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## Part 1 An Introduction to Polycondensation

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**Chapter 2Step-Growth Polymerization**Part 1An Introduction to Polycondensation**Part 2Kinetics of Polycondensation**Topics for Today The same reactivity of the functional groups Foundations of Kinetics---Kinetic equation What’s the reaction order ? Kinetics of Linear Polycondensation**What’s important for Today**Concept: The same reactivity of the functional groups Kinetics of Linear Polycondensation Self-Catalyzed System External-Catalyzed System**Assumption:**The same reactivity of the functional groups Most common polycondensation reactions are reversible equilibrium reactions. All polycondensation reactions are stepwise reactions between functional groups. The reactivity of a functional group is indepen-dent of the size of the molecule to which it is attached.**polyester：－COOH ＋－OH → －OCO－＋H2O**Essentially, the kinetics of a polyesteri-fication reaction is the same as that for the esterification. Polyamide:－COOH ＋－NH2→－CONH－＋H2O**Theoretical Considerations**According to the molecular collision theory, the activity of functional groups are shown by the reaction rate constant. The function of reaction rate of condensation as well as polycondensation to the temperature can be shown by Arrhenius Equation.**The observed reactivity of a functional group is depen-dent**on its collision frequency rather than the diffusion rate of the whole molecule. A terminal functional group has a much greater mobility than that of the whole polymer chain. Since the diffusion rate of macromolecule is low, the functional groups will undergo enough times of collisions before diffusing apart. As the result, the reactivity of a functional group is independent on the size of the molecule attached.**Foundations of Kinetics**Twofold studies on chemical reaction a) Thermodynamics ① Criterion of reactions ΔG＝ΔH－TΔS For a spontaneous reaction: ΔG＜0 ② Here we focus on the equilibrium of the reactions and the corresponding influence on of the products.**b) Chemical kinetics**Chemical kinetics studies the rate of the chemical reaction and the corresponding influencing factors. e.g., the concentration of reactants, temperatures and etc. Turning the possibility of reaction predicted by thermodynamics into reality: how rapidly the products are formed.**The rate of chemical reaction**Definition： The change of the moles of substances (reactants or products) in a unit spacewith time in a reaction system. R = ±**For the liquid phase reaction, V is considered constant due**to its little change: R ＝ ± The rate of the reaction：the change of the concentration of reactants or products in a unit time.**＝ ＝ ＝**aA ＋ bB → eE + fF where：RA，RB，……represents the rate of the reac- tion expressed by the change of the concen- tration of A、B、E、F, respectively. a、b、e、f are the stoichiometric numbers of the corresponding substances in the reaction equation. The unit ofR is mol/l·S**Kinetics equation**The quantitative influences of various factors ( e.g. temperature, concentration, medium, initiator, etc.) on R. aA + bB + ………→ eE + fF + ……… At a constant temperature, the concentrations of the reactants have an effect on the rate. The experiments show ： R = k ……… (CA、CB……is refered to the concentrations of the reactants )**k depends on the characteristic of reaction, i.e., depends**on the temperature. • In constant concentrations，the bigger the k，the more rapidly the reactions proceed. k: rate constant, the rate of reaction as the concentrations of reactants by unitage. k = = = ……… 、 ……is refered to the stoichiometric numbers of the corresponding substance, which are positive for products and negative for reactants.**α+β+ ……＝ n，is called the overall reaction order.**Example 1：2NO + O2→ 2NO2 R = k α、β……are called fractional reaction order, indicating the influences of A, B,…….. on the rate of reaction respectively. It means that this reaction is second order for NO，first order for O2 and third order overall.**Example 2：(with catalyst)**nHOROH + nHOOCR’COOH → [OROOCR’CO]n This reaction is first order in di-alcohol as well as diacid and second order overall. R = k[COOH][OH] = kC2**What’s the reaction order ?**Kinetics equation： rA = － = kA I. Zero order reaction： The rate of reaction is independent on the concentration of the substance. CA0－ CA = kAt zero order reaction kinetics equation**The characteristics of zero order reaction：**(2) The dimension of kA is concerntration/time (3) The half-life t1/2, which is the time that the concerntration of a reactant fall to half of initial value, is directly proportional to initial concern-tration CA0and inversely proportional to kA. (1) The plot of CA against t givesa straight line with a slope equal to -kA。 CA0－ CA = kAtt1/2＝ CA0/2kA**Ⅱ. First order reaction**rA = kACAorrA = － = kACA kA = ln orlnCA = －kA·t + lnCA0 the kinetics equation：**The characteristics of the first order reaction:**(2) The dimension of kA is 1/time, i.e., kAof the first order reaction is independent on the concern- tration. (1) The plot of ln CA againstt gives a straight line with a slope equal to -kA. t1/2＝ ln2/kA = 0.6931/ kA**Ⅲ. Second order reaction**rA= kAorrA = － = kA － = kAt (A) The rate of the reaction is merely proportional to the second power of the concerntration of one reactant. (B)The rate of the reaction is proportional to the product of the concentrations of two reactants. RP = k2CACB equal to A) as CA = CB**the characteristics of the second order reaction**(2) The dimension of kA is 1/concerntration · 1/time (1) The plot of 1/CA against t gives a straight line with a slop equal to kA. (3) t1/2＝ 1 / kACA0**To Construct the Kinetic Equation**Firstly, measuring the data of concentration of reactants with time; Secondly, transforming and analysing the data in the suitable way; Thirdly, calculating the reaction order and the rate constant to construct the kinetics equation.