representation of the exact H(eff) and allowed for Gaussian fluctuations of this field. All applications of both AF and EH approaches have thus far relied upon some form of Gaussian, or "one-loop" approximation for fluctuations of a chemical potential and/or order parameter field about a mean-field saddle-point. The one-loop EH approximation of Holyst and Vilgis and the one-loop AF theory are equivalent to one another, but not to the one-loop MFEH theory. The one-loop AF and MFEH theories are shown to yield predictions for the inverse structure factor S(-1)(q) that (in the absence of further approximations to either theory) differ by a function that is independent of the Flory-Huggins interaction parameter χ. As a result, these theories yield predictions for the peak scattering intensity that exhibit a similar χ-dependence near a spinodal. The Fredrickson-Helfand theory for the structure factor in disordered diblock copolymer melts is an asymptotic approximation to the MFEH one-loop theory that captures the dominant asymptotic behavior of very long, symmetric copolymers very near the order-disorder transition.

    View details for DOI 10.1063/1.3548888

    View details for Web of Science ID 000287811300037

    View details for PubMedID 21361554

  • Counting polymer knots to find the entanglement length SOFT MATTER Qin, J., Milner, S. T. 2011; 7 (22): 10676-10693

    View details for DOI 10.1039/c1sm05972f

    View details for Web of Science ID 000296388300025

  • Phase Behavior of Nonfrustrated ABC Triblock Copolymers: Weak and Intermediate Segregation MACROMOLECULES Qin, J., Bates, F. S., Morse, D. C. 2010; 43 (11): 5128-5136

    View details for DOI 10.1021/ma100400q

    View details for Web of Science ID 000278109700037

  • Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers JOURNAL OF CHEMICAL PHYSICS Meuler, A. J., Ellison, C. J., Qin, J., Evans, C. M., Hillmyer, M. A., Bates, F. S. 2009; 130 (23)


    Four hydroxyl-terminated poly(isoprene-b-styrene) diblock copolymers with comparable molecular weights and compositions (equivalent volume fractions of polyisoprene and polystyrene) but different polystyrene block polydispersity indices (M(w)/M(n)=1.06,1.16,1.31,1.44) were synthesized by anionic polymerization using either sec-butyllithium or the functional organolithium 3-triisopropylsilyloxy-1-propyllithium. Poly(ethylene oxide) (PEO) blocks were grown from the end of each of these parent diblocks to yield four series of poly(isoprene-b-styrene-b-ethylene oxide) (ISO) triblock terpolymers that were used to interrogate the effects of varying the polydispersity of the middle bridged polystyrene block. In addition to the neat triblock samples, 13 multicomponent blends were prepared at four different compositions from the ISO materials containing a polystyrene segment with M(w)/M(n)=1.06; these blends were used to probe the effects of increasing the polydispersity of the terminal PEO block. The melt-phase behavior of all samples was characterized using small-angle X-ray scattering and dynamic mechanical spectroscopy. Numerous polydispersity-driven morphological transitions are reported, including transitions from lamellae to core-shell gyroid, from core-shell gyroid to hexagonally packed cylinders, and from network morphologies [either O(70) (the orthorhombic Fddd network) or core-shell gyroid] to lamellae. Domain periodicities and order-disorder transition temperatures also vary with block polydispersities. Self-consistent field theory calculations were performed to supplement the experimental investigations and help elucidate the molecular factors underlying the polydispersity effects. The consequences of varying the polydispersity of the terminal PEO block are comparable to the polydispersity effects previously reported in AB diblock copolymers. Namely, domain periodicities increase with increasing polydispersity and domain interfaces tend to curve toward polydisperse blocks. The changes in phase behavior that are associated with variations in the polydispersity of the middle bridged polystyrene block, however, are not analogous to those reported in AB diblock copolymers, as increases in this middle block polydispersity are not always accompanied by (i) increased domain periodicities and (ii) a tendency for domain interfaces to curve toward the polydisperse domain. These results highlight the utility of polydispersity as a tool to tune the phase behavior of ABC block terpolymers.

    View details for DOI 10.1063/1.3140205

    View details for Web of Science ID 000267166200053

    View details for PubMedID 19548752

  • Renormalized one-loop theory of correlations in polymer blends JOURNAL OF CHEMICAL PHYSICS Qin, J., Morsea, D. C. 2009; 130 (22)


    The renormalized one-loop theory is a coarse-grained theory of corrections to the random phase approximation (RPA) theory of composition fluctuations. We present predictions of corrections to the RPA for the structure function S(k) and to the random walk model of single-chain statics in binary homopolymer blends. We consider an apparent interaction parameter chi(a) that is defined by applying the RPA to the small k limit of S(k). The predicted deviation of chi(a) from its long chain limit is proportional to N(-1/2), where N is the chain length. This deviation is positive (i.e., destabilizing) for weakly nonideal mixtures, with chi(a)N less than or approximately 1, but negative (stabilizing) near the critical point. The positive correction to chi(a) for low values of chi(a)N is a result of the fact that monomers in mixtures of shorter chains are slightly less strongly shielded from intermolecular contacts. The predicted depression in chi(a) near the critical point is a result of long-wavelength composition fluctuations. The one-loop theory predicts a shift in the critical temperature of O(N(-1/2)), which is much greater than the predicted O(N(-1)) width of the Ginzburg region. Chain dimensions are found to deviate slightly from those of a random walk even in a one-component melt and contract slightly as thermodynamic repulsion is increased. Predictions for S(k) and single-chain properties are compared to published lattice Monte Carlo simulations.

