Viscosity-induced resonance

Viscosity-induced resonance broadening. Syn. viscosity broadening. The increase in the line width of peaks in a spectrum caused by the decrease in theTj relaxation time that results from a slowing of the molecular tumbling rate. Saturated solutions and solutions at a temperature Just above their freezing point often show this broadening behavior. 

T is the absolute temperature in Kelvin, R amounts to 8.31 J mol K- and t is the viscosity in kg m- s (Pa s). At room temperature and normal viscosity of the solvent, the rate constant becomes 10 ° P mol s". Energy transfer can be caused even by induced resonance without any impact up to distances of 5-10 nm, a process of quantum mechanical origin [8, 9]. Under these conditions the bimolecular rate constant is independent of the viscosity of the solvent and approaches values up to 10" P mol" S". Strictly speaking this process cannot be treated as a normal bimolecular reaction. 

Temperature dependence is a second major issue. It is small for AT-cut crystals however, temperature fluctuations cause fluctuations in Rq inversely proportional to Q [7]. This effect is small compared to temperature effects having their origin in properties of the measurand. In liquid apph-cations, the most temperature-sensitive value is the liquid viscosity. Here, temperature-induced variations in frequency increase with whereas mass sensitivity increases with m. Therefore, an elevated resonance frequency is helpful. 

In nematic liquid crystals, the viscosity depends on the relative orientation between the shear gradient and the orientation of the nematic phase. Close to a surface, the orientation is usually governed by surface orientational anchoring [77]. Anchoring transitions, for instance induced by the adsorption of an analyte molecule to the surface [78], can therefore be easily detected with the QCM [79,80]. This reorientation induced by adsorption amounts to an amplification scheme the expected shift in the resonance frequency and bandwidth... 

Here d and pf are the thickness and the density of the film. These equations are valid in a particular case, when d < S. The general case for arbitrary df was given in [44]. The first terms in Eqs. 16 and 17 yield the liquid-induced frequency shift and half-width of the resonance in the absence of a film. The terms in brackets describe the influence of fhe viscosity and density of a film of thickness df. According to Eqs. 16 and 17, the ratio of the film-induced halfwidth to the film-induced frequency shift is proportional to d(/S. Thus, for d /S < 1, the contribution of the thin interfacial film to the width is much smaller than its contribution to the frequency shift. For the film acts... 

However, in contrast to the previous case, it cannot be related to the mass of trapped hquid. The correction to the width of the resonance depends on the viscosity and is substantially less than the layer-induced shift. 

The variables A/, /o, Aw, Apie o. and Fq represent, respectively, the crystal s measured frequency shift, initial resonant frequency, mass change, surface area, shear modulus, and density [6]. TSM resonators immersed in liquid present a special case because acoustic energy dissipation through the fluid lowers Q as well. Additional formulas need to be applied to account for the liquid s viscosity and loading [6]. Figure 2 shows a comparison between shifts induced by solid and hquid loading on resonators. 

In order to study the viscosity effect on the quenching of triplet excited state of (53) by TEMPO, chemically induced dynamic electron polarization and transient absorption spectra have been measured in ethylene glycol, 1,2-propanol and their mixtures. The results indicate that the quenching rate constant is viscosity-dependent and decreases linearly with the increase in solvent viscosity. The spectroscopy and dynamics of near-threshold excited states of the isolated chloranil radical anion have been studied using photoelectron imaging taken at 480 nm, which clearly indicates resonance-enhanced photodetachment via a bound electronic excited state. Time-resolved photoelectron imaging reveals that the excited state rapidly decays on a timescale of 130 fs via internal conversion. ... 

The considerations above apply to fast dynamic processes in the sense that the amplitude of the modulation of the resonance frequency Amq (induced by modulation of the local field) multiplied with the correlation time Tc is much smaller than unity. This Redfield regime [27] is usually attained in solutions with low viscosity [2], but may also apply to small-amplitude libration in solids [28]. For slower reorientation in solutions with high viscosity or in soft matter above the glass transition temperature (slow tumbling), spectral lineshapes are directly influenced by exchange between different orientations of the molecule (Section 4.1). Relaxation times in solids outside the Redfield regime carmot be predicted from first principles except for a few crystalline systems with very simple structure and few defects [29]. In such systems, qualitative or semi-quantitative analysis of relaxation data can still provide some information on dynamics. 

Equations (1.16) and (1.17) show that Af and AD are related not only to the inherent properties of the quartz crystal but also to the solvent viscosity and density. Therefore, the shifts in A/and AD induced by the polymer behavior at the resonator surface can be extracted by taking the background response of the blank resonator as a Ref. [19]. 

Fig. 5,5. Reversible acid induced transition of staphylococcal nuclease observed by different methods (a) emission fluorescence of Trp 140 (according to Epstein et aL, 1971a) (b) changes in reduced viscosity ( , ) and molar ellipticity (A A) at 220 nm ( , A) measurements made on decreasing pH ( , A), measurements made upon increasing pH (from Anfinsen et aL, 1972) (c) emission fluorescence of Trp 140 ( ), tryrosine ( ), and tyrosine absorption at 287 nm ( ) (from Anfinsen et aL, 1972) (d) areas of imidazole C2 proton resonances of each of the four histidine H-1, H-2, H-3, H-4 (from Anfinsen et aL, 1972).

---