The statistical concentration fluctuations in a solution of polystyrene in cyclohexane near its critical temperature have been directly observed by means of a specially thermostatted phase-contrast optical microscope. A technique which may be of use in the determination of the spatial and temporal persistence of these fluctuations is also described.

In an investigation of the effect of electric fields on the critical opalescence, time-dependent phenomena have been observed which are related to theoretical relaxation times of concentration fluctuations for a binary mixture. Rectangular dc pulses of 25 to 60 kV/cm and 10–200-μsec duration have been applied to a critical mixture nitrobenzene and 2,2,4-trimethylpentane at a series of temperatures above the critical solution temperature. Relaxation times associated with the change in the transmitted light intensity were found to be independent of the pulse width and the field strength. The relaxation times are proportional to (T—Tc)−0.9 and have magnitudes comparable with relaxation times determined from the frequency broadening of light scattered from similar binary systems. It has also been possible to extend the agreement between the Debye theory of the electric field effect on critical opalescence and the experimental results to within 0.1°C of the critical temperature.

The critical opalescence of polystyrene—cyclohexane mixtures has been studied by means of small-angle x-ray scattering for polystyrene samples of molecular weight 118 000 and 147 000. The upper limit of s/λ (s = 2 sin½θ, where θ is the scattering angle, and λ is the wavelength in the medium) was extended to 0.025 Å−1, approximately 50 times greater than the upper limit accessible to visible light. At large values of s/λ, plots of the reciprocal of the intensity vs (s/λ)2 showed downward curvature. The experimental results can be represented by I = [A+B(s/λ)2]−1+C. The magnitude of the ratio of the two terms in the expression representing the intensity is consistent with the conclusion that the constant term C represents the scattering from density fluctuations, and the angular distribution of the scattering caused by concentration fluctuations is accurately represented by [A+B(s/λ)2]−1 over the range of s/λ investigated for the polystyrene—cyclohexane system. However, this is not true for mixtures of ordinary liquids for which the constant term is much too large to be interpreted as a density scattering term.

The free energy involved in the concentration fluctuations of a liquid mixture is changed by an electric field. The effect becomes observable near the critical point. It increases with decreasing distance from the critical temperature and it is proportional to the square of the field intensity and to the second derivative of the dielectric constant with respect to the concentration. Temperature as well as field strength dependence are in agreement with a theory built along classical lines. The effect can be interpreted as a shift of the critical temperature and the sign of this shift is also predicted correctly. Experiments performed with a field intensity of 45 000 V/cm on the system nitrobenzene-2,2,4-trimethylpentane give a value of 0.015° for this shift (which is a depression), while the theory predicts the same.

Critical opalescence of the binary liquid mixture perfluorotributylamine and isopentane is investigated. By combining light scattering and x-ray scattering measurements, data over a broad range of values of s/λ[s=2 sin (Θ/2), λ is wavelength] are obtained. The second moment of the averaged intermolecular pair potential is determined. It is shown how deviations from straight line behavior in plots of reciprocal intensity versus (s/λ)2 are determined by the shape of the intermolecular pair potential curve.

In a recent publication,1 anomalous behavior of the angular dissymmetry of visible light as well as of the temperature dependence of the extrapolated zero-angle scattering for the critical mixture, aniline-cyclohexane, has been reported. On closer examination, we notice in that work that we took the mean concentration of the horizontal portion of the coexistence curve as the critical solution concentration.2-4 Since phase separation temperatures and the shape of the coexistence curve (especially the concentration where the maximum consolute temperature appears) are very sensitive to impurities such as water,5 it is clear that the optical measurements should be carried out on mixtures over a range of concentrations near the critical mixing point before we can claim the anomalous behavior on the scattering curves. In addition, it is of interest to find out whether other binary critical mixtures (with aniline as one of

AbstractMeasurements of the viscosity of critical mixtures were extended to high polymer solutions (polystyrene–cyclohexane). An anomaly is found in the temperature coefficient of the viscosity. An empirical expression for the viscosities of critical mixtures as a function of ΔT/Tc, where ΔT = T − Tc, and Tc is the critical temperature, is derived.

