Service Life Prediction - American Chemical Society

Chapter 23

Downloaded by PENNSYLVANIA STATE UNIV on September 17, 2012 | http://pubs.acs.org Publication Date: November 21, 2001 | doi: 10.1021/bk-2002-0805.ch023

The Pulsing of Free-Amine during Polymer Hydrolysis Sam C. Saunders SCS Inc., 218 Main Street, Pmb 184, Kirkland,WA98033-6108

We explicate a question in physical chemistry concerning hydrolysis in acrylic melamine which is analogous to the oscillation of water levels in coupled tanks, under related conditions. But polymer hydrolysis is more complicated; it involves slower reaction rates, partial-yields and moisture infusion due to the ambient relative humidity. Convolutions of the different concentrations are used to represent successivefirst-orderreactions in the governing coupled differential system, rather than characteristic equations and eigenvalues obtained from a computer program. We give explicit formulae from hydrolytic degradation for the concentrations of certain compounds which are of chemical interest. This analysis makes transparent when and why pulsing occurs, to the confoundment of others besides physical chemists.

Introduction At a recent conference on the service life of polymer coatings, a preliminary report was made on quantitative prediction of concentrations in polymers by chemical degradation due to hydrolysis, e.g., humidity and acid rain, affecting car paint. The mathematical analysis showed "pulsing" could occur, under some conditions, in the generation of free-amine (and other degradation products) in such polymers as acrylic-partially-alkylated melamine coating. But the audience was sceptical. The physical chemist's questions about the mathematical demonstration were pointed: "Please explain to us the chemical reason there should be acceleration and deceleration of the chemical activity, with a period as long as three weeks, in polymers such as these?" This should be interpreted as: "This mathematical torn-foolery seems unrelated to the chemistry and is so esoteric that until a chemical

468

© 2002 American Chemical Society

In Service Life Prediction; Martin, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2001.

469 explanation, which is physically intuitive, can be provided it is insufficiently convincing." The experimentalist's explanations of the origin of the observed variations in the FTIR responses, see Figure 1, in the chemical hydrolysis of melamine, see Figure 2, were: 1. During the early measurement period in FTIR analysis, when percentage changes were lower than the measurement error a systematic error of over and under compensation often resulted in the early oscillation that later disappeared.


2. The mechanism that controlled humidity during exposure may havefluctuatedwith a common period which generated the pulse. (Unfortunately no records were found in the humidity control that exhibited such pulsing.)

Representation of Hydrolytic Degradation To analyse Nguyen's degradation scheme, see [3], which is quoted in Figure 2 and depicted in Figure 7, we construct a mathematical model for two important scenarios by denoting

—

respectively, as zero-order,first-orderand reversiblefirst-orderreactions, namely,

The subscripts indicate possible choices for Oj for j = 1,2 and E* for k = 1,2 where [X] represents water, [Ο] is melamine methylol. Here [β] is a unknown mixture of the three chemical complexes below, each of which is assumed to have the same reaction constant. This is an approximation to the average of three different reaction constants for:

^CH -OCH 2

3

^CHs-O-R [β7Γ|—Ν

Βι:|-Ν \ H

^CH -OCH 2

3

Ν

Θ" ν

κ

\ H

\CH -0-R' 2

It is the accumulation of end-products | Ει | and | E | which are of interest; | Εχ | is -NH , primary 2

2

amine, and | E | is -N-CH -N while | D i | is »-C and [57] is C-C. 2

2

Here η, λ, with affixes, arefirst-orderreaction rates and p, with affixes, represents fractional yield. The problem is to obtain formulae which represent the concentration over time of E i and E , the two 2

ultimate degradation products, involving all combinations of intermediate products. Some additional




-α ο


1

f

1

Hydrolytic and Post Cure Damage (H + PC) Chain Scission 1085 cm' ,50*C, No UV Exposure

Figure 1: Selected Figures of Hydrological Changes from FTIR Spectroscopy

«1HRH 0.008mm VP 19^%RH 20.8mm VP 41.1%RH 45.6mm VP 72.7HEH 79.4mm VP • 90.8%RH 99.5mm VP

Hydrolytic and Post-Cure Damage (H + PQ 1630 cm' 50*C ,No UV Exposure


472 analysis, not given here, would be required to determine formulae for the concentrations of carbonylic acid and amide. However the actual problem in the chemistry of hydrolysis is more complicated than that of three coupled water tanks. Hydrolysis involves a sequence of reactions which begin with

IH2O | and at

the end of the chemical sequence a fraction of the | Η 01 with which it began is resupplied. As a 2

by-product, the hydrolysis cycle contributes to the production of free-amine which is the initiator of the, chemical degradation. Chemical behavior during hydrolysis resembles that shown in Figure 7.


A quantitative analysis of this situation cannot depend only on a linear system of differential equations because of two important complications: (i) partial-yield reactions, i.e., only a fraction of the reagent consumed becomes the chemical species of interest, (ii) the infusion of water due to relative humidity. To attack these problems we adopt a different method.

A Single Tank The bottom pressure, due to the weight of water, is proportional to the depth of water. The volume (amount) 2

of water is V = irr • y where r is the radius of the tank and y is the depth of water. With outflow but no inflow the rate of change of the volume of water is ^

2

= —κ{πε ) - y

for some 0 < κ < 1.

Here κ is the nozzle efficiency and ε is the drain radius. 2

2

Since wr · y* = — ττε · κ · y it follows that y* = —ηy Figure 3 A draining tank with inflow

for some η > 0. Therefore the water level of a draining tank, _,?

as in Figure 3, is an exponentially decreasing function of time, namely, y(t) = y(0)e *

for all t > 0.

This type of behavior often arises elsewhere in science, e.g., in (i) Newton's law of cooling, (ii) the electrical charge draining from a capacitor, or (iii) Carbon C 1 4 decaying to C i . Such representation 2

of "flow" using the appropriate parameters, namely, WATER VOLUME,

WATER DEPTH,

TANK BASE AREA,

and

DRAIN AREA

can be reinterpreted in other situations, respectively, as HEAT, CHARGE,

TEMPERATURE, VOLTAGE,

SPECIFIC HEAT,

CAPACITANCE,

THERMAL CONDUCTIVITY, ΟΓ

ELECTRICAL CONDUCTIVITY

and, most importantly as we argue subsequently, the same model applies in allfirst-orderchemical reactions during hydrolysis in polymers, where correspondingly we have the concepts


473 MATERIAL MASS,

SPECIES CONCENTRATION,

REACTION CONSTANT.

We assert the reason for the counter-intuitive behavior of coupled tanks is not due to any electrical or hydrologie properties but follows by mathematical implication from the common governing law, as expressed, e.g., in eqn(l) below, of a tank with constant inflow and gravitational outflow: y' = μ- ην\

therefore y(t) = - + [ y(0) - - ) e"**

for all t > 0.

(1)


Two Coupled Tanks The differential system forflow-rateis

yi = -myi + »?2y2,

1/2 = +myi-my2> The solution is checked to be of the form:

y*

Service Life Prediction - American Chemical Society

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