Edward M. Purcell

Life at low Reynolds number

Editor’s note: This is a reprint (slightly edited) of a paper of the same title that appeared in the book Physics and Our World: A Symposium in Honor of Victor F. Weisskopf, published by the American Institute of Physics (1976). The personal tone of the original talk has been preserved in the paper, which was itself a slightly edited transcript of a tape. The figures reproduce transparencies used in the talk. The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side. Some essential hand waving could not be reproduced.

Physics of chemoreception.

Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design.

Structural Investigations by Means of Nuclear Magnetism. I. Rigid Crystal Lattices

Experimental absorption line shapes at nuclear magnetic resonance are given for several simple assemblies of nuclei, with spin ½, in the solid state at temperatures between 90° and 95°K. Analysis of these data is facilitated by the theory of Van Vleck which relates the second moment of the absorption line in a rigid lattice to nuclear spins, gyromagnetic ratios, and internuclear distances, and which provides, therefore, an objective and general method for determining structural parameters from the experimental line shapes.1,2‐dichloroethane exhibits a proton resonance with line structure characteristic of nuclear magnetic moments interacting in pairs to produce the broadening of the absorption line. Consideration of both fine structure and second moment leads to an inferred H–H distance of 1.71±0.02A in the —CH2Cl group. In conjunction with the expected C–H bond distance of from 1.09A to 1.10A, this implies that the H–C–H bond angle is between 4° 30′ and 9° less than tetrahedral. Absorption line shapes fo...

On the alignment of interstellar dust

Abstract Two alignment mechanisms have been investigated by means of a Monte Carlo model. In the mechanism suggested by Gold, needles or flakes which have a sufficiently high velocity with respect to the gas around them are aligned in consequence of the anisotropy of the angular momentum acquired by a grain in collision with gas atoms. Spheroids exhibited, in the Monte Carlo runs, the expected alignment. The quantitative dependence of both angular momentum alignment and axis alignment on grain shape and velocity has been established with an accuracy of 5 to 10 percent. The maintenance of grain velocity by radiation pressure and the effect of a magnetic constraint on the trajectory of a charged grain are discussed. With paramagnetic relaxation incorporated, the Monte Carlo model exhibits Davis-Greenstein alignment. The results for different grain shapes, grain temperatures, and magnetic viscosities are compared with the theoretical predictions of Jones and Spitzer. Because the lowfrequency magnetic viscosity in any paramagnetic system with dipole-dipole coupling only is independent of the dipole strength and concentration, protons are as effectives as electrons. The viscosity arising from diamagnetic relaxation in graphite is estimated to be much too small for effective alignment of graphite flakes.

A Theoretical Study of Magnetic Cooling Experiments

The experimental results obtained by several investigators on the magnetic cooling method are investigated in the light of (1) the electric crystalline fields acting on the magnetic ions of the paramagnetic salts used in the experiments, and (2) the magnetic dipole‐dipole coupling between these ions. These two factors produce anomalous specific heats and departures of the magnetic susceptibility from Curies law at temperatures below 1°K with which the magnetic method is concerned. Thus the empirical Curie temperature, proportional to the reciprocal of the susceptibility, deviates from the true Kelvin temperature in this region. By the methods developed and discussed in the preceding paper by Van Vleck, numerical calculations of the specific heat and susceptibility have been performed for several salts. The experimental specific heat measured on a Curie scale has been corrected to the Kelvin scale and compared with the calculated results. Fairly good quantitative agreement is obtained, although there is some uncertainty as to the effect of (2) on the susceptibility and hence on the relation between the empirical and Kelvin temperature scales.

Nuclear resonance in crystals

Abstract In crystals, the nuclear spin-lattice relaxation time, t 1 , is generally very long while the spin-spin relaxation time, t 2 , is very short. In very few instances, however, is t 1 as long as it ought to be in a perfect crystal. Usually the dominant relaxation process involves not the lattice vibrations but internal molecular or ionic rotations, or possibly paramagnetic impurities. The temperature dependence of t 1 gives considerable information about internal rotation. Experiments on a number of crystals, including the ammonium halides, are described, and the relation of these studies to line-shape investigations is discussed. The coupling of a nuclear electric quadrupole to a vibrating lattice can be much stronger than the dipole effect. Pound has found examples in which this effect is dominant at room temperature, and has identified the mechanism as quadrupole coupling by selectively saturating one line of a quadrupole multiplet while observing the intensity of another. The relaxation time is not far from that predicted by Wallers theory, adapted to this case. The availability of crystals with a long relaxation time at room temperature has led to studies of the persistence of nuclear polarization when the crystal is removed from the magnet — in effect, “adiabatic demagnetization” from room temperature. It is possible to reserve the field in the crystal quickly, without reversing the polarization; the spin temperature is then negative, and the crystal emits, rather than absorbing, at resonance. These experiments raise a number of interesting questions about the state of the system when H 0 is comparable to, or less than, the internal fields, and make possible resonance studies in this new region.

Helmholtz coils revisited

Two circular coaxial current rings of radius a, separated by a distance b, are usually called Helmholtz coils if b=a. That is the well‐known prescription for greatest uniformity of field in the neighborhood of the center of symmetry. Examined here is the magnetic field of a pair of current rings at a distance r from the center large compared to the ring radius a. Expanding the distant field in powers of a/r, each term may be associated with a magnetic 2k‐pole source and a field falling off as (a/r)k+2. The dipole field k=1, falling as (a/r)3, has as its source the total dipole moment of the two rings. It eventually swamps the contribution of higher multipoles. The term (a/r)5 with k=3 has for its source the octupole (23‐pole) moment of the pair of rings. Its coefficient vanishes if b=a. Thus the Helmholtz pair, thanks to its seemingly irrelevant specialization for uniform central field, is also endowed with zero octupole moment. The term‐by‐term connection between the expansion of the distant field and th...

New Practical Physics

In ways no one predicted physics in our time has been astonishingly useful and continually surprising. Has our teaching kept up? Some thoughts about tools and ideas from physics for the college student who wants to be some kind of scientist. [Reprinted from AAPT Pathways (Proceedings of the Fiftieth Anniversary Symposium of the AAPT), edited by Melba Phillips (American Association of Physics Teachers, Stony Brook, New York, 1981)]