Figure 1. Average kinetic temperature profile from three time steps at T = 159, 159.5, and 160. U = 0.2 C, other conditions as given in the text. P which follows immediately behind the shock front. In analogy to the crystalline case, we believe that the propagation of the thermally equilibrated region behind a shock front may be identified as second sound in a liquid. But further work is required to establish this point on a satisfactory basis. 1. 2. 3. W. G. Hoover, Phys. Rev. Lett. 42, 1531 (1979). D. H. Tsai and R. A. MacDonald, High Temperatures-High Pressures, 8, 403 (1976); R. A. MacDonald and D. H. Tsai, Physics Reports, 46, 1 (1978). V. Y. Klimenko and A. N. Dremin, Detonatsiya, Chernogolovka, Akad. Nauk USSR (0. N. Breusov, et al. eds) 79 (1978). We thank Dr. Hoover for giving us this reference. ON THE MEASUREMENT OF SINGLE CHAIN NEUTRON SCATTERING Charles C. Han (Polymer Science and Standard Division) and Chung Yup Kim and Hyuk Yu University of Wisconsin and A. Z. Akcasu and G. C. Summerfield and S. N. Jahshan (Department of Engineering Science, State University of New York 1-5 A number of authors have reported the measurement of single chain polymer configurations in concentrated solutions and in bulk using small angle neutron scattering and samples composed of mixtures of normal and deuterated polymers. The measurements of the single chain configurations have always involved taking the limit of small relative concentrations of the deuterated polymer. This was done to eliminate interference effects in scattering from different chains. The difficulty with this procedure is, of course, that it emphasizes the least reliable results, namely those from the small relative concentrations of marked polymer. Most analyses that have been done thus far seem to have relied on ideas that were developed for light and x-ray scattering where the limit of zero concentration was required to eliminate the interchain interference. With the introduction of isotopic marking, one has an entirely new dimension. That is, the scattering signal from the marked chains can be changed without any change in the underlying solvent polymer interactions. This is done by changing the relative normal and marked polymer concentrations while keeping the overall polymer concentration the same. As we shall see, this permits the measurement of the single chain scattering without taking limiting values of small concentrations of the marked polymer. Another way of stating this is that the "background" correction can be made by simply performing experiments at different concentrations of marked polymer. Suppose we have a solution composed of solvent molecules at positions Rs and polymer molecules with centers of mass at RM and monomers at tij. The concentrations of solvent and polymer are taken to be Cs [molecules/ cm and c Ср [monomers/cm3], respectively. Further, we assume that some 3 P 3, of the polymer molecules are "marked" by having deuterium substituted for all of the protons. If we take the concentrations of marked and normal polymer to be co and C, respectively, we have CD p = CD + CH (1) If we assume that the solution is in compressible in which case we 6 have shown the intermediate coherent neutron small angle scattering function is Mj M'j' exp[iQ·(R+r.)] exp(−1Q*(R,(t) + I ̧,(t))] > exp[19⋅ (R+)] exp[-19⋅ (Ry(t) +1,(t))] > (2) + < Σ aap, with S, M and P stand for solvent, inonomer and polymer. Also, since part of the polymers are marked by deuteration, we will have In fact we need only divide the measured S(Q,t) at two values of 2 cp by the factors ( - a!)2 at those values of CD and subtract to obtain the single chain contributions. Also, we can in some cases, choose the which eliminates everything but the single chain term in (2). Now let us specialize to the case of elastic scattering in bulk material for which (2) reduces to where Np is the total number of polymer chains in the sample. We have used two samples composed of mixtures of polyisoprene and deuterated polyisoprene. The molecular weight, as measured by Gel Permeaton Chromatography, of the deuterated polyisoprene was 104 g/mol. The first sample contained 6.9 weight percent deuterated polyisoprene. This gives the average monomer scattering length for sample one to be The second sample contained 14.5 weight percent deuterated material with The SANS experiments were performed at the NBS reactor. The neutron beam had 5.8 A wavelength with a resolution of 1 A. It was obtained using a helical slot velocity selector and nitrogen cooled Be and Pb filters. Beam size at the sample was 8 mm x 8 mm and a 50-cm linear position sensitive He-3 detector was used. Data acquisition time for each sample was The background and incoherent scattering were approximately forty hours. |