Photon correlation spectroscopy of polymer solutions

A polynomial subdistribution method for analyzing the correlation profile in photon correlation spectroscopy of polymer solutions is described. This method generates a continuous distribution function from the measured photoelectron time-correlation function, which can be related to particle size or molecular weight distribution of solute. The method is tested using simulated data for unimodal and bimodal distributions and compared with cumulant and histogram methods, respectively. The polynomial subdistribution method has an advantage in that it not only generates a continuous distribution curve but also works well for bimodal distributions whose peaks are close together.     

Photon correlation spectroscopy of compatible polymer blends

The dynamics of concentration fluctuations in compatible polymer mixtures can be investigated by dynamic light scattering. The experiment yields both the dynamic and static structure factors from which the mutual diffusion coefficient and the segment-segment interaction parameter can be obtained. Examples of applications are the unentangled blends poly(ethylene oxide/poly(propylene oxide) and polystyrene/poly(phenylmethylsiloxane) in the one phase region.     

Photon correlation spectroscopy of polymers in the glassy state

Photon correlation spectroscopy has proven to be a very useful technique for studying slowly relaxing density and optical anisotropy fluctuations in bulk polymers near the glass transition. When some of the fluctuations achieve relaxation times much longer than the typical averaging time for the intensity autocorrelation function (10⁴ s), the result must be treated in the partially heterodyned limit. Also, when the sample is near the glass transition but not at equilibrium the correlation function is not stationary in time because the system is relaxing as a whole toward the equilibrium state. The above effects are discussed theoretically and demonstrated experimentally in polystyrene as a function of temperature and pressure. Light scattering with coherent excitation also fluctuates in space as well as in time (as shown in the accompanying paper). The consequences of this effect are discussed. When most of the intensity is associated with fluctuations whose relaxation times are very long in polystyrene, there is still a broad relaxation function evident. This is characteristic of a secondary relaxation process.     

Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet cooled platinum silicides

The cavity ringdown technique (CRLAS) has been employed to measure the gas phase absorption spectrum of the platinum silicide molecule in the 350 nm region. All nine of the measured rovibronic bands are assigned to a single 1 sigma-1 sigma electronic transition, with a ground state vibrational frequency of omega "e = 549.0(3) cm-1, and a bond length of r"0 = 2.069(1) angstroms. The results of this study are compared with experimental data for the coinage metal silicides. Additionally, time-of-flight mass spectrometric results indicate that a variety of polyatomic metal silicides are formed in our molecular jet expansion.     

Probing state-to-state reaction dynamics using H-atom Rydberg tagging time-of-flight spectroscopy

In the last decade or so, the H-atom Rydberg tagging time-of-flight (HRTOF) technique has made a significant impact in the study of state-to-state reaction dynamics, and especially in the study of transition state dynamics of elementary chemical reactions and quantum state resolved dynamics of molecular photodissociation of important molecules. In this perspective, we will discuss mainly the state-to-state dynamics of three important elementary reactions: H + H(2), O((1)D) + H(2) and F + H(2) that have been studied in our laboratory in recent years using the HRTOF method. In addition, we will also mention briefly the experimental results of other reactive systems. In the end, we will also present a brief research outlook in the study of molecular reaction dynamics using this powerful experimental method.     

Photon correlation spectroscopy of polystyrene near the glass–rubber relaxation

Polarized Rayleigh scattering is studied near the glass-rubber relaxation in atactic polystyrene using photon correlation spectroscopy. Average relaxation times determined from the data agree well with previous results obtained using depolarized Rayleigh scattering. The light scattering results follow the same trend observed by dielectric and mechanical relaxation studies, but the times for orientational relaxation are longer by approximately two orders of magnitude. Also, an extensive discussion of the experimental techniques necessary to use photon correlation spectroscopy of polymers near the glass-rubber relaxation is presented.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

A collinear tandem time-of-flight mass spectrometer for infrared photodissociation spectroscopy of mass-selected ions

