High yield accelerated reactions in nonvolatile microthin films: chemical derivatization for analysis of single-cell intracellular fluid† †Dedicated to Keith R. Jennings, a pioneer in mass spectrometry, on his 85th birthday. ‡ ‡Electronic supplementary information (ESI) available. See DOI: 10.1039/c8sc03382j

The identification of trace components from an individual cell can require derivatization under mild conditions for successful analysis by mass spectrometry (MS).


Kinetics of Second Order Irreversible Reactions
Consider the Schiff base reaction below: Considering reaction with equal amounts of reactants, assume that the (1)

=-= 2
Integrating eq. (1) we get: (2) Notably, the slope of the kinetics curve is a function of c 0 . If the slopes of two reaction systems are compared (their ratio representing the apparent acceleration factor), [1] we find a dependence on both the ratio of concentrations and the rate constants (the latter being the rate acceleration factor). For example, when comparing system 1 and system 2, we can get: When performing analysis by mass spectrometry, concentrations are estimated using ion abundances. The ionization efficiency of the amine in a Schiff base reaction is significantly higher than that for a saccharide but similar to that of the Schiff base product. Therefore, the concentration ratio [P]/[SM] can be approximated by the ratio of ion abundances (peak intensities of the Schiff base product vs. the amine). The conversion ratio is measured by Schiff base ion intensity/(Schiff base intensity + amine ion intensity). This again assumes, as is common, that ionization efficiency similarities allow ion abundances to stand in for concentrations, as discussed, for example, in a previous publication. [2]

Kinetics of Second Order Reversible Reactions
There is no absolutely irreversible reaction. Every reaction given a finite temperature, will reach equilibrium if the reaction time is sufficient. Reaction equilibrium is reached when the forward reaction rate is equal to the backward reaction rate. Consider a second order reversible reaction generating a larger molecule (P) with the loss of a small molecule (W): When equilibrium is reached, we can get: In equation 5, k f and k b are the rate constants for the forward and backward reactions, respectively. Rearranging eq. 5 we can get the well-known relationship between k f , k b and equilibrium constant K: Consider the situation that all reactants have equal initial concentrations, c 0 . At time t, Considering the backward reaction, the reaction rate equation can be rewritten as follows: From equation 7, if the equilibrium constant K is large enough, or [P] = c 0 -c = [W] is small enough, we will get:  Figure S6 shows the Schiff base reaction in 25 °C microthin film for 1440 minutes. The first five 5 points were acquired at reaction times of less than 70 minutes and [P]/[SM] is less than 3. In this region, the extent of reaction is not high enough to generate large amounts of product so the backward reaction is still negligible. This explains why the first 5 points show a very good linear relationship in Figure S6 but the sixth point shows a downward deflection from the line. For the sake of discussion, we can call the region that obeys the irreversible rate equation the kinetics-controlled region and the region that shows deflection from the irreversible rate equation curve the thermodynamicscontrolled region. Obviously, the reaction rate in the kinetics-controlled region is the maximum reaction rate. Given these definitions, we discuss the second case, that in which [W] is very small. This occurs in the 65 °C microthin film reaction, in which the thinner film and the higher temperature contribute enormously to water escaping from the microthin film reactor. Comparing Figure 3a and Figure S6,

[P]/[SM] plotted against reaction time in the 25 °C microthin film follows a linear relationship even when [P]/[SM] is more than 70 (conversion > 98.5%) while we see downward deflection in the 65 °C microthin film when [P]/[SM] is less than 3 (conversion < 75%
). This result indicates that the ease of water escaping in the microthin film not only enhances the reaction yield, but also increases the period of kinetics-control of the reaction. For reaction in a microthin film, a reasonable assumption is that the rate of small molecules escaping from the system is faster than the reaction rate (otherwise the water generated by reaction could lead to an increase in the volume increase of the thin film).This assumption helps us to solve equation 7. Let's assume that [W] = w, which is constant for the same microthin film and environment. We can rewrite equation 7 as follows: Rearranging this equation we get:

Setting
, eq.13 can be rewritten as: From equation 15, we find that a is related to reaction thermodynamics only and k f is only related to the reaction kinetics. These two parameters express the thermodynamic control and the kinetic control of the reaction rate.
It is notable that AAF is a measure of both extent of reaction and the intrinsic rate acceleration factor (k 1 /k 2 ). To calculate AAF, the apparent acceleration factor, one just Although AAF is just crude comparison for reaction rates in different systems, but it is easy to get and could be used to evaluate the reaction rate of different systems. Figure S1. Typical mass spectra for Schiff base reaction between DBPA and glucose in the microthin film reactor. The reaction temperature was 25 °C.