title: Studies of catalysis of the hydrolysis of phenyl glycinate and some related esters

authors: Lee, Lim Eng

abstract: This thesis reports the results and conclusions from the first kinetic studies undertaken of the hydrolysis of phenyl ester of an α-amino acid (glycine), previous studies having been limited to 4-nitrophenyl esters. Some data on 4-methoxyphenyl glycinate are also reported, together with some new data on 4-nitrophenyl esters required for comparison purposes. 
Studies have concentrated on catalysts previously reported as effective in the hydrolysis of 4-nitrophenyl esters of amino acids, the aim being to determine if results for a phenyl ester with a relatively poor leaving group might help in determining mechanisms involved in catalysis. 

(i) HCO₃⁻. Unlike the case for 4-nitrophenyl esters, phenyl glycinate hydrolysis is catalysed in bicarbonate solutions not by CO₂ as previously suggested but by HCO₃⁻, the kinetic form is given by 
Rate= k[neutral ester][HCO₃⁻] 
Kinetically equivalent forms involving CO₂ and CO₃²⁻ terms have been excluded. Comparison of the catalytic effect of HCO₃⁻ with that of imidazole and that of HPO₄²⁻ excludes the possibilities of general base and nucleophilic catalysis by HCO₃⁻ and a mechanism involving initial nucleophilic addition of amine to HCO₃⁻ followed by intramolecular nucleophilic substitution is suggested as most likely.

(ii) 4-nitrobenzaldehyde. Phenyl and 4-methoxyphenyl glycinate show the same kinetic form as 4-nitrophenyl esters but the catalytic effects are much smaller and consistent only with rate-determining attack on ester carbonyl. This supports the concept of rate-determining decomposition of a carbinolamine species, which is also consistent with an observed small effect of temperature on the overall catalytic rate constant.

(iii) Imidazole. Unlike the case for 4-nitrophenyl esters, the kinetics are dominated for both neutral and protonated phenyl glycinate species by a term second order in imidazole, which is consistent with general base catalysis of nucleophilic substitution by imidazole in the formation of an acylimidazole intermediate. A term first order in imidazole makes a minor contribution and probably represents general base catalysis as indicated through comparison of the magnitude of the catalytic effect of imidazole with that of HPO₄²⁻, which is also reported on for the first time in this thesis. 

(iv) N-ethylmorpholine. An unusual non-linear dependence of the observed first order rate constants on catalyst concentration is shown to be consistent with complexing of N-ethylmorpholine and ester prior to reaction. Equilibrium constants for complex formation and rate constants for decomposition are evaluated. However, the effects of model compounds as tests for medium effects of the amine and its cation throw some doubt on the validity of this interpretation. In particular, dioxane, as a model for N-ethylmorpholine, has an inhibitory effect on the hydrolysis of unprecedented magnitude.

(v) Hydroxide. Alkaline hydrolysis of phenyl glycinate  has been studied so as to obtain rate constants for both the neutral and cationic ester species. The latter is about 300 times more reactive.

Studies on 4-nitrophenyl esters have also been advanced in tandem with those of the phenyl and 4-methoxyphenyl esters. The kinetic form for catalysis in bicarbonate solutions has been confirmed as involving CO₂ and not HCO₃⁻, as is consistent with carbamate formation, but whether formation or decomposition of carbamate is rate-determining is still uncertain. The small effect of temperature on reaction rate together with the lack of base catalysis in the reaction support rate-limiting decomposition of carbamate, but the overall rate is close to that predicted by interpolation from other studies for carbamate formation. The possibility of hydrolysis at the zwitterion stage is considered. New data are also reported for 4-nitrobenzaldehyde catalysis for comparison with those of the phenyl and 4-methoxyphenyl esters.

text: Studies of catalysis of the hydrolysis of phenyl glycinate and some related esters This thesis reports the results and conclusions from the first kinetic studies undertaken of the hydrolysis of phenyl ester of an α-amino acid (glycine), previous studies having been limited to 4-nitrophenyl esters. Some data on 4-methoxyphenyl glycinate are also reported, together with some new data on 4-nitrophenyl esters required for comparison purposes. 
Studies have concentrated on catalysts previously reported as effective in the hydrolysis of 4-nitrophenyl esters of amino acids, the aim being to determine if results for a phenyl ester with a relatively poor leaving group might help in determining mechanisms involved in catalysis. 