The particle scattering factor P (ϑ) with Gaussian statistics for polydispersed systems has been treated. For a polystyrene sample with a sharp molecular weight distribution ( M w /M n < 1.02, M w = 1.5 X 10 6 ), the measured angular dependence of scattered intensity indicates that the polymer coil does obey Gaussian statistics. This holds for a range of concentrations provided the variation of the constant representing the radius of gyration with concentration is adjusted.

For some liquid mixtures, anomalies—for instance, in the coexistence curve—have been observed. Experiments are reported on the angular dissymmetry of visible light as well as on the temperature dependence of the zero-angle scattering for two liquid mixtures. The mixture methanol-cyclohexane behaves normally, the other, aniline-cyclohexane, shows anomalies.

Visible light scattered by binary mixtures of critical concentration of ordinary molecules at small temperature distances above the critical temperature shows an angular dissymmetry which can be related to the range of molecular forces. The theory of critical opalescence is extended to polymer solutions of high molecular weight for which an additional dissymmetry due to the extension of the polymer coil is observed. The range of molecular forces and the radius of gyration at the critical concentration can be determined simultaneously by measurements of the angular dependence of scattered intensity at different temperatures above the critical temperature. Results of experiments on a solution of polystyrene (Mn=2 820 000) in cyclohexane are reported.

In the vicinity of the critical point, angular dissymmetry of scattering is observed. Its amount is connected with the range of molecular forces. Integrated over all angles it reveals that the total scattering is less than that calculated according to Einstein. At the same time the scattered light is less blue than we would expect according to Rayleigh. This effect has been investigated on the system polystyrene-cyclohexane by measurements of the wavelength dependence of the total turbidity of the solution at its critical concentration as a function of the temperature. The interaction ranges as calculated from the data are in good agreement with values calculated from dissymmetry measurements.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSPECTROPHOTOMETRY AND LIGHT SCATTERING ON SUPPORTED PLATINUM1,2P. Debye and B. ChuCite this: J. Phys. Chem. 1962, 66, 6, 1021–1027Publication Date (Print):June 1, 1962Publication History Published online1 May 2002Published inissue 1 June 1962https://doi.org/10.1021/j100812a014RIGHTS & PERMISSIONSArticle Views28Altmetric-Citations7LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (783 KB) Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTA LIGHT SCATTERING STUDY OF THE AGGREGATION OF ACIDIFIED SODIUM SILICATE SOLUTIONS1P. Debye and Robert V. NaumanCite this: J. Phys. Chem. 1961, 65, 1, 10–12Publication Date (Print):January 1, 1961Publication History Published online1 May 2002Published inissue 1 January 1961https://pubs.acs.org/doi/10.1021/j100819a004https://doi.org/10.1021/j100819a004research-articleACS PublicationsRequest reuse permissionsArticle Views92Altmetric-Citations11LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTHE SLOW CHANGE IN TURBIDITY OF SODIUM SILICATE SOLUTIONS1P. Debye and Robert V. NaumanCite this: J. Phys. Chem. 1961, 65, 1, 5–7Publication Date (Print):January 1, 1961Publication History Published online1 May 2002Published inissue 1 January 1961https://pubs.acs.org/doi/10.1021/j100819a002https://doi.org/10.1021/j100819a002research-articleACS PublicationsRequest reuse permissionsArticle Views147Altmetric-Citations7LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTHE REFRACTIVE INDICES OF SODIUM SILICATE SOLUTIONS1P. Debye and Robert V. NaumanCite this: J. Phys. Chem. 1961, 65, 1, 8–9Publication Date (Print):January 1, 1961Publication History Published online1 May 2002Published inissue 1 January 1961https://pubs.acs.org/doi/10.1021/j100819a003https://doi.org/10.1021/j100819a003research-articleACS PublicationsRequest reuse permissionsArticle Views217Altmetric-Citations3LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation P. Debye, H. Coll, D. Woermann; Critical Opalescence of Polystyrene Solutions. J. Chem. Phys. 1 March 1960; 32 (3): 939–940. https://doi.org/10.1063/1.1730821 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioThe Journal of Chemical Physics Search Advanced Search |Citation Search

Light scattering measurements on the system cyclohexane-polystyrene (molecular weight range 69 000 to 1 000 000) show an angular dissymmetry of critical opalescence in essential agreement with theory. The interaction range between polymer segments as calculated from the data appeared to be considerably smaller than the radius of gyration of the polymer coil. The dependence of critical temperature and concentration on the molecular weight is shown.