    View details for DOI 10.1063/1.3124799

    View details for Web of Science ID 000266968800031

    View details for PubMedID 19530784

  • Bicontinuous Polymeric Microemulsions from Polydisperse Diblock Copolymers JOURNAL OF PHYSICAL CHEMISTRY B Ellison, C. J., Meuler, A. J., Qin, J., Evans, C. M., Wolf, L. M., Bates, F. S. 2009; 113 (12): 3726-3737


    Polymeric bicontinuous microemulsions are thermodynamically stable structures typically formed by ternary blends of immiscible A and B homopolymers and a macromolecular surfactant such as an AB diblock copolymer. Investigations of these bicontinuous morphologies have largely focused on model systems in which all components have narrow molecular weight distributions. Here we probe the effects of AB diblock polydispersity in ternary blends of polystyrene (PS), polyisoprene (PI), and poly(styrene-b-isoprene) (PS-PI). Three series of blends were prepared using the same PS and PI homopolymers; two of them contain nearly monodisperse components while the third includes a polydisperse PS-PI diblock. The PS and PI homopolymers and two of the PS-PI diblocks were prepared by anionic polymerization using sec-butyllithium and have narrow molecular weight distributions. The polydisperse PS-PI diblock was prepared by anionic polymerization using the functional organolithium 3-tert-butyldimethylsilyloxy-1-propyllithium; this diblock has a polydisperse PS block (Mw/Mn = 1.57) and a nearly monodisperse PI block (Mw/Mn < 1.1). The phase behavior of the three series of blends was probed using a combination of dynamic mechanical spectroscopy, small-angle X-ray scattering, and cloud point measurements, and a bicontinuous microemulsion channel was identified in each system. These results prove that monodisperse components are not required to form bicontinuous microemulsions and highlight the utility of polydispersity as a tool to tune polymer blend phase behavior. The random-phase approximation, originally advanced by de Gennes, and self-consistent field theory are used to provide a theoretical supplement to the experimental work. These theories are able to predict the directions of the polydispersity-driven shifts in domain spacing, order-disorder transition temperatures, and the location of the microemulsion channel. Self-consistent field theory is also used in conjunction with the experimental data from a series of nearly monodisperse blends to probe the variations of chi with temperature. A single linear relation of the form chi = alpha/T + beta does not describe chi at all blend compositions. Rather, two separate relations describe chi as a function of temperature; one is obtained from data on the diblock-rich side of the bicontinuous microemulsion channel while the other is obtained from data on the homopolymer-rich side of the channel. The blend morphology, rather than the composition (homopolymer fraction), apparently dictates whether the system is in the "diblock chi" or "homopolymer chi" regime. These results reinforce the notion that a true understanding of chi still eludes the polymer science community.

    View details for DOI 10.1021/jp807343b

    View details for Web of Science ID 000264348900017

    View details for PubMedID 19673066

  • Linear response and stability of ordered phases of block copolymer melts MACROMOLECULES Ranjan, A., Qin, J., Morse, D. C. 2008; 41 (3): 942-954

    View details for DOI 10.1021/ma0714316

    View details for Web of Science ID 000252944900062

  • Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts PHYSICAL REVIEW E Grzywacz, P., Qin, J., Morse, D. C. 2007; 76 (6)


    Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, i.e., by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor S(-1)(k) predicted by a "one-loop" approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of an UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to S(-1)(k) is shown to be the sum of (i) a k -independent contribution that arises from a renormalization of the effective chi parameter, (ii) a k-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to k(2) that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a k-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.

    View details for DOI 10.1103/PhysRevE.76.061802

    View details for Web of Science ID 000251985600060

    View details for PubMedID 18233860

  • SCFT study of nonfrustrated ABC triblock copolymer melts MACROMOLECULES Tyler, C. A., Qin, J., Bates, F. S., Morse, D. C. 2007; 40 (13): 4654-4668

    View details for DOI 10.1021/ma062778w

    View details for Web of Science ID 000247340700040

  • Calculation of resistivity of the insulating layer in tunneling-magnetoresistive head by fast Green function method Chinese Physics Letters Wei, D., Piao, K., Qin, J., Dong, Z. 2005; 22: 2063-2065
  • Thermodynamic behavior of a nano-sized magnetic grain near the superparamagnetic limit IEICE Trans. Elec. Qin, J., Wei, D. 2003; E86-C: 1825-1829