(i) HCO₃⁻. Unlike the case for 4-nitrophenyl esters, phenyl glycinate hydrolysis is catalysed in bicarbonate solutions not by CO₂ as previously suggested but by HCO₃⁻, the kinetic form is given by 
Rate= k[neutral ester][HCO₃⁻] 
Kinetically equivalent forms involving CO₂ and CO₃²⁻ terms have been excluded. Comparison of the catalytic effect of HCO₃⁻ with that of imidazole and that of HPO₄²⁻ excludes the possibilities of general base and nucleophilic catalysis by HCO₃⁻ and a mechanism involving initial nucleophilic addition of amine to HCO₃⁻ followed by intramolecular nucleophilic substitution is suggested as most likely.

(ii) 4-nitrobenzaldehyde. Phenyl and 4-methoxyphenyl glycinate show the same kinetic form as 4-nitrophenyl esters but the catalytic effects are much smaller and consistent only with rate-determining attack on ester carbonyl. This supports the concept of rate-determining decomposition of a carbinolamine species, which is also consistent with an observed small effect of temperature on the overall catalytic rate constant.

(iii) Imidazole. Unlike the case for 4-nitrophenyl esters, the kinetics are dominated for both neutral and protonated phenyl glycinate species by a term second order in imidazole, which is consistent with general base catalysis of nucleophilic substitution by imidazole in the formation of an acylimidazole intermediate. A term first order in imidazole makes a minor contribution and probably represents general base catalysis as indicated through comparison of the magnitude of the catalytic effect of imidazole with that of HPO₄²⁻, which is also reported on for the first time in this thesis. 

(iv) N-ethylmorpholine. An unusual non-linear dependence of the observed first order rate constants on catalyst concentration is shown to be consistent with complexing of N-ethylmorpholine and ester prior to reaction. Equilibrium constants for complex formation and rate constants for decomposition are evaluated. However, the effects of model compounds as tests for medium effects of the amine and its cation throw some doubt on the validity of this interpretation. In particular, dioxane, as a model for N-ethylmorpholine, has an inhibitory effect on the hydrolysis of unprecedented magnitude.

(v) Hydroxide. Alkaline hydrolysis of phenyl glycinate  has been studied so as to obtain rate constants for both the neutral and cationic ester species. The latter is about 300 times more reactive.

Studies on 4-nitrophenyl esters have also been advanced in tandem with those of the phenyl and 4-methoxyphenyl esters. The kinetic form for catalysis in bicarbonate solutions has been confirmed as involving CO₂ and not HCO₃⁻, as is consistent with carbamate formation, but whether formation or decomposition of carbamate is rate-determining is still uncertain. The small effect of temperature on reaction rate together with the lack of base catalysis in the reaction support rate-limiting decomposition of carbamate, but the overall rate is close to that predicted by interpolation from other studies for carbamate formation. The possibility of hydrolysis at the zwitterion stage is considered. New data are also reported for 4-nitrobenzaldehyde catalysis for comparison with those of the phenyl and 4-methoxyphenyl esters.

year: 1979

title: Wittrick-Williams algorithm proof of bracketing and convergence theorems for eigenvalues of constrained structures with positive and negative penalty parameters

authors: Ilanko, Sinniah

subjects: Wittrick-Williams algorithm

abstract: The well-established Wittrick-Williams algorithm is used to derive novel and general proofs that show that the eigenvalues of systems with constraints can be bracketed by replacing the constraints by positive and negative pairs of either ordinary or inertial penalty parameters. It is also shown that convergence occurs from both above and below when the numerical values of these parameters are increased towards infinity. The proofs are applicable in many contexts but are derived in that of structural systems, for which the eigenvalues are either buckling load factors or the squares of natural frequencies of vibration; ordinary penalty parameters are stiffnesses of translational and rotational springs; and inertial penalty parameters are either masses or rotary inertias. The penalty parameters can be used to constrain a system or to impose constraints between systems. It is shown that the use of inertial penalty parameters has several advantages compared with using ordinary ones. Then the pth eigenvalue of a system with n constraints is bounded closely from above by the (p+n)th eigenvalue of the system with very large positive inertial penalty parameters and from below by the pth eigenvalue, when large negative values are used instead. This work is expected to enhance the versatility of numerical eigenproblem methods, e.g. the Rayleigh-Ritz method.