An apparatus based on collinear tandem time-of-flight mass spectrometer has been designed for the measurement of infrared photodissociation spectroscopy of mass-selected ions in the gas phase.The ions from a pulsed laser vaporization supersonic ion source are skimmed and mass separated by a Wiley-McLaren time-of-flight mass spectrometer.The ion of interest is mass selected,decelerated and dissociated by a tunable IR laser.The fragment and parent ions are reaccelerated and mass analyzed by the second time-of-flight mass spectrometer.A simple new assembly integrated with mass gate,deceleration and reacceleration ion optics was designed,which allows us to measure the infrared spectra of mass selected ions with high sensitivity and easy timing synchronization.     

Photon correlation spectroscopy of poly(methyl methacrylate) near the glass transition

Poly(methyl methacrylate) (PMMA) has been studied by photon correlation spectroscopy in the temperature range 120–150°C. The relaxation functions for longitudinal density fluctuations were determined and analyzed using the empirical function ?(t) = exp[?(t/τ)^β]. The average relaxation times were calculated for each temperature and compared to mechanical and dielectric relaxation data. The agreement between the various techniques for the primary glass–rubber relaxation was good. The relaxation function observed by light scattering became increasingly broad as the temperature was lowered. This is similar to the results reported previously for poly(ethyl methacrylate) (PEMA). In fact, the light-scattering relaxation function is dominated by the secondary relaxations in these two polymers. Nevertheless, the average relaxation time 〈τ〉 is dominated by the longest relaxation times associated with the primary glass–rubber relaxation.     

Photon correlation spectroscopy of syndiotactic poly (n-butyl methacrylate) near the glass transition

Slow relaxing longitudinal density fluctuations in bulk syndiotactic poly (n-butyl methacrylate) [PBMA] were studied by photon correlation spectroscopy as a function of temperature from 70 to 90°C. The shape of the light-scattering relaxation function broadened as the temperature approached the glass transition (T_g = 55°C). The average relaxation time shifted with temperature, consistent with previous studies of PBMA. The relaxation functions were analyzed in terms of a distribution of relaxation rates. The calculated distribution was clearly bimodal and the shape altered with temperature. The higher frequency peak in the distribution corresponds well with previous mechanical and dielectric relaxation studies of the intramolecular relaxation of the acrylate ester side chain. The resolution of the distribution into two modes is due to a well-defined side-chain motion with relaxation strength comparable to the primary glass-rubber relaxation. © 1994 John Wiley & Sons, Inc.     

Photon correlation spectroscopy of bulk poly(n-hexyl methacrylate) near the glass transition

Slowly relaxing longitudinal density fluctuations in an optically perfect sample of bulk poly(n-hexyl methacrylate) (PHMA) have been studied by photon correlation spectroscopy in the temperature range 10–36°C. The glass transition temperature for this sample was measured to be T_g = −3°C by differential scanning calorimetry. The optical purity of the sample was verified by Rayleigh-Brillouin spectroscopy and the Landau-Placzek ratio was observed to be 2.3 at 25°C. Light-scattering relaxation functions were obtained over the time range 10⁻⁶-1 s. The shape of the relaxation functions broadened as the temperature was lowered towards the glass transition. Quantitative analysis of the results was carried out using the Kohlrausch-Williams-Watts (KWW) function to obtain average relaxation times, 〈τ〉, and width parameters, β. The width parameter decreased from 0.43 to 0.21 over the temperature interval, as suggested by visual inspection. Average relaxation times shifted with temperature in a manner consistent with previous mechanical studies of the primary glass-rubber relaxation in PHMA. The relaxation functions were also analyzed in terms of a distribution of relaxation rates, G(Γ). The calculated distributions were unimodal at all temperatures. The average relaxation times obtained from G(Γ) were in agreement with the KWW analysis, and the shape of the distribution broadened as the sample was cooled. The rate at which G(Γ) displayed a maximum correlated well with the corresponding frequency of maximum dielectric loss for PHMA. The temperature dependence of these two quantities could be reproduced with an Arrhenius activation energy of 21 Kcal/mol. A consistent picture of the molecular dynamics of PHMA near the glass transition requires a strong secondary relaxation process with a different temperature dependence from the primary glass-rubber relaxation. The present results suggest that the behavior of PHMA is similar to the other poly(alkyl methacrylates). © 1996 John Wiley & Sons, Inc.     