**If plots of CA～t，ln CA～t，1/ CA～t，1/CA2**～tgive straight lines, they are zero order, first order, second order, third order, respectively. The slopes equal to the rate constants.**lnCA－ lnCA0 = kAt first order**1/CA－ 1/CA0 = kAt second order CA0 － CA = kAt zero order 1/CA2－ 1/CA02 = kAt third order**Kinetics of Linear Polycondensation**The rate of polymerization can be expressed as the disappeared rate of one of the functional groups. e.g. -d[COOH]/dt (polyesterification) By reducing the water continuously, the polyesterification can be regarded as an irreversible system. Acids act as catalyst Self-catalyzed system (no strong acids added) ←third order reaction External catalyzed system(strong acids added) ←second order reaction**Case 1 Self-Catalyzed System**general reaction R = The dicarboxylic acid acts as catalyst itself. [HA] is replaced by [COOH] Initially, Co=[COOH]=[OH] integrate C=C0( 1 - P )**Discussion**1. data processing： a. Drawing a plot of versus t or versus t. If the plot were linear, third order reaction would be confirmed. b. The rake ratio is . Thus, The value of k3 can be obtained.**2. The plot of 1/(1-P)2 with t shows the deviation from**linearity before 80% of reaction extent Flory ascribed the deviation from linearity to the great changes which take place in the reaction medium. Concretely, the change of the polarity of the reaction mixture happened as the polar carboxylic acid groups are converted to the less polar ester linkages. In the initial stages of reaction,**Case 2 External-Catalyzed System**general reaction Added strong acids kcat[H+]>>k3[COOH]，k3[COOH] can ignore [H+] is invariant, setting k2=kcat [H+] Second order reaction**Discussion**Drawing a plot of versus t，the plot should be linear. The value of k2 can be obtained by the rake ratio. 1. data processing： 2. The general linearity of the plot as P≥0.8 confirms that the second reaction order and the concept of indepence of the functional group reactivity on the molecular size.**The nonlinearity in the initial region of External-Catalyzed**system catalysis reaction is, like that in Self-Catalyzed system, the characteristics of esterifications rather than polyesterifications.It takes 3/4 of the overall time between P=0.80～0.99.It is noted that =5 as P=0.80, i.e., it is esterifications rather than polyesterifications before 80% of reaction extent.**Self-Catalyzed，∝t；**External Catalysis,∝t； It is clear that of external-catalyzed system increase much more quickly than that of self-catalyzed system. Then comparing the k2，k3：(hexylic diacid and decadialcohol) 4.Comparing above-mentioned two systems Self-Catalyzed, k2 =0.0175, External Catalysis k3 = 0.097 Practically, the external-catalyzed system is more useful to the industry.**Part 3Molecular Weight and MWD**Topics for Today Factors Influence on the Molecular Weight Molecular WeightControlin LinearPolycondensation Molecular Weight Distributionsin LinearPolycondensation**Outlines for Today**Influent Factors: K, k, catalyst way, P Control way and q, r slightly over weight of one reactant add monofunctional monomer MWD: by probability statistics, Mn, Mw, Polydispersity**The Factors Influence on the Molecular Weight of**Polycondensation Closed system： = + 1 The Balanced Characteristic Unclossed system： =**The Catalyzed System**Self-Catalyzed system： = 2k3 t + 1 External Catalysis system： = k2C0t + 1**The Extent of Reaction**With the same mole ratio of groups ： =**Molecular WeightControlin LinearPolycondensation**Key: Deactivation of the functional end groups, i.e., stabilization of molecular weight • One way is slightly over weight of one reactants (non-stoichiometric). Finally another reactant completely react and all the chain ends posses thesame functional group. • Another way is to add a spot of monofunctional monomer.**Case 1 Non-stoichiometric of Functional Groups**For the systems of a-R-a + b-R‘-b, not a-R-b The numbers of A and B functional groups are given by Na and Nb, respectively. and if the reaction tends to the end, B-B is present in excess. The stoichiometric imbalance r of the two functional groups is given by r=Na/Nb( r≤1).**The non-stoichiometric reactants**At time of 0 , a-R-a b-R'-b The number of group A is Na The number of group B is Nb The number of a-R-a is given by Na/2 The number of b-R-b is given by Nb/2 The total of monomer molecules (namely the total of construction units) is given by（Na＋Nb）/2**The total of macromolecules**At time of t , • The extent of reaction of group a is given by Pa • Reacted a ： NaPa b : NaPa • Unreacteda ：Na(1－ Pa) b : Nb － NaPa Then • The total of unreacted a andb is given by: Na＋Nb－2NaPa • The total of macromolecules is : (Na＋Nb－2NaPa ) /2**Thus**Substitute r=Na/Nb The group A is used up ( Pa=1) The moles of the two groups are equal（r=1） If r =1**Theoretically, if the mole ratio of the two functional**groups in the systems of a-R-a + b-R‘-b can be kept equal，the average degree of the condensation polymer will reach the maximum to the end of reaction.**Excessive mole-percent q**• The Excessive percentage q ofb-R‘-b molecule is often used besides r. • The q is defined as: namely**Case 2 Adding monofunctional monomerR"-b to capture the end**group • R"-b can react with group a in the polymer. • By this method, the end groups are captured, giving the stabilized molecular weight. • The molecular weight of polymer can be adjusted by R”-b. • This method can be used for both the system a-R-a / b-R’-b and the system of a-R-b.**① The systems of a-R-a + b-R‘-bwiththe same mole ratio**The number of the R"-b is NC The coefficient 2 of Nc is required since quantitatively one molecule R”-b has the same effect as one excess molecule b-R’-b on restricting the polymer chain growing.**② The system of a-R-b**The number of the R"-b is NC**Example：**If the numbers of r and Pa are substituted for the equation , the average degree of polymerization will be obtained. 1 mol aRa + 1mol bR’b + 0.1%R”b