text: Wittrick-Williams algorithm proof of bracketing and convergence theorems for eigenvalues of constrained structures with positive and negative penalty parameters The well-established Wittrick-Williams algorithm is used to derive novel and general proofs that show that the eigenvalues of systems with constraints can be bracketed by replacing the constraints by positive and negative pairs of either ordinary or inertial penalty parameters. It is also shown that convergence occurs from both above and below when the numerical values of these parameters are increased towards infinity. The proofs are applicable in many contexts but are derived in that of structural systems, for which the eigenvalues are either buckling load factors or the squares of natural frequencies of vibration; ordinary penalty parameters are stiffnesses of translational and rotational springs; and inertial penalty parameters are either masses or rotary inertias. The penalty parameters can be used to constrain a system or to impose constraints between systems. It is shown that the use of inertial penalty parameters has several advantages compared with using ordinary ones. Then the pth eigenvalue of a system with n constraints is bounded closely from above by the (p+n)th eigenvalue of the system with very large positive inertial penalty parameters and from below by the pth eigenvalue, when large negative values are used instead. This work is expected to enhance the versatility of numerical eigenproblem methods, e.g. the Rayleigh-Ritz method.

year: 2007

title: Tūrangawaewae mō te Kīngitanga

authors: Takerei, Mamae Rangiaroha Tuānewa

subjects: Tūrangawaewae

abstract: Tūrangawaewae is an iconic marae located at the heart of the Kīngitanga. Established by Te Pūea Hērangi and other whānau, this marae has come to represent the struggles, successes and history of the Kīngitanga movement. Tūrangawaewae is therefore the embodiment of the Kīngitanga and the people of Waikato.
From very humble beginnings, and forged on the tireless efforts of Te Pūea and her followers, this marae has hosted world leaders, monarchs and aristocracy from across the world. All have come to Tūrangawaewae to forge relationships with the Kīngitanga, with Māori and with the New Zealand government. It has become a hallowed place when histories are shared and futures are created.
This thesis looks at how Tūrangawaewae encapsulates the Kīngitanga and all that it means. It explores this history of its establishment and highlight the central figures and the motivations behind the building of this marae and complex. In addition, this thesis will show how the different building and features of the marae showcase the ideology of the Kīngitanga movement and its leaders. Based on a traditional approach to Waikato knowledge, and founded on firsthand experience, this thesis reveals an insides perspective of the kīngitanga, the people, various events and the marae of Tūrangawaewae.

text: Tūrangawaewae mō te Kīngitanga Tūrangawaewae is an iconic marae located at the heart of the Kīngitanga. Established by Te Pūea Hērangi and other whānau, this marae has come to represent the struggles, successes and history of the Kīngitanga movement. Tūrangawaewae is therefore the embodiment of the Kīngitanga and the people of Waikato.
From very humble beginnings, and forged on the tireless efforts of Te Pūea and her followers, this marae has hosted world leaders, monarchs and aristocracy from across the world. All have come to Tūrangawaewae to forge relationships with the Kīngitanga, with Māori and with the New Zealand government. It has become a hallowed place when histories are shared and futures are created.
This thesis looks at how Tūrangawaewae encapsulates the Kīngitanga and all that it means. It explores this history of its establishment and highlight the central figures and the motivations behind the building of this marae and complex. In addition, this thesis will show how the different building and features of the marae showcase the ideology of the Kīngitanga movement and its leaders. Based on a traditional approach to Waikato knowledge, and founded on firsthand experience, this thesis reveals an insides perspective of the kīngitanga, the people, various events and the marae of Tūrangawaewae.

year: 2019