Speciation of prehydrolyzed Al salt coagulants with electrospray ionization time-of-flight mass spectrometry and Al NMR spectroscopy

Based on the speciation results of the most two concerned coagulant component (i.e., monomer and Keggin-Al₁₃), Al species in polymeric Al salt coagulants were fully investigated with the combination of electrospray ionization time-of-flight mass spectrometry and ²⁷Al NMR spectroscopy. Keggin-Al₁₃⁷⁺ could transform into Al₁₃ⁿ⁺ (n = 1-3) by dehydrogen reaction without destroying the Keggin structure in mass spectrometer. There exist differences in the intensity and the observed sequence of the Al₁₃ⁿ⁺ (n = 1-3) species in the mass spectra of polymeric Al coagulants. Several other polymers (i.e., Al₁₉³⁺, Al₂₀³⁺ and Al₁₆ⁿ⁺, n = 1-3) might also be formed by the decomposition and repolymerization of Keggin-Al₁₃⁷⁺. Like monomeric Al salt coagulant, species in polymeric Al coagulants with low basicity were mainly detected as low polymers with mono-charge in mass spectrometry. With the increase of basicity, the dominant species often transform into high polymers with higher charges and fewer categories. The Al₁₃³⁺ species detected in monomeric Al coagulant should have octahedral structure and be formed by self hydrolysis, which is different with the species detected in purified Al₁₃ coagulant. On the whole, the detected species in mass spectrometry could roughly represent their dissolution status in original solutions and could also be used to explain the difference of their coagulation performance in water treatment process.     

Photon correlation spectroscopy of crosslinked polystyrene networks in the swollen state: Influence of macromolecular polydispersity

We report measurements of the correlation function of light scattered from thermally excited longitudinal fluctuations in crosslinked polystyrene networks at equilibrium. In order to investigate the influence of the polydispersity of linear chain elements between successive branch points, we synthesized a network by means of anionic block copolymerization, using a mixture of two “precursor” polystyrenes of different molecular weights to initiate polymerization of a small amount of divinyl-benzene (DVB). The correlation function for fluctuations having a wave vector K, has the form of an exponential decay, exp (?Γ). The decay rate is given by Γ = D′K², where D′ represents the diffusion constant of longitudinal modes of the network. We also present measurements of the correlation function of light scattered from gels prepared by anionic block copolymerization of styrene and DVB with only one “precursor” polystyrene and by a free-radical process. In the latter case, the gels should have a wide distribution of linear chain lengths between branch points.     

Photon emission statistics and photon tracking in single-molecule spectroscopy of molecular aggregates: dimers and trimers

Based on the generating function formalism, we investigate broadband photon statistics of emission for single dimers and trimers driven by a continuous monochromatic laser field. In particular, we study the first and second moments of the emission statistics, which are the fluorescence excitation line shape and Mandel's Q parameter. Numerical results for this line shape and the Q parameter versus laser frequency in the limit of long measurement times are obtained. We show that in the limit of small Rabi frequencies and laser frequencies close to resonance with one of the one-exciton states, the results for the line shape and Q parameter reduce to those of a two-level monomer. For laser frequencies halfway the transition frequency of a two-exciton state, the photon bunching effect associated with two-photon absorption processes is observed. This super-Poissonian peak is characterized in terms of the ratio between the two-photon absorption line shape and the underlying two-level monomer line shapes. Upon increasing the Rabi frequency, the Q parameter shows a transition from super- to sub- to super-Poissonian statistics. Results of broadband photon statistics are also discussed in the context of a transition (frequency) resolved photon detection scheme, photon tracking, which provides a greater insight in the different physical processes that occur in the multi-